Average Error: 14.0 → 0.8
Time: 3.8s
Precision: binary64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{\frac{x}{\sinh y}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{\frac{x}{\sinh y}}
(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))
↓
(FPCore (x y) :precision binary64 (/ (sin x) (/ x (sinh y))))
double code(double x, double y) {
	return (sin(x) * sinh(y)) / x;
}
↓
double code(double x, double y) {
	return sin(x) / (x / sinh(y));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original14.0
Target0.2
Herbie0.8
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  3. Applied associate-/l*_binary640.8

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

  4. Final simplification0.8

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

Reproduce

herbie shell --seed 2020219 
(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))