Average Error: 13.8 → 0.1
Time: 4.0s
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 r475405 = x;
        double r475406 = sin(r475405);
        double r475407 = y;
        double r475408 = sinh(r475407);
        double r475409 = r475406 * r475408;
        double r475410 = r475409 / r475405;
        return r475410;
}
↓
double f(double x, double y) {
        double r475411 = x;
        double r475412 = sin(r475411);
        double r475413 = r475412 / r475411;
        double r475414 = y;
        double r475415 = sinh(r475414);
        double r475416 = r475413 * r475415;
        return r475416;
}

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*0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  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 2020002 
(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))