Average Error: 13.9 → 0.3
Time: 5.1s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)
double f(double x, double y) {
        double r524114 = x;
        double r524115 = sin(r524114);
        double r524116 = y;
        double r524117 = sinh(r524116);
        double r524118 = r524115 * r524117;
        double r524119 = r524118 / r524114;
        return r524119;
}
↓
double f(double x, double y) {
        double r524120 = x;
        double r524121 = sin(r524120);
        double r524122 = y;
        double r524123 = sinh(r524122);
        double r524124 = 1.0;
        double r524125 = r524124 / r524120;
        double r524126 = r524123 * r524125;
        double r524127 = r524121 * r524126;
        return r524127;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.9
Target0.2
Herbie0.3
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  3. Applied *-un-lft-identity13.9

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  7. Applied div-inv0.3

    \[\leadsto \sin x \cdot \color{blue}{\left(\sinh y \cdot \frac{1}{x}\right)}\]

  8. Final simplification0.3

    \[\leadsto \sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2020025 
(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))