Average Error: 13.7 → 0.2
Time: 4.4s
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 r570631 = x;
        double r570632 = sin(r570631);
        double r570633 = y;
        double r570634 = sinh(r570633);
        double r570635 = r570632 * r570634;
        double r570636 = r570635 / r570631;
        return r570636;
}
↓
double f(double x, double y) {
        double r570637 = x;
        double r570638 = sin(r570637);
        double r570639 = y;
        double r570640 = sinh(r570639);
        double r570641 = r570640 / r570637;
        double r570642 = r570638 * r570641;
        return r570642;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.7
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.7

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

  3. Applied *-un-lft-identity13.7

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

  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 2020024 +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))