Average Error: 13.8 → 0.1
Time: 19.5s
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 r22046087 = x;
        double r22046088 = sin(r22046087);
        double r22046089 = y;
        double r22046090 = sinh(r22046089);
        double r22046091 = r22046088 * r22046090;
        double r22046092 = r22046091 / r22046087;
        return r22046092;
}
↓
double f(double x, double y) {
        double r22046093 = y;
        double r22046094 = sinh(r22046093);
        double r22046095 = x;
        double r22046096 = sin(r22046095);
        double r22046097 = r22046096 / r22046095;
        double r22046098 = r22046094 * r22046097;
        return r22046098;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.8
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.8

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

  3. Applied associate-/l*0.7

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  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 2019170 +o rules:numerics
(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))