Average Error: 14.2 → 0.3
Time: 7.6s
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 r473548 = x;
        double r473549 = sin(r473548);
        double r473550 = y;
        double r473551 = sinh(r473550);
        double r473552 = r473549 * r473551;
        double r473553 = r473552 / r473548;
        return r473553;
}
↓
double f(double x, double y) {
        double r473554 = x;
        double r473555 = sin(r473554);
        double r473556 = y;
        double r473557 = sinh(r473556);
        double r473558 = r473557 / r473554;
        double r473559 = r473555 * r473558;
        return r473559;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 14.2

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

  3. Applied *-un-lft-identity14.2

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

  4. Applied times-frac0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 
(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))