Average Error: 6.5 → 0.7
Time: 2.4s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.76620071270604 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq -4.4937687213996554 \cdot 10^{-213}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \leq 5.691663400962288 \cdot 10^{+112}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -6.76620071270604 \cdot 10^{+219}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \leq -4.4937687213996554 \cdot 10^{-213}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \leq 0:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;x \cdot y \leq 5.691663400962288 \cdot 10^{+112}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* x y) -6.76620071270604e+219)
   (/ x (/ z y))
   (if (<= (* x y) -4.4937687213996554e-213)
     (/ (* x y) z)
     (if (<= (* x y) 0.0)
       (* y (/ x z))
       (if (<= (* x y) 5.691663400962288e+112)
         (* (* x y) (/ 1.0 z))
         (* x (/ y z)))))))
double code(double x, double y, double z) {
	return (((double) (x * y)) / z);
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((((double) (x * y)) <= -6.76620071270604e+219)) {
		tmp = (x / (z / y));
	} else {
		double tmp_1;
		if ((((double) (x * y)) <= -4.4937687213996554e-213)) {
			tmp_1 = (((double) (x * y)) / z);
		} else {
			double tmp_2;
			if ((((double) (x * y)) <= 0.0)) {
				tmp_2 = ((double) (y * (x / z)));
			} else {
				double tmp_3;
				if ((((double) (x * y)) <= 5.691663400962288e+112)) {
					tmp_3 = ((double) (((double) (x * y)) * (1.0 / z)));
				} else {
					tmp_3 = ((double) (x * (y / z)));
				}
				tmp_2 = tmp_3;
			}
			tmp_1 = tmp_2;
		}
		tmp = tmp_1;
	}
	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

Original6.5
Target6.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 5 regimes

  2. if (*.f64 x y) < -6.76620071270604e219

    1. Initial program 31.7

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

    3. Applied associate-/l*_binary640.9

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

    if -6.76620071270604e219 < (*.f64 x y) < -4.49376872139965541e-213

    1. Initial program 0.2

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

    if -4.49376872139965541e-213 < (*.f64 x y) < 0.0

    1. Initial program 14.0

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

    3. Applied associate-/l*_binary640.3

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

    5. Applied associate-/r/_binary640.2

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

    if 0.0 < (*.f64 x y) < 5.6916634009622879e112

    1. Initial program 0.5

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

    3. Applied div-inv_binary640.5

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

    if 5.6916634009622879e112 < (*.f64 x y)

    1. Initial program 15.7

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

    3. Applied *-un-lft-identity_binary6415.7

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

    4. Applied times-frac_binary643.5

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

    5. Simplified3.5

      \[\leadsto \color{blue}{x} \cdot \frac{y}{z}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.76620071270604 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq -4.4937687213996554 \cdot 10^{-213}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \cdot y \leq 5.691663400962288 \cdot 10^{+112}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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))