Average Error: 14.1 → 0.2
Time: 27.1s
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 r591187 = x;
        double r591188 = sin(r591187);
        double r591189 = y;
        double r591190 = sinh(r591189);
        double r591191 = r591188 * r591190;
        double r591192 = r591191 / r591187;
        return r591192;
}
↓
double f(double x, double y) {
        double r591193 = x;
        double r591194 = sin(r591193);
        double r591195 = r591194 / r591193;
        double r591196 = 1.0;
        double r591197 = y;
        double r591198 = sinh(r591197);
        double r591199 = r591196 / r591198;
        double r591200 = r591195 / r591199;
        return r591200;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 
(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))