Average Error: 31.1 → 0.0
Time: 40.6s
Precision: 64
Internal Precision: 2368
$\frac{x - \sin x}{x - \tan x}$
$\begin{array}{l} \mathbf{if}\;x \le -0.027373454593039987 \lor \neg \left(x \le 0.02882443620224173\right):\\ \;\;\;\;\log \left(e^{\frac{x - \sin x}{x - \tan x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{40} \cdot {x}^{2} - \left(\frac{1}{2} + {x}^{4} \cdot \frac{27}{2800}\right)\\ \end{array}$

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Results

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Derivation

1. Split input into 2 regimes
2. if x < -0.027373454593039987 or 0.02882443620224173 < x

1. Initial program 0.0

$\frac{x - \sin x}{x - \tan x}$
2. Using strategy rm

$\leadsto \color{blue}{\log \left(e^{\frac{x - \sin x}{x - \tan x}}\right)}$

if -0.027373454593039987 < x < 0.02882443620224173

1. Initial program 62.7

$\frac{x - \sin x}{x - \tan x}$
2. Taylor expanded around 0 0.0

$\leadsto \color{blue}{\frac{9}{40} \cdot {x}^{2} - \left(\frac{27}{2800} \cdot {x}^{4} + \frac{1}{2}\right)}$
3. Recombined 2 regimes into one program.
4. Applied simplify0.0

$\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;x \le -0.027373454593039987 \lor \neg \left(x \le 0.02882443620224173\right):\\ \;\;\;\;\log \left(e^{\frac{x - \sin x}{x - \tan x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{9}{40} \cdot {x}^{2} - \left(\frac{1}{2} + {x}^{4} \cdot \frac{27}{2800}\right)\\ \end{array}}$

Runtime

Time bar (total: 40.6s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "(x-sin(x))/(x-tan(x))"
(/ (- x (sin x)) (- x (tan x))))