Average Error: 58.5 → 0.0
Time: 3.4s
Precision: 64
\[-0.00017 \lt x\]
\[e^{x} - 1\]
↓
\[\mathsf{expm1}\left(x\right)\]
e^{x} - 1
↓
\mathsf{expm1}\left(x\right)
double f(double x) {
        double r4440000 = x;
        double r4440001 = exp(r4440000);
        double r4440002 = 1.0;
        double r4440003 = r4440001 - r4440002;
        return r4440003;
}
↓
double f(double x) {
        double r4440004 = x;
        double r4440005 = expm1(r4440004);
        return r4440005;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original58.5
Target0.5
Herbie0.0
\[x \cdot \left(\left(1 + \frac{x}{2}\right) + \frac{x \cdot x}{6}\right)\]

Derivation

  1. Initial program 58.5

    \[e^{x} - 1\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (x)
  :name "expm1 (example 3.7)"
  :pre (< -0.00017 x)

  :herbie-target
  (* x (+ (+ 1 (/ x 2)) (/ (* x x) 6)))

  (- (exp x) 1))