Average Error: 13.3 → 0.1
Time: 15.7s
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 r379303 = x;
        double r379304 = sin(r379303);
        double r379305 = y;
        double r379306 = sinh(r379305);
        double r379307 = r379304 * r379306;
        double r379308 = r379307 / r379303;
        return r379308;
}
↓
double f(double x, double y) {
        double r379309 = x;
        double r379310 = sin(r379309);
        double r379311 = r379310 / r379309;
        double r379312 = y;
        double r379313 = sinh(r379312);
        double r379314 = r379311 * r379313;
        return r379314;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.3
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.3

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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 2019208 
(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))