Average Error: 14.2 → 0.1
Time: 3.7s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{1}{\frac{x}{\sin x}} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{1}{\frac{x}{\sin x}} \cdot \sinh y
double f(double x, double y) {
        double r508041 = x;
        double r508042 = sin(r508041);
        double r508043 = y;
        double r508044 = sinh(r508043);
        double r508045 = r508042 * r508044;
        double r508046 = r508045 / r508041;
        return r508046;
}
↓
double f(double x, double y) {
        double r508047 = 1.0;
        double r508048 = x;
        double r508049 = sin(r508048);
        double r508050 = r508048 / r508049;
        double r508051 = r508047 / r508050;
        double r508052 = y;
        double r508053 = sinh(r508052);
        double r508054 = r508051 * r508053;
        return r508054;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 14.2

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

  3. Applied associate-/l*0.9

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

  5. Applied associate-/r/0.1

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

  7. Applied clear-num0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 +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))