Average Error: 6.3 → 1.1
Time: 2.0s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -4.3616144883237111 \cdot 10^{241}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.67324085857136302 \cdot 10^{-117}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.22528 \cdot 10^{-320}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.7247330451549739 \cdot 10^{217}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -4.3616144883237111 \cdot 10^{241}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\

\mathbf{elif}\;x \cdot y \le -1.67324085857136302 \cdot 10^{-117}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;x \cdot y \le 1.22528 \cdot 10^{-320}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 5.7247330451549739 \cdot 10^{217}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (x * y)) <= -4.361614488323711e+241)) {
		VAR = ((double) (((double) (x / z)) / ((double) (1.0 / y))));
	} else {
		double VAR_1;
		if ((((double) (x * y)) <= -1.673240858571363e-117)) {
			VAR_1 = ((double) (1.0 / ((double) (z / ((double) (x * y))))));
		} else {
			double VAR_2;
			if ((((double) (x * y)) <= 1.2252828016863e-320)) {
				VAR_2 = ((double) (x * ((double) (y / z))));
			} else {
				double VAR_3;
				if ((((double) (x * y)) <= 5.724733045154974e+217)) {
					VAR_3 = ((double) (1.0 / ((double) (z / ((double) (x * y))))));
				} else {
					VAR_3 = ((double) (x / ((double) (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
Target6.5
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* x y) < -4.361614488323711e+241

    1. Initial program 38.8

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

    3. Applied associate-/l*0.6

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

    5. Applied div-inv0.7

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

    6. Applied associate-/r*0.3

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

    if -4.361614488323711e+241 < (* x y) < -1.673240858571363e-117 or 1.2252828016863e-320 < (* x y) < 5.724733045154974e+217

    1. Initial program 0.3

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

    3. Applied clear-num0.8

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

    if -1.673240858571363e-117 < (* x y) < 1.2252828016863e-320

    1. Initial program 10.7

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

    3. Applied *-un-lft-identity10.7

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

    4. Applied times-frac1.8

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

    5. Simplified1.8

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

    if 5.724733045154974e+217 < (* x y)

    1. Initial program 29.5

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

    3. Applied associate-/l*1.2

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -4.3616144883237111 \cdot 10^{241}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.67324085857136302 \cdot 10^{-117}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.22528 \cdot 10^{-320}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.7247330451549739 \cdot 10^{217}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020140 
(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))