Average Error: 13.4 → 0.2
Time: 6.1s
Precision: binary64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}
double code(double x, double y) {
	return ((double) (((double) (((double) sin(x)) * ((double) sinh(y)))) / x));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) sin(x)) / x)) / ((double) (1.0 / ((double) sinh(y))))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.4
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

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 div-inv0.8

    \[\leadsto \frac{\sin x}{\color{blue}{x \cdot \frac{1}{\sinh y}}}\]

  6. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}}\]

  7. Final simplification0.2

    \[\leadsto \frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}\]

Reproduce

herbie shell --seed 2020162 
(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))