Average Error: 6.2 → 1.3
Time: 2.5s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -2.34371146593399062 \cdot 10^{270} \lor \neg \left(x \cdot y \le -1.162945835723597 \cdot 10^{-58} \lor \neg \left(x \cdot y \le 1.97135463763262383 \cdot 10^{-288}\right) \land x \cdot y \le 1.18648507240730839 \cdot 10^{117}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -2.34371146593399062 \cdot 10^{270} \lor \neg \left(x \cdot y \le -1.162945835723597 \cdot 10^{-58} \lor \neg \left(x \cdot y \le 1.97135463763262383 \cdot 10^{-288}\right) \land x \cdot y \le 1.18648507240730839 \cdot 10^{117}\right):\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{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)) <= -2.3437114659339906e+270) || !((((double) (x * y)) <= -1.162945835723597e-58) || (!(((double) (x * y)) <= 1.971354637632624e-288) && (((double) (x * y)) <= 1.1864850724073084e+117))))) {
		VAR = ((double) (y * ((double) (x / z))));
	} else {
		VAR = ((double) (((double) (x * y)) * ((double) (1.0 / 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
Target6.4
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -2.34371146593399062e270 or -1.162945835723597e-58 < (* x y) < 1.97135463763262383e-288 or 1.18648507240730839e117 < (* x y)

    1. Initial program 13.2

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

    3. Applied associate-/l*2.6

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
    4. Using strategy rm

    5. Applied associate-/r/2.4

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

    if -2.34371146593399062e270 < (* x y) < -1.162945835723597e-58 or 1.97135463763262383e-288 < (* x y) < 1.18648507240730839e117

    1. Initial program 0.2

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

    2. Simplified9.7

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm

    4. Applied div-inv9.8

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

    5. Applied associate-*r*0.3

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -2.34371146593399062 \cdot 10^{270} \lor \neg \left(x \cdot y \le -1.162945835723597 \cdot 10^{-58} \lor \neg \left(x \cdot y \le 1.97135463763262383 \cdot 10^{-288}\right) \land x \cdot y \le 1.18648507240730839 \cdot 10^{117}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))