Average Error: 0.1 → 0.1
Time: 5.6s
Precision: binary64
Cost: 13120
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\cosh x \cdot \sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\cosh x \cdot \sin y}{y}
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y) :precision binary64 (/ (* (cosh x) (sin y)) y))
double code(double x, double y) {
	return cosh(x) * (sin(y) / y);
}
↓
double code(double x, double y) {
	return (cosh(x) * sin(y)) / 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
Herbie0.1
\[\frac{\cosh x \cdot \sin y}{y}\]

Alternatives

Alternative 1
Error0.9
Cost7104
\[\frac{\sin y \cdot \left(1 + 0.5 \cdot \left(x \cdot x\right)\right)}{y}\]
Alternative 2
Error1.3
Cost6592
\[\frac{\sin y}{y}\]
Alternative 3
Error31.0
Cost6464
\[\cosh x\]
Alternative 4
Error31.6
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

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

  3. Applied associate-*r/_binary64_143420.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(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)))