Average Error: 6.3 → 0.5
Time: 2.8s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -inf.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -3.20700691556906445 \cdot 10^{-212}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.5973998642370275 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \le 4.09863767648200739 \cdot 10^{175}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y = -inf.0:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -3.20700691556906445 \cdot 10^{-212}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 3.5973998642370275 \cdot 10^{-163}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;x \cdot y \le 4.09863767648200739 \cdot 10^{175}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double code(double x, double y, double z) {
	return (((double) (x * y)) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (x * y)) <= -inf.0)) {
		VAR = (x / (z / y));
	} else {
		double VAR_1;
		if ((((double) (x * y)) <= -3.2070069155690644e-212)) {
			VAR_1 = (((double) (x * y)) / z);
		} else {
			double VAR_2;
			if ((((double) (x * y)) <= 3.5973998642370275e-163)) {
				VAR_2 = ((double) (y * (x / z)));
			} else {
				double VAR_3;
				if ((((double) (x * y)) <= 4.0986376764820074e+175)) {
					VAR_3 = (((double) (x * y)) / z);
				} else {
					VAR_3 = (x / (z / y));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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
Target6.3
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -inf.0 or 4.09863767648200739e175 < (* x y)

    1. Initial program 33.8

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

    3. Applied associate-/l*1.1

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

    if -inf.0 < (* x y) < -3.20700691556906445e-212 or 3.5973998642370275e-163 < (* x y) < 4.09863767648200739e175

    1. Initial program 0.2

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

    if -3.20700691556906445e-212 < (* x y) < 3.5973998642370275e-163

    1. Initial program 9.7

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

    3. Applied add-cube-cbrt10.0

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

    4. Applied times-frac1.0

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

    5. Taylor expanded around 0 9.7

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

    6. Simplified0.8

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y = -inf.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -3.20700691556906445 \cdot 10^{-212}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.5973998642370275 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \le 4.09863767648200739 \cdot 10^{175}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))