Average Error: 2.7 → 1.7
Time: 9.2s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq 1.3992999450336832 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \leq 1.3992999450336832 \cdot 10^{+25}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{1}{\frac{\sin y}{y}}}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= x 1.3992999450336832e+25)
   (/ (/ x z) (/ 1.0 (/ (sin y) y)))
   (* (* x (/ (sin y) y)) (/ 1.0 z))))
double code(double x, double y, double z) {
	return (x * (sin(y) / y)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.3992999450336832e+25) {
		tmp = (x / z) / (1.0 / (sin(y) / y));
	} else {
		tmp = (x * (sin(y) / y)) * (1.0 / z);
	}
	return tmp;
}

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

Original2.7
Target0.2
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 1.3993e25

    1. Initial program 3.4

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

    3. Applied associate-/l*_binary64_51322.0

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\frac{\sin y}{y}}}}\]
    4. Using strategy rm

    5. Applied div-inv_binary64_50692.1

      \[\leadsto \frac{x}{\color{blue}{z \cdot \frac{1}{\frac{\sin y}{y}}}}\]

    6. Applied associate-/r*_binary64_51312.1

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{\frac{1}{\frac{\sin y}{y}}}}\]

    if 1.3993e25 < x

    1. Initial program 0.2

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

    3. Applied div-inv_binary64_50690.4

      \[\leadsto \color{blue}{\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.3992999450336832 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020231 
(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))