Average Error: 13.4 → 0.1
Time: 30.2s
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 r230439 = x;
        double r230440 = sin(r230439);
        double r230441 = y;
        double r230442 = sinh(r230441);
        double r230443 = r230440 * r230442;
        double r230444 = r230443 / r230439;
        return r230444;
}
↓
double f(double x, double y) {
        double r230445 = x;
        double r230446 = sin(r230445);
        double r230447 = r230446 / r230445;
        double r230448 = y;
        double r230449 = sinh(r230448);
        double r230450 = r230447 * r230449;
        return r230450;
}

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 +o rules:numerics
(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))