Average Error: 5.9 → 0.5
Time: 1.6s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -3.2359822670691754 \cdot 10^{209} \lor \neg \left(x \cdot y \le -7.67586713260681024 \cdot 10^{-151} \lor \neg \left(x \cdot y \le 2.7396961141736525 \cdot 10^{-253} \lor \neg \left(x \cdot y \le 1.14755430941295989 \cdot 10^{234}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -3.2359822670691754 \cdot 10^{209} \lor \neg \left(x \cdot y \le -7.67586713260681024 \cdot 10^{-151} \lor \neg \left(x \cdot y \le 2.7396961141736525 \cdot 10^{-253} \lor \neg \left(x \cdot y \le 1.14755430941295989 \cdot 10^{234}\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) <= -3.2359822670691754e+209) || !(((x * y) <= -7.67586713260681e-151) || !(((x * y) <= 2.7396961141736525e-253) || !((x * y) <= 1.1475543094129599e+234))))) {
		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

Original5.9
Target6.2
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -3.2359822670691754e+209 or -7.67586713260681e-151 < (* x y) < 2.7396961141736525e-253 or 1.1475543094129599e+234 < (* x y)

    1. Initial program 15.0

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

    3. Applied associate-/l*0.8

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

    if -3.2359822670691754e+209 < (* x y) < -7.67586713260681e-151 or 2.7396961141736525e-253 < (* x y) < 1.1475543094129599e+234

    1. Initial program 0.2

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

    3. Applied associate-/l*9.8

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

    4. Taylor expanded around 0 0.2

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -3.2359822670691754 \cdot 10^{209} \lor \neg \left(x \cdot y \le -7.67586713260681024 \cdot 10^{-151} \lor \neg \left(x \cdot y \le 2.7396961141736525 \cdot 10^{-253} \lor \neg \left(x \cdot y \le 1.14755430941295989 \cdot 10^{234}\right)\right)\right):\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020058 +o rules:numerics
(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))