Average Error: 13.9 → 0.8
Time: 17.7s
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 r20504950 = x;
        double r20504951 = sin(r20504950);
        double r20504952 = y;
        double r20504953 = sinh(r20504952);
        double r20504954 = r20504951 * r20504953;
        double r20504955 = r20504954 / r20504950;
        return r20504955;
}
↓
double f(double x, double y) {
        double r20504956 = x;
        double r20504957 = sin(r20504956);
        double r20504958 = y;
        double r20504959 = sinh(r20504958);
        double r20504960 = r20504956 / r20504959;
        double r20504961 = r20504957 / r20504960;
        return r20504961;
}

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 +o rules:numerics
(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))