Average Error: 14.1 → 0.2
Time: 22.2s
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 r607205 = x;
        double r607206 = sin(r607205);
        double r607207 = y;
        double r607208 = sinh(r607207);
        double r607209 = r607206 * r607208;
        double r607210 = r607209 / r607205;
        return r607210;
}
↓
double f(double x, double y) {
        double r607211 = x;
        double r607212 = sin(r607211);
        double r607213 = r607212 / r607211;
        double r607214 = 1.0;
        double r607215 = y;
        double r607216 = sinh(r607215);
        double r607217 = r607214 / r607216;
        double r607218 = r607213 / r607217;
        return r607218;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 14.1

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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 2020042 +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))