Average Error: 57.8 → 1.9

Time: 5.1s

Precision: 64

could not determine a ground truth for program body (more)
1. x = -2.3820831826475924e+172

\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

↓

\[\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}\]

\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}

↓

\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}

double code(double x) {
	return ((exp(x) - exp(-x)) / (exp(x) + exp(-x)));
}

↓

double code(double x) {
	return ((x + (0.13333333333333333 * pow(x, 5.0))) - (0.3333333333333333 * pow(x, 3.0)));
}

Error

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Initial program 57.8
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
Taylor expanded around 0 1.9
\[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]
Final simplification1.9
\[\leadsto \left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}\]

herbie shell --seed 2020049 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))