Average Error: 6.1 → 0.7
Time: 1.1m
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -6.939593118092855 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.454055052210347 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.8266963535821708 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.1730839583412028 \cdot 10^{+147}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -6.939593118092855 \cdot 10^{+188}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -1.454055052210347 \cdot 10^{-302}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;x \cdot y \le 1.8266963535821708 \cdot 10^{-240}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.1730839583412028 \cdot 10^{+147}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r32048194 = x;
        double r32048195 = y;
        double r32048196 = r32048194 * r32048195;
        double r32048197 = z;
        double r32048198 = r32048196 / r32048197;
        return r32048198;
}
↓
double f(double x, double y, double z) {
        double r32048199 = x;
        double r32048200 = y;
        double r32048201 = r32048199 * r32048200;
        double r32048202 = -6.939593118092855e+188;
        bool r32048203 = r32048201 <= r32048202;
        double r32048204 = z;
        double r32048205 = r32048200 / r32048204;
        double r32048206 = r32048199 * r32048205;
        double r32048207 = -1.454055052210347e-302;
        bool r32048208 = r32048201 <= r32048207;
        double r32048209 = 1.0;
        double r32048210 = r32048204 / r32048201;
        double r32048211 = r32048209 / r32048210;
        double r32048212 = 1.8266963535821708e-240;
        bool r32048213 = r32048201 <= r32048212;
        double r32048214 = 1.1730839583412028e+147;
        bool r32048215 = r32048201 <= r32048214;
        double r32048216 = r32048215 ? r32048211 : r32048206;
        double r32048217 = r32048213 ? r32048206 : r32048216;
        double r32048218 = r32048208 ? r32048211 : r32048217;
        double r32048219 = r32048203 ? r32048206 : r32048218;
        return r32048219;
}

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
Target5.4
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -6.939593118092855e+188 or -1.454055052210347e-302 < (* x y) < 1.8266963535821708e-240 or 1.1730839583412028e+147 < (* x y)

    1. Initial program 17.1

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

    3. Applied *-un-lft-identity17.1

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

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

    if -6.939593118092855e+188 < (* x y) < -1.454055052210347e-302 or 1.8266963535821708e-240 < (* x y) < 1.1730839583412028e+147

    1. Initial program 0.2

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

    3. Applied clear-num0.6

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -6.939593118092855 \cdot 10^{+188}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.454055052210347 \cdot 10^{-302}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.8266963535821708 \cdot 10^{-240}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.1730839583412028 \cdot 10^{+147}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))