Average Error: 2.8 → 1.5
Time: 7.7s
Precision: binary64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq 2.2974278247676085 \cdot 10^{+25}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \leq 2.2974278247676085 \cdot 10^{+25}:\\
\;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (/ (sin y) y)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= x 2.2974278247676085e+25)
   (* (/ (sin y) y) (/ x z))
   (/ (* x (/ (sin y) y)) 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 <= 2.2974278247676085e+25) {
		tmp = (sin(y) / y) * (x / z);
	} else {
		tmp = (x * (sin(y) / y)) / 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

Original2.8
Target0.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 2.29742782476760854e25

    1. Initial program 3.5

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

    3. Applied add-cube-cbrt_binary64_130714.3

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

    4. Applied associate-/r*_binary64_129804.3

      \[\leadsto \color{blue}{\frac{\frac{x \cdot \frac{\sin y}{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}}\]

    5. Simplified2.6

      \[\leadsto \frac{\color{blue}{\frac{\sin y}{y} \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}}{\sqrt[3]{z}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity_binary64_130362.6

      \[\leadsto \frac{\frac{\sin y}{y} \cdot \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\color{blue}{1 \cdot \sqrt[3]{z}}}\]

    8. Applied times-frac_binary64_130422.7

      \[\leadsto \color{blue}{\frac{\frac{\sin y}{y}}{1} \cdot \frac{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}}\]

    9. Simplified2.7

      \[\leadsto \color{blue}{\frac{\sin y}{y}} \cdot \frac{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}}}{\sqrt[3]{z}}\]

    10. Simplified1.9

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

    if 2.29742782476760854e25 < x

    1. Initial program 0.2

      \[\frac{x \cdot \frac{\sin y}{y}}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2974278247676085 \cdot 10^{+25}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021098 
(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))