Average Error: 13.9 → 0.3
Time: 4.6s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)
double f(double x, double y) {
        double r555071 = x;
        double r555072 = sin(r555071);
        double r555073 = y;
        double r555074 = sinh(r555073);
        double r555075 = r555072 * r555074;
        double r555076 = r555075 / r555071;
        return r555076;
}
↓
double f(double x, double y) {
        double r555077 = x;
        double r555078 = sin(r555077);
        double r555079 = y;
        double r555080 = sinh(r555079);
        double r555081 = 1.0;
        double r555082 = r555081 / r555077;
        double r555083 = r555080 * r555082;
        double r555084 = r555078 * r555083;
        return r555084;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original13.9
Target0.2
Herbie0.3
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  3. Applied *-un-lft-identity13.9

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

  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. Using strategy rm

  7. Applied div-inv0.3

    \[\leadsto \sin x \cdot \color{blue}{\left(\sinh y \cdot \frac{1}{x}\right)}\]

  8. Final simplification0.3

    \[\leadsto \sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2020025 +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))