Average Error: 14.0 → 0.1
Time: 5.4s
Precision: binary64
Cost: 13120
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{\sin x}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{\sin x}{x}
(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))
↓
(FPCore (x y) :precision binary64 (* (sinh y) (/ (sin x) x)))
double code(double x, double y) {
	return (sin(x) * sinh(y)) / x;
}
↓
double code(double x, double y) {
	return sinh(y) * (sin(x) / x);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Alternatives

Alternative 1
Error0.2
Cost13120
\[\sin x \cdot \frac{\sinh y}{x}\]
Alternative 2
Error1.2
Cost6720
\[y \cdot \frac{\sin x}{x}\]
Alternative 3
Error16.2
Cost7362
\[\begin{array}{l} \mathbf{if}\;x \leq -3.1061016710757383:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 9982058009076348:\\ \;\;\;\;\frac{1}{\frac{1}{\sinh y}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 4
Error46.2
Cost64
\[0\]
Alternative 5
Error61.7
Cost64
\[1\]

Error

Derivation

  1. Initial program 14.0

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

  3. Applied associate-/l*_binary64_146860.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied associate-/r/_binary64_146870.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(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))