Average Error: 13.4 → 0.1
Time: 6.0s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{x} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{x} \cdot \sinh y
double f(double x, double y) {
        double r518880 = x;
        double r518881 = sin(r518880);
        double r518882 = y;
        double r518883 = sinh(r518882);
        double r518884 = r518881 * r518883;
        double r518885 = r518884 / r518880;
        return r518885;
}
↓
double f(double x, double y) {
        double r518886 = x;
        double r518887 = sin(r518886);
        double r518888 = r518887 / r518886;
        double r518889 = y;
        double r518890 = sinh(r518889);
        double r518891 = r518888 * r518890;
        return r518891;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.4
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.4

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

  3. Applied associate-/l*0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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))