Average Error: 0.1 → 0.1
Time: 5.8s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y} \]
↓
\[0.5 \cdot \frac{\sin y \cdot \left(e^{x} + \frac{1}{e^{x}}\right)}{y} \]
\cosh x \cdot \frac{\sin y}{y}
↓
0.5 \cdot \frac{\sin y \cdot \left(e^{x} + \frac{1}{e^{x}}\right)}{y}

(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y)
 :precision binary64
 (* 0.5 (/ (* (sin y) (+ (exp x) (/ 1.0 (exp x)))) y)))
double code(double x, double y) {
	return cosh(x) * (sin(y) / y);
}
↓
double code(double x, double y) {
	return 0.5 * ((sin(y) * (exp(x) + (1.0 / exp(x)))) / 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
\[\frac{\cosh x \cdot \sin y}{y} \]

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded in x around inf 0.1

    \[\leadsto \color{blue}{0.5 \cdot \frac{\sin y \cdot \left(\frac{1}{e^{x}} + e^{x}\right)}{y}} \]

  3. Final simplification0.1

    \[\leadsto 0.5 \cdot \frac{\sin y \cdot \left(e^{x} + \frac{1}{e^{x}}\right)}{y} \]

Reproduce

herbie shell --seed 2022068 
(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)))