Average Error: 6.2 → 1.2
Time: 3.7s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -3.31339811201577016 \cdot 10^{90} \lor \neg \left(x \cdot y \le -1.1561705956488784 \cdot 10^{-114} \lor \neg \left(x \cdot y \le 4.5976295247838462 \cdot 10^{-171} \lor \neg \left(x \cdot y \le 2.79318987605712984 \cdot 10^{220}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -3.31339811201577016 \cdot 10^{90} \lor \neg \left(x \cdot y \le -1.1561705956488784 \cdot 10^{-114} \lor \neg \left(x \cdot y \le 4.5976295247838462 \cdot 10^{-171} \lor \neg \left(x \cdot y \le 2.79318987605712984 \cdot 10^{220}\right)\right)\right):\\
\;\;\;\;\frac{x}{\frac{z}{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)) <= -3.31339811201577e+90) || !((((double) (x * y)) <= -1.1561705956488784e-114) || !((((double) (x * y)) <= 4.597629524783846e-171) || !(((double) (x * y)) <= 2.79318987605713e+220))))) {
		VAR = ((double) (x / ((double) (z / y))));
	} 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

Original6.2
Target6.6
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -3.31339811201577016e90 or -1.1561705956488784e-114 < (* x y) < 4.5976295247838462e-171 or 2.79318987605712984e220 < (* x y)

    1. Initial program 11.6

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

    3. Applied associate-/l*2.1

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

    if -3.31339811201577016e90 < (* x y) < -1.1561705956488784e-114 or 4.5976295247838462e-171 < (* x y) < 2.79318987605712984e220

    1. Initial program 0.3

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -3.31339811201577016 \cdot 10^{90} \lor \neg \left(x \cdot y \le -1.1561705956488784 \cdot 10^{-114} \lor \neg \left(x \cdot y \le 4.5976295247838462 \cdot 10^{-171} \lor \neg \left(x \cdot y \le 2.79318987605712984 \cdot 10^{220}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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))