Average Error: 0.0 → 0.1
Time: 5.6s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y} \]
↓
\[\frac{\sin x}{\sqrt[3]{{\left(\frac{y}{\sinh y}\right)}^{3}}} \]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\sqrt[3]{{\left(\frac{y}{\sinh y}\right)}^{3}}}

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (/ (sin x) (cbrt (pow (/ y (sinh y)) 3.0))))
double code(double x, double y) {
	return sin(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return sin(x) / cbrt(pow((y / sinh(y)), 3.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Applied egg-rr0.1

    \[\leadsto \frac{\sin x}{\color{blue}{\sqrt[3]{{\left(\frac{y}{\sinh y}\right)}^{3}}}} \]

  4. Final simplification0.1

    \[\leadsto \frac{\sin x}{\sqrt[3]{{\left(\frac{y}{\sinh y}\right)}^{3}}} \]

Reproduce

herbie shell --seed 2022130 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))