Average Error: 0.2 → 0.2
Time: 4.4s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y \cdot \left(e^{x} + e^{-x}\right)}{y \cdot 2}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\sin y \cdot \left(e^{x} + e^{-x}\right)}{y \cdot 2}
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y)
 :precision binary64
 (/ (* (sin y) (+ (exp x) (exp (- x)))) (* y 2.0)))
double code(double x, double y) {
	return cosh(x) * (sin(y) / y);
}
↓
double code(double x, double y) {
	return (sin(y) * (exp(x) + exp(-x))) / (y * 2.0);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.2

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

  3. Applied cosh-def_binary640.2

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

  4. Applied frac-times_binary640.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020231 
(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)))