Average Error: 6.2 → 1.8
Time: 2.8s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -2.4396634972759232 \cdot 10^{292}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -3.08805406789778334 \cdot 10^{-230}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.787826098283795 \cdot 10^{-310}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -2.4396634972759232 \cdot 10^{292}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -3.08805406789778334 \cdot 10^{-230}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 5.787826098283795 \cdot 10^{-310}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\

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

\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)) <= -2.4396634972759232e+292)) {
		VAR = ((double) (x * ((double) (y / z))));
	} else {
		double VAR_1;
		if ((((double) (x * y)) <= -3.0880540678977833e-230)) {
			VAR_1 = ((double) (((double) (x * y)) / z));
		} else {
			double VAR_2;
			if ((((double) (x * y)) <= 5.7878260982838e-310)) {
				VAR_2 = ((double) (((double) (x / z)) / ((double) (1.0 / y))));
			} else {
				VAR_2 = ((double) (((double) (x * y)) / z));
			}
			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

Original6.2
Target6.4
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -2.4396634972759232e+292

    1. Initial program 56.8

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

    3. Applied *-un-lft-identity56.8

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

    if -2.4396634972759232e+292 < (* x y) < -3.0880540678977833e-230 or 5.7878260982838e-310 < (* x y)

    1. Initial program 2.3

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

    if -3.0880540678977833e-230 < (* x y) < 5.7878260982838e-310

    1. Initial program 14.4

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

    3. Applied associate-/l*0.2

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

    5. Applied div-inv0.2

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

    6. Applied associate-/r*0.2

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{\frac{1}{y}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -2.4396634972759232 \cdot 10^{292}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -3.08805406789778334 \cdot 10^{-230}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 5.787826098283795 \cdot 10^{-310}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020147 
(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))