Average Error: 14.3 → 0.2
Time: 12.5s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
double f(double x, double y) {
        double r486933 = x;
        double r486934 = sin(r486933);
        double r486935 = y;
        double r486936 = sinh(r486935);
        double r486937 = r486934 * r486936;
        double r486938 = r486937 / r486933;
        return r486938;
}
↓
double f(double x, double y) {
        double r486939 = x;
        double r486940 = sin(r486939);
        double r486941 = y;
        double r486942 = sinh(r486941);
        double r486943 = r486942 / r486939;
        double r486944 = r486940 * r486943;
        return r486944;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.3
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.3

    \[\frac{\sin x \cdot \sinh y}{x}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity14.3

    \[\leadsto \frac{\sin x \cdot \sinh y}{\color{blue}{1 \cdot x}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{\sin x}{1} \cdot \frac{\sinh y}{x}}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{\sin x} \cdot \frac{\sinh y}{x}\]

  6. Final simplification0.2

    \[\leadsto \sin x \cdot \frac{\sinh y}{x}\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))