Average Error: 14.3 → 0.2
Time: 30.6s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}
double f(double x, double y) {
        double r294106 = x;
        double r294107 = sin(r294106);
        double r294108 = y;
        double r294109 = sinh(r294108);
        double r294110 = r294107 * r294109;
        double r294111 = r294110 / r294106;
        return r294111;
}
↓
double f(double x, double y) {
        double r294112 = x;
        double r294113 = sin(r294112);
        double r294114 = r294113 / r294112;
        double r294115 = 1.0;
        double r294116 = y;
        double r294117 = sinh(r294116);
        double r294118 = r294115 / r294117;
        double r294119 = r294114 / r294118;
        return r294119;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 14.3

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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 div-inv0.9

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

  6. Applied associate-/r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 +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))