Average Error: 6.3 → 1.1
Time: 2.1s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.00574974617706634 \cdot 10^{108} \lor \neg \left(x \cdot y \le -1.13772324721350758 \cdot 10^{-297} \lor \neg \left(x \cdot y \le 2.12799919492553092 \cdot 10^{-211} \lor \neg \left(x \cdot y \le 2.68127311261756407 \cdot 10^{79}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.00574974617706634 \cdot 10^{108} \lor \neg \left(x \cdot y \le -1.13772324721350758 \cdot 10^{-297} \lor \neg \left(x \cdot y \le 2.12799919492553092 \cdot 10^{-211} \lor \neg \left(x \cdot y \le 2.68127311261756407 \cdot 10^{79}\right)\right)\right):\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{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)) <= -1.0057497461770663e+108) || !((((double) (x * y)) <= -1.1377232472135076e-297) || !((((double) (x * y)) <= 2.127999194925531e-211) || !(((double) (x * y)) <= 2.681273112617564e+79))))) {
		VAR = ((double) (x * ((double) (y / z))));
	} else {
		VAR = ((double) (((double) (x * y)) * ((double) (1.0 / z))));
	}
	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
Target6.1
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 2 regimes

  2. if (* x y) < -1.00574974617706634e108 or -1.13772324721350758e-297 < (* x y) < 2.12799919492553092e-211 or 2.68127311261756407e79 < (* x y)

    1. Initial program 13.4

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

    3. Applied *-un-lft-identity13.4

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

    4. Applied times-frac2.2

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

    5. Simplified2.2

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

    if -1.00574974617706634e108 < (* x y) < -1.13772324721350758e-297 or 2.12799919492553092e-211 < (* x y) < 2.68127311261756407e79

    1. Initial program 0.2

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

    3. Applied div-inv0.3

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.00574974617706634 \cdot 10^{108} \lor \neg \left(x \cdot y \le -1.13772324721350758 \cdot 10^{-297} \lor \neg \left(x \cdot y \le 2.12799919492553092 \cdot 10^{-211} \lor \neg \left(x \cdot y \le 2.68127311261756407 \cdot 10^{79}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(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))