Average Error: 14.0 → 0.1
Time: 17.4s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{\sin x}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{\sin x}{x}
double f(double x, double y) {
        double r28924976 = x;
        double r28924977 = sin(r28924976);
        double r28924978 = y;
        double r28924979 = sinh(r28924978);
        double r28924980 = r28924977 * r28924979;
        double r28924981 = r28924980 / r28924976;
        return r28924981;
}
↓
double f(double x, double y) {
        double r28924982 = y;
        double r28924983 = sinh(r28924982);
        double r28924984 = x;
        double r28924985 = sin(r28924984);
        double r28924986 = r28924985 / r28924984;
        double r28924987 = r28924983 * r28924986;
        return r28924987;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  3. Applied associate-/l*0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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))