Average Error: 6.2 → 1.7
Time: 2.6s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -4.4795481217015377 \cdot 10^{-218} \lor \neg \left(x \cdot y \le 1.36108928858102591 \cdot 10^{-243}\right) \land x \cdot y \le 5.58670820551259035 \cdot 10^{230}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -4.4795481217015377 \cdot 10^{-218} \lor \neg \left(x \cdot y \le 1.36108928858102591 \cdot 10^{-243}\right) \land x \cdot y \le 5.58670820551259035 \cdot 10^{230}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{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)) <= -4.4795481217015377e-218) || (!(((double) (x * y)) <= 1.361089288581026e-243) && (((double) (x * y)) <= 5.58670820551259e+230)))) {
		VAR = ((double) (((double) (x * y)) / z));
	} else {
		VAR = ((double) (x * ((double) (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
Target6.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -4.4795481217015377e-218 or 1.36108928858102591e-243 < (* x y) < 5.58670820551259035e230

    1. Initial program 2.3

      \[\frac{x \cdot y}{z}\]

    if -4.4795481217015377e-218 < (* x y) < 1.36108928858102591e-243 or 5.58670820551259035e230 < (* x y)

    1. Initial program 15.7

      \[\frac{x \cdot y}{z}\]

    2. Simplified0.2

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -4.4795481217015377 \cdot 10^{-218} \lor \neg \left(x \cdot y \le 1.36108928858102591 \cdot 10^{-243}\right) \land x \cdot y \le 5.58670820551259035 \cdot 10^{230}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))