Average Error: 13.4 → 0.1
Time: 4.4s
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 r620379 = x;
        double r620380 = sin(r620379);
        double r620381 = y;
        double r620382 = sinh(r620381);
        double r620383 = r620380 * r620382;
        double r620384 = r620383 / r620379;
        return r620384;
}
↓
double f(double x, double y) {
        double r620385 = x;
        double r620386 = sin(r620385);
        double r620387 = r620386 / r620385;
        double r620388 = y;
        double r620389 = sinh(r620388);
        double r620390 = r620387 * r620389;
        return r620390;
}

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*0.7

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  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 2020027 
(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))