From mboxrd@z Thu Jan  1 00:00:00 1970
Return-Path: <r.sherman@upcmail.nl>
Received: from mail2-relais-roc.national.inria.fr (mail2-relais-roc.national.inria.fr [192.134.164.83])
	by sympa.inria.fr (Postfix) with ESMTPS id 66A3E7FD28
	for <caml-list@sympa.inria.fr>; Tue, 10 Nov 2015 21:14:31 +0100 (CET)
IronPort-PHdr: 9a23:foTOBRZSHDjyQftn1ylJxBb/LSx+4OfEezUN459isYplN5qZpci7bnLW6fgltlLVR4KTs6sC0LqL9fy9EjVav96oizMrTt9lb1c9k8IYnggtUoauKHbQC7rUVRE8B9lIT1R//nu2YgB/Ecf6YEDO8DXptWZBUiv2OQc9HOnpAIma153xjLDvvcGOKFwS2nKUWvBbElaflU3prM4YgI9veO4a6yDihT92QdlQ3n5iPlmJnhzxtY+a9Z9n9DlM6bp6r5YTGfayQ6NtRrVdCHEiMnspzMztrxjKCwWVtVUGVWBDqB1CDhLZpCr6U430uy2y4vA7wymXJ8j/S5gpQT+n5qZvDhns3nRUfwUl+X3a35QjxJlQpwis8kRy
Authentication-Results: mail2-smtp-roc.national.inria.fr; spf=None smtp.pra=r.sherman@upcmail.nl; spf=Pass smtp.mailfrom=r.sherman@upcmail.nl; spf=None smtp.helo=postmaster@fep21.mx.upcmail.net
Received-SPF: None (mail2-smtp-roc.national.inria.fr: no sender
  authenticity information available from domain of
  r.sherman@upcmail.nl) identity=pra; client-ip=62.179.121.41;
  receiver=mail2-smtp-roc.national.inria.fr;
  envelope-from="r.sherman@upcmail.nl";
  x-sender="r.sherman@upcmail.nl";
  x-conformance=sidf_compatible
Received-SPF: Pass (mail2-smtp-roc.national.inria.fr: domain of
  r.sherman@upcmail.nl designates 62.179.121.41 as permitted
  sender) identity=mailfrom; client-ip=62.179.121.41;
  receiver=mail2-smtp-roc.national.inria.fr;
  envelope-from="r.sherman@upcmail.nl";
  x-sender="r.sherman@upcmail.nl";
  x-conformance=sidf_compatible; x-record-type="v=spf1"
Received-SPF: None (mail2-smtp-roc.national.inria.fr: no sender
  authenticity information available from domain of
  postmaster@fep21.mx.upcmail.net) identity=helo;
  client-ip=62.179.121.41;
  receiver=mail2-smtp-roc.national.inria.fr;
  envelope-from="r.sherman@upcmail.nl";
  x-sender="postmaster@fep21.mx.upcmail.net";
  x-conformance=sidf_compatible
X-IronPort-Anti-Spam-Filtered: true
X-IronPort-Anti-Spam-Result: A0DAAwCjT0JWbyl5sz5exTqHXTwQAQEBAQEBAQEQAQoNCgYjLoItgjEVNAoCNgIFFgsCCwMCAQIBWAgBAYguAaMZj3CRCYEBhVOKJYJOgUQFlkiIDY42kyg4gXWCOoYgAQEB
X-IPAS-Result: A0DAAwCjT0JWbyl5sz5exTqHXTwQAQEBAQEBAQEQAQoNCgYjLoItgjEVNAoCNgIFFgsCCwMCAQIBWAgBAYguAaMZj3CRCYEBhVOKJYJOgUQFlkiIDY42kyg4gXWCOoYgAQEB
X-IronPort-AV: E=Sophos;i="5.20,271,1444687200"; 
   d="scan'208";a="186994469"
Received: from fep21.mx.upcmail.net ([62.179.121.41])
  by mail2-smtp-roc.national.inria.fr with ESMTP; 10 Nov 2015 21:13:51 +0100
Received: from edge02.upcmail.net ([192.168.13.237])
          by viefep21-int.chello.at
          (InterMail vM.8.01.05.18 201-2260-151-151-20140610) with ESMTP
          id <20151110201350.NSXD29532.viefep21-int.chello.at@edge02.upcmail.net>
          for <caml-list@inria.fr>; Tue, 10 Nov 2015 21:13:50 +0100
Received: from [95.96.99.169] ([95.96.99.169])
	by edge02.upcmail.net with edge
	id fwDo1r01V3fGmAf01wDpsr; Tue, 10 Nov 2015 21:13:49 +0100
X-SourceIP: 95.96.99.169
From: Robert Sherman <r.sherman@upcmail.nl>
To: caml-list@inria.fr
Message-ID: <56424FFD.9040807@upcmail.nl>
Date: Tue, 10 Nov 2015 20:13:49 +0000
User-Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:38.0) Gecko/20100101
 Thunderbird/38.3.0
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 7bit
X-Validation-by: r.sherman@upcmail.nl
Subject: [Caml-list] a small correction in OCaml tutorial Jason Hickey about
 second derivatives

Dear Reader,

In the book of Jason Hickey:
Introduction to Objective Caml
Section 3.1.3: Higher order functions, page 19 and 20
something regrettable is found:
The nice concept of Higher order function finds an
anti-apothesis under the remark that results of the second derivative 
function are "way off!"
Indeed, their values ought to be 6.0 and 60.0, but give both float 0.
Of course this should not be mentioned in a book, for this is not good 
for OCaml.
Jason Hickey gives an example like:  let f' = deriv f .... with 
differential dx = 1.0e-11
But is simply repairable, see here under:

While in Xavier Leroy et al.:
An introduction to OCaml
We find in Section 1.3 of page 15: let deriv f dx = ..... with 
differential dx = 1.0e-6
But they avoid the second derivative, what should not have worked much 
better.
However the cure is simply to prevent:
Just give dx a coarser value, even dx = 1.0e-5 comes with at least 4 
significant good digits
Using the definition of the second derivative should gain 1 or 2 digits.

Hope you will test these facts and make Jason Hickey a bit happier.

Robert Sherman
Zaandam
Pays Bas