Average Error: 13.8 → 0.1
Time: 4.2s
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 r585379 = x;
        double r585380 = sin(r585379);
        double r585381 = y;
        double r585382 = sinh(r585381);
        double r585383 = r585380 * r585382;
        double r585384 = r585383 / r585379;
        return r585384;
}
↓
double f(double x, double y) {
        double r585385 = x;
        double r585386 = sin(r585385);
        double r585387 = r585386 / r585385;
        double r585388 = y;
        double r585389 = sinh(r585388);
        double r585390 = r585387 * r585389;
        return r585390;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.8
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.8

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

  3. Applied associate-/l*0.9

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  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 2020021 
(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))