Average Error: 14.8 → 0.2
Time: 5.1s
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 r518910 = x;
        double r518911 = sin(r518910);
        double r518912 = y;
        double r518913 = sinh(r518912);
        double r518914 = r518911 * r518913;
        double r518915 = r518914 / r518910;
        return r518915;
}
↓
double f(double x, double y) {
        double r518916 = x;
        double r518917 = sin(r518916);
        double r518918 = y;
        double r518919 = sinh(r518918);
        double r518920 = r518919 / r518916;
        double r518921 = r518917 * r518920;
        return r518921;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.8
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.8

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

  3. Applied *-un-lft-identity14.8

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

  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 2020020 
(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))