Average Error: 6.3 → 1.3
Time: 2.0s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7684606799376647 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \leq -3.397438454592452 \cdot 10^{-145}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 1.844858969842158 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4.824493902384278 \cdot 10^{+144}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -1.7684606799376647 \cdot 10^{+102}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;x \cdot y \leq -3.397438454592452 \cdot 10^{-145}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;x \cdot y \leq 1.844858969842158 \cdot 10^{-259}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \leq 4.824493902384278 \cdot 10^{+144}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\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) -1.7684606799376647e+102)
   (* y (/ x z))
   (if (<= (* x y) -3.397438454592452e-145)
     (/ 1.0 (/ z (* x y)))
     (if (<= (* x y) 1.844858969842158e-259)
       (/ x (/ z y))
       (if (<= (* x y) 4.824493902384278e+144)
         (/ 1.0 (/ z (* x y)))
         (* 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) <= -1.7684606799376647e+102) {
		tmp = y * (x / z);
	} else if ((x * y) <= -3.397438454592452e-145) {
		tmp = 1.0 / (z / (x * y));
	} else if ((x * y) <= 1.844858969842158e-259) {
		tmp = x / (z / y);
	} else if ((x * y) <= 4.824493902384278e+144) {
		tmp = 1.0 / (z / (x * y));
	} 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

Original6.3
Target6.7
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 x y) < -1.7684606799376647e102 or 4.82449390238427774e144 < (*.f64 x y)

    1. Initial program 16.8

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

    3. Applied add-cube-cbrt_binary6417.7

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

    4. Applied times-frac_binary643.4

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

    5. Taylor expanded around 0 16.8

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

    6. Simplified3.4

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

    if -1.7684606799376647e102 < (*.f64 x y) < -3.3974384545924519e-145 or 1.84485896984215809e-259 < (*.f64 x y) < 4.82449390238427774e144

    1. Initial program 0.2

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

    3. Applied clear-num_binary640.7

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

    if -3.3974384545924519e-145 < (*.f64 x y) < 1.84485896984215809e-259

    1. Initial program 10.0

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

    3. Applied associate-/l*_binary640.7

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.7684606799376647 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \leq -3.397438454592452 \cdot 10^{-145}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 1.844858969842158 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4.824493902384278 \cdot 10^{+144}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020220 
(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))