Average Error: 13.8 → 0.2
Time: 4.9s
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 r579701 = x;
        double r579702 = sin(r579701);
        double r579703 = y;
        double r579704 = sinh(r579703);
        double r579705 = r579702 * r579704;
        double r579706 = r579705 / r579701;
        return r579706;
}
↓
double f(double x, double y) {
        double r579707 = x;
        double r579708 = sin(r579707);
        double r579709 = y;
        double r579710 = sinh(r579709);
        double r579711 = r579710 / r579707;
        double r579712 = r579708 * r579711;
        return r579712;
}

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 +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))