Average Error: 6.5 → 0.3
Time: 2.5s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -4.46060635921538881 \cdot 10^{292} \lor \neg \left(x \cdot y \le -1.0274306680362397 \cdot 10^{-250} \lor \neg \left(x \cdot y \le 5.13450776540910696 \cdot 10^{-245} \lor \neg \left(x \cdot y \le 8.74146484840982345 \cdot 10^{238}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -4.46060635921538881 \cdot 10^{292} \lor \neg \left(x \cdot y \le -1.0274306680362397 \cdot 10^{-250} \lor \neg \left(x \cdot y \le 5.13450776540910696 \cdot 10^{-245} \lor \neg \left(x \cdot y \le 8.74146484840982345 \cdot 10^{238}\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 ((x * y) / z);
}
↓
double code(double x, double y, double z) {
	double temp;
	if ((((x * y) <= -4.460606359215389e+292) || !(((x * y) <= -1.0274306680362397e-250) || !(((x * y) <= 5.134507765409107e-245) || !((x * y) <= 8.741464848409823e+238))))) {
		temp = (x / (z / y));
	} else {
		temp = ((x * y) / z);
	}
	return temp;
}

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
Target6.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -4.460606359215389e+292 or -1.0274306680362397e-250 < (* x y) < 5.134507765409107e-245 or 8.741464848409823e+238 < (* x y)

    1. Initial program 21.6

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

    3. Applied associate-/l*0.3

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

    if -4.460606359215389e+292 < (* x y) < -1.0274306680362397e-250 or 5.134507765409107e-245 < (* x y) < 8.741464848409823e+238

    1. Initial program 0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -4.46060635921538881 \cdot 10^{292} \lor \neg \left(x \cdot y \le -1.0274306680362397 \cdot 10^{-250} \lor \neg \left(x \cdot y \le 5.13450776540910696 \cdot 10^{-245} \lor \neg \left(x \cdot y \le 8.74146484840982345 \cdot 10^{238}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020053 
(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))