Average Error: 6.4 → 1.5
Time: 2.6s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq -1.4935222272750587 \cdot 10^{-59} \lor \neg \left(x \cdot y \leq 1.9184481596225994 \cdot 10^{-169}\right) \land x \cdot y \leq 1.6286506104480705 \cdot 10^{+152}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -\infty:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \leq -1.4935222272750587 \cdot 10^{-59} \lor \neg \left(x \cdot y \leq 1.9184481596225994 \cdot 10^{-169}\right) \land x \cdot y \leq 1.6286506104480705 \cdot 10^{+152}:\\
\;\;\;\;\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) (- INFINITY))
   (/ x (/ z y))
   (if (or (<= (* x y) -1.4935222272750587e-59)
           (and (not (<= (* x y) 1.9184481596225994e-169))
                (<= (* x y) 1.6286506104480705e+152)))
     (/ 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) <= -((double) INFINITY)) {
		tmp = x / (z / y);
	} else if (((x * y) <= -1.4935222272750587e-59) || (!((x * y) <= 1.9184481596225994e-169) && ((x * y) <= 1.6286506104480705e+152))) {
		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

Original6.4
Target6.0
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 x y) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*_binary640.3

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

    if -inf.0 < (*.f64 x y) < -1.493522227275059e-59 or 1.91844815962259944e-169 < (*.f64 x y) < 1.6286506104480705e152

    1. Initial program 0.2

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

    3. Applied clear-num_binary640.6

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

    if -1.493522227275059e-59 < (*.f64 x y) < 1.91844815962259944e-169 or 1.6286506104480705e152 < (*.f64 x y)

    1. Initial program 9.6

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

    3. Applied associate-/l*_binary642.7

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

    5. Applied associate-/r/_binary642.4

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \leq -1.4935222272750587 \cdot 10^{-59} \lor \neg \left(x \cdot y \leq 1.9184481596225994 \cdot 10^{-169}\right) \land x \cdot y \leq 1.6286506104480705 \cdot 10^{+152}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020268 
(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))