Average Error: 39.7 → 0.0
Time: 8.7s
Precision: 64
\[\frac{e^{x} - 1}{x}\]
↓
\[\frac{\mathsf{expm1}\left(x\right)}{x}\]
\frac{e^{x} - 1}{x}
↓
\frac{\mathsf{expm1}\left(x\right)}{x}
double f(double x) {
        double r1940989 = x;
        double r1940990 = exp(r1940989);
        double r1940991 = 1.0;
        double r1940992 = r1940990 - r1940991;
        double r1940993 = r1940992 / r1940989;
        return r1940993;
}
↓
double f(double x) {
        double r1940994 = x;
        double r1940995 = expm1(r1940994);
        double r1940996 = r1940995 / r1940994;
        return r1940996;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original39.7
Target38.9
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;x \lt 1 \land x \gt -1:\\ \;\;\;\;\frac{e^{x} - 1}{\log \left(e^{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{x} - 1}{x}\\ \end{array}\]

Derivation

  1. Initial program 39.7

    \[\frac{e^{x} - 1}{x}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(x\right)}{x}}\]

  3. Final simplification0.0

    \[\leadsto \frac{\mathsf{expm1}\left(x\right)}{x}\]

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (x)
  :name "Kahan's exp quotient"

  :herbie-target
  (if (and (< x 1) (> x -1)) (/ (- (exp x) 1) (log (exp x))) (/ (- (exp x) 1) x))

  (/ (- (exp x) 1) x))