Average Error: 6.1 → 1.8
Time: 9.3s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.28814127502927457 \cdot 10^{-255} \lor \neg \left(x \cdot y \le 2.06616796455329214 \cdot 10^{-194} \lor \neg \left(x \cdot y \le 2.76589914113834434 \cdot 10^{248}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.28814127502927457 \cdot 10^{-255} \lor \neg \left(x \cdot y \le 2.06616796455329214 \cdot 10^{-194} \lor \neg \left(x \cdot y \le 2.76589914113834434 \cdot 10^{248}\right)\right):\\
\;\;\;\;\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)) <= -1.2881412750292746e-255) || !((((double) (x * y)) <= 2.066167964553292e-194) || !(((double) (x * y)) <= 2.7658991411383443e+248)))) {
		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

Original6.1
Target6.1
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -1.28814127502927457e-255 or 2.06616796455329214e-194 < (* x y) < 2.76589914113834434e248

    1. Initial program 2.4

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

    if -1.28814127502927457e-255 < (* x y) < 2.06616796455329214e-194 or 2.76589914113834434e248 < (* x y)

    1. Initial program 15.3

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

    3. Applied *-un-lft-identity15.3

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.28814127502927457 \cdot 10^{-255} \lor \neg \left(x \cdot y \le 2.06616796455329214 \cdot 10^{-194} \lor \neg \left(x \cdot y \le 2.76589914113834434 \cdot 10^{248}\right)\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020163 
(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))