Average Error: 0.4 → 0.2
Time: 8.3s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x} \cdot 100\right)\right)\]
\frac{x \cdot 100}{x + y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x} \cdot 100\right)\right)
double f(double x, double y) {
        double r631107 = x;
        double r631108 = 100.0;
        double r631109 = r631107 * r631108;
        double r631110 = y;
        double r631111 = r631107 + r631110;
        double r631112 = r631109 / r631111;
        return r631112;
}
↓
double f(double x, double y) {
        double r631113 = x;
        double r631114 = y;
        double r631115 = r631114 + r631113;
        double r631116 = r631113 / r631115;
        double r631117 = 100.0;
        double r631118 = r631116 * r631117;
        double r631119 = expm1(r631118);
        double r631120 = log1p(r631119);
        return r631120;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.4

    \[\frac{x \cdot 100}{x + y}\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.4

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x \cdot 100}{x + y}\right)\right)}\]

  4. Simplified0.2

    \[\leadsto \mathsf{log1p}\left(\color{blue}{\mathsf{expm1}\left(\frac{x}{y + x} \cdot 100\right)}\right)\]

  5. Final simplification0.2

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{y + x} \cdot 100\right)\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))