Average Error: 6.4 → 0.3
Time: 4.3s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.746092237969938 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq -6.101342492244879 \cdot 10^{-297}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 7.307020503887261 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2.47984642565512 \cdot 10^{+226}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -4.746092237969938 \cdot 10^{+196}:\\
\;\;\;\;x \cdot \left(y \cdot \frac{1}{z}\right)\\

\mathbf{elif}\;x \cdot y \leq -6.101342492244879 \cdot 10^{-297}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \leq 7.307020503887261 \cdot 10^{-233}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \leq 2.47984642565512 \cdot 10^{+226}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* x y) -4.746092237969938e+196)
   (* x (* y (/ 1.0 z)))
   (if (<= (* x y) -6.101342492244879e-297)
     (/ (* x y) z)
     (if (<= (* x y) 7.307020503887261e-233)
       (/ x (/ z y))
       (if (<= (* x y) 2.47984642565512e+226) (/ (* x y) z) (* y (/ x 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) <= -4.746092237969938e+196) {
		tmp = x * (y * (1.0 / z));
	} else if ((x * y) <= -6.101342492244879e-297) {
		tmp = (x * y) / z;
	} else if ((x * y) <= 7.307020503887261e-233) {
		tmp = x / (z / y);
	} else if ((x * y) <= 2.47984642565512e+226) {
		tmp = (x * y) / z;
	} else {
		tmp = y * (x / 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

Original6.4
Target6.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (*.f64 x y) < -4.74609223796993785e196

    1. Initial program 22.4

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

    3. Applied add-cube-cbrt_binary64_1989123.1

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

    4. Applied times-frac_binary64_198622.1

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

    6. Applied add-cube-cbrt_binary64_198912.4

      \[\leadsto \frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}}}\]
    7. Using strategy rm

    8. Applied div-inv_binary64_198532.4

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)} \cdot \frac{y}{\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}}\]

    9. Applied associate-*l*_binary64_197972.0

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}}\right)}\]

    10. Simplified0.8

      \[\leadsto x \cdot \color{blue}{\left(\frac{1}{z} \cdot y\right)}\]

    if -4.74609223796993785e196 < (*.f64 x y) < -6.10134249224487921e-297 or 7.30702050388726106e-233 < (*.f64 x y) < 2.4798464256551202e226

    1. Initial program 0.2

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

    if -6.10134249224487921e-297 < (*.f64 x y) < 7.30702050388726106e-233

    1. Initial program 14.6

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

    3. Applied associate-/l*_binary64_198010.2

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

    if 2.4798464256551202e226 < (*.f64 x y)

    1. Initial program 33.0

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

    3. Applied associate-/l*_binary64_198010.8

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

    5. Applied associate-/r/_binary64_198020.7

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.746092237969938 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;x \cdot y \leq -6.101342492244879 \cdot 10^{-297}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 7.307020503887261 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2.47984642565512 \cdot 10^{+226}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(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))