Average Error: 0.1 → 0.2
Time: 19.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}{2 \cdot y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}{2 \cdot y}
double code(double x, double y) {
	return ((double) (((double) cosh(x)) * ((double) (((double) sin(y)) / y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) sin(y)) / 0.5)) * ((double) cosh(x)))) / ((double) (2.0 * y))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  3. Applied cosh-def0.1

    \[\leadsto \color{blue}{\frac{e^{x} + e^{-x}}{2}} \cdot \frac{\sin y}{y}\]

  4. Applied frac-times0.2

    \[\leadsto \color{blue}{\frac{\left(e^{x} + e^{-x}\right) \cdot \sin y}{2 \cdot y}}\]

  5. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}}{2 \cdot y}\]

  6. Final simplification0.2

    \[\leadsto \frac{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}{2 \cdot y}\]

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))