Average Error: 14.5 → 0.2
Time: 11.5s
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 r9980719 = x;
        double r9980720 = sin(r9980719);
        double r9980721 = y;
        double r9980722 = sinh(r9980721);
        double r9980723 = r9980720 * r9980722;
        double r9980724 = r9980723 / r9980719;
        return r9980724;
}
↓
double f(double x, double y) {
        double r9980725 = x;
        double r9980726 = sin(r9980725);
        double r9980727 = y;
        double r9980728 = sinh(r9980727);
        double r9980729 = r9980728 / r9980725;
        double r9980730 = r9980726 * r9980729;
        return r9980730;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.5
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.5

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

  3. Applied *-un-lft-identity14.5

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

  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 2019156 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"

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

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