Average Error: 13.9 → 0.8
Time: 17.1s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{\frac{x}{\sinh y}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{\frac{x}{\sinh y}}
double f(double x, double y) {
        double r31568690 = x;
        double r31568691 = sin(r31568690);
        double r31568692 = y;
        double r31568693 = sinh(r31568692);
        double r31568694 = r31568691 * r31568693;
        double r31568695 = r31568694 / r31568690;
        return r31568695;
}
↓
double f(double x, double y) {
        double r31568696 = x;
        double r31568697 = sin(r31568696);
        double r31568698 = y;
        double r31568699 = sinh(r31568698);
        double r31568700 = r31568696 / r31568699;
        double r31568701 = r31568697 / r31568700;
        return r31568701;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.9
Target0.2
Herbie0.8
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  3. Applied associate-/l*0.8

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2019174 
(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))