Average Error: 14.0 → 0.2
Time: 5.0s
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 r540678 = x;
        double r540679 = sin(r540678);
        double r540680 = y;
        double r540681 = sinh(r540680);
        double r540682 = r540679 * r540681;
        double r540683 = r540682 / r540678;
        return r540683;
}
↓
double f(double x, double y) {
        double r540684 = x;
        double r540685 = sin(r540684);
        double r540686 = y;
        double r540687 = sinh(r540686);
        double r540688 = r540687 / r540684;
        double r540689 = r540685 * r540688;
        return r540689;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.0
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  3. Applied *-un-lft-identity14.0

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

  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 2020057 +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))