Average Error: 6.6 → 0.9
Time: 2.6s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -8.51580745389782995 \cdot 10^{184} \lor \neg \left(x \cdot y \le -4.78204861129760943 \cdot 10^{-159} \lor \neg \left(x \cdot y \le 5.734800247804464 \cdot 10^{-99} \lor \neg \left(x \cdot y \le 1.1176947562290144 \cdot 10^{258}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -8.51580745389782995 \cdot 10^{184} \lor \neg \left(x \cdot y \le -4.78204861129760943 \cdot 10^{-159} \lor \neg \left(x \cdot y \le 5.734800247804464 \cdot 10^{-99} \lor \neg \left(x \cdot y \le 1.1176947562290144 \cdot 10^{258}\right)\right)\right):\\
\;\;\;\;x \cdot \frac{y}{z}\\

\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)) <= -8.51580745389783e+184) || !((((double) (x * y)) <= -4.782048611297609e-159) || !((((double) (x * y)) <= 5.734800247804464e-99) || !(((double) (x * y)) <= 1.1176947562290144e+258))))) {
		VAR = ((double) (x * ((double) (y / z))));
	} else {
		VAR = ((double) (((double) (x * y)) / 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

Original6.6
Target6.2
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -8.51580745389782995e184 or -4.78204861129760943e-159 < (* x y) < 5.734800247804464e-99 or 1.1176947562290144e258 < (* x y)

    1. Initial program 13.3

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

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

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

    4. Applied times-frac1.6

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

    5. Simplified1.6

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

    if -8.51580745389782995e184 < (* x y) < -4.78204861129760943e-159 or 5.734800247804464e-99 < (* x y) < 1.1176947562290144e258

    1. Initial program 0.3

      \[\frac{x \cdot y}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -8.51580745389782995 \cdot 10^{184} \lor \neg \left(x \cdot y \le -4.78204861129760943 \cdot 10^{-159} \lor \neg \left(x \cdot y \le 5.734800247804464 \cdot 10^{-99} \lor \neg \left(x \cdot y \le 1.1176947562290144 \cdot 10^{258}\right)\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020152 
(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))