Average Error: 2.9 → 3.0
Time: 5.9s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z} \]
↓
\[\frac{x}{z} \cdot \frac{\sin y}{y} \]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\frac{x}{z} \cdot \frac{\sin y}{y}

(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z) :precision binary64 (* (/ x z) (/ (sin y) y)))
double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / z;
}
↓
double code(double x, double y, double z) {
	return (x / z) * (sin(y) / y);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.9
Target0.3
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array} \]

Derivation

  1. Initial program 2.9

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

  2. Applied associate-/l*_binary643.0

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

  3. Applied associate-/r/_binary643.0

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

  4. Final simplification3.0

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

Reproduce

herbie shell --seed 2022125 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))