Average Error: 13.8 → 0.2
Time: 4.8s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
double f(double x, double y) {
        double r517099 = x;
        double r517100 = sin(r517099);
        double r517101 = y;
        double r517102 = sinh(r517101);
        double r517103 = r517100 * r517102;
        double r517104 = r517103 / r517099;
        return r517104;
}
↓
double f(double x, double y) {
        double r517105 = x;
        double r517106 = sin(r517105);
        double r517107 = y;
        double r517108 = sinh(r517107);
        double r517109 = r517108 / r517105;
        double r517110 = r517106 * r517109;
        return r517110;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.8
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.8

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

  3. Applied *-un-lft-identity13.8

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019356 
(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))