Average Error: 6.3 → 0.9
Time: 4.7s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1215731702497594 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \leq -9.392040062208773 \cdot 10^{-211}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 3.2890969509079325 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 7.963271108241615 \cdot 10^{+149}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -1.1215731702497594 \cdot 10^{+146}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;x \cdot y \leq -9.392040062208773 \cdot 10^{-211}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \leq 3.2890969509079325 \cdot 10^{-161}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \leq 7.963271108241615 \cdot 10^{+149}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* x y) -1.1215731702497594e+146)
   (* y (/ x z))
   (if (<= (* x y) -9.392040062208773e-211)
     (/ (* x y) z)
     (if (<= (* x y) 3.2890969509079325e-161)
       (/ x (/ z y))
       (if (<= (* x y) 7.963271108241615e+149) (/ (* x y) z) (* x (/ y z)))))))
double code(double x, double y, double z) {
	return (x * y) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((x * y) <= -1.1215731702497594e+146) {
		tmp = y * (x / z);
	} else if ((x * y) <= -9.392040062208773e-211) {
		tmp = (x * y) / z;
	} else if ((x * y) <= 3.2890969509079325e-161) {
		tmp = x / (z / y);
	} else if ((x * y) <= 7.963271108241615e+149) {
		tmp = (x * y) / z;
	} else {
		tmp = x * (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

Original6.3
Target6.2
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (*.f64 x y) < -1.1215731702497594e146

    1. Initial program 18.9

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

    3. Applied add-cube-cbrt_binary64_2091419.6

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

    4. Applied times-frac_binary64_208852.7

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

    5. Taylor expanded around 0 18.9

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

    6. Simplified2.9

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

    if -1.1215731702497594e146 < (*.f64 x y) < -9.3920400622087728e-211 or 3.28909695090793254e-161 < (*.f64 x y) < 7.96327110824161511e149

    1. Initial program 0.2

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

    if -9.3920400622087728e-211 < (*.f64 x y) < 3.28909695090793254e-161

    1. Initial program 10.1

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

    3. Applied associate-/l*_binary64_208240.8

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

    if 7.96327110824161511e149 < (*.f64 x y)

    1. Initial program 17.9

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

    3. Applied *-un-lft-identity_binary64_2087917.9

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

    4. Applied times-frac_binary64_208853.3

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

    5. Simplified3.3

      \[\leadsto \color{blue}{x} \cdot \frac{y}{z}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1215731702497594 \cdot 10^{+146}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \leq -9.392040062208773 \cdot 10^{-211}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 3.2890969509079325 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 7.963271108241615 \cdot 10^{+149}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020342 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))