Average Error: 58.5 → 0.0
Time: 2.9s
Precision: 64
\[-0.00017 \lt x\]
\[e^{x} - 1\]
↓
\[(e^{x} - 1)^*\]
e^{x} - 1
↓
(e^{x} - 1)^*
double f(double x) {
        double r5164437 = x;
        double r5164438 = exp(r5164437);
        double r5164439 = 1.0;
        double r5164440 = r5164438 - r5164439;
        return r5164440;
}
↓
double f(double x) {
        double r5164441 = x;
        double r5164442 = expm1(r5164441);
        return r5164442;
}

Error

Bits error versus x

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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

    \[\leadsto \color{blue}{(e^{x} - 1)^*}\]

  3. Final simplification0.0

    \[\leadsto (e^{x} - 1)^*\]

Reproduce

herbie shell --seed 2019104 +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))