Average Error: 0.1 → 0.1
Time: 5.1s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{1 \cdot \left(\sin y \cdot \cosh x\right)}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{1 \cdot \left(\sin y \cdot \cosh x\right)}{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) (1.0 * ((double) (((double) sin(y)) * ((double) cosh(x)))))) / y));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.1

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

  3. Applied associate-*r/0.1

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

  4. Simplified0.1

    \[\leadsto \frac{\color{blue}{\sin y \cdot \cosh x}}{y}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.1

    \[\leadsto \frac{\color{blue}{1 \cdot \left(\sin y \cdot \cosh x\right)}}{y}\]

  7. Final simplification0.1

    \[\leadsto \frac{1 \cdot \left(\sin y \cdot \cosh x\right)}{y}\]

Reproduce

herbie shell --seed 2020114 +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)))