Average Error: 14.1 → 0.1
Time: 20.6s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sinh y}{\frac{x}{\sin x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sinh y}{\frac{x}{\sin x}}
double f(double x, double y) {
        double r25443828 = x;
        double r25443829 = sin(r25443828);
        double r25443830 = y;
        double r25443831 = sinh(r25443830);
        double r25443832 = r25443829 * r25443831;
        double r25443833 = r25443832 / r25443828;
        return r25443833;
}
↓
double f(double x, double y) {
        double r25443834 = y;
        double r25443835 = sinh(r25443834);
        double r25443836 = x;
        double r25443837 = sin(r25443836);
        double r25443838 = r25443836 / r25443837;
        double r25443839 = r25443835 / r25443838;
        return r25443839;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 14.1

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

  3. Applied *-commutative14.1

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

  4. Applied associate-/l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))