Average Error: 5.8 → 0.5
Time: 10.6s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.833851608776524 \cdot 10^{+306}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.5178017273940387 \cdot 10^{-265}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.93442146399531 \cdot 10^{+132}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.833851608776524 \cdot 10^{+306}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;x \cdot y \le -1.5178017273940387 \cdot 10^{-265}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le -0.0:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 1.93442146399531 \cdot 10^{+132}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r36586657 = x;
        double r36586658 = y;
        double r36586659 = r36586657 * r36586658;
        double r36586660 = z;
        double r36586661 = r36586659 / r36586660;
        return r36586661;
}
↓
double f(double x, double y, double z) {
        double r36586662 = x;
        double r36586663 = y;
        double r36586664 = r36586662 * r36586663;
        double r36586665 = -1.833851608776524e+306;
        bool r36586666 = r36586664 <= r36586665;
        double r36586667 = 1.0;
        double r36586668 = z;
        double r36586669 = r36586668 / r36586662;
        double r36586670 = r36586669 / r36586663;
        double r36586671 = r36586667 / r36586670;
        double r36586672 = -1.5178017273940387e-265;
        bool r36586673 = r36586664 <= r36586672;
        double r36586674 = r36586664 / r36586668;
        double r36586675 = -0.0;
        bool r36586676 = r36586664 <= r36586675;
        double r36586677 = r36586668 / r36586663;
        double r36586678 = r36586662 / r36586677;
        double r36586679 = 1.93442146399531e+132;
        bool r36586680 = r36586664 <= r36586679;
        double r36586681 = r36586663 / r36586668;
        double r36586682 = r36586662 * r36586681;
        double r36586683 = r36586680 ? r36586674 : r36586682;
        double r36586684 = r36586676 ? r36586678 : r36586683;
        double r36586685 = r36586673 ? r36586674 : r36586684;
        double r36586686 = r36586666 ? r36586671 : r36586685;
        return r36586686;
}

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

Original5.8
Target5.9
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* x y) < -1.833851608776524e+306

    1. Initial program 58.8

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

    3. Applied clear-num58.8

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    4. Using strategy rm

    5. Applied associate-/r*0.4

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

    if -1.833851608776524e+306 < (* x y) < -1.5178017273940387e-265 or -0.0 < (* x y) < 1.93442146399531e+132

    1. Initial program 0.4

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

    if -1.5178017273940387e-265 < (* x y) < -0.0

    1. Initial program 16.4

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

    3. Applied associate-/l*0.1

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

    if 1.93442146399531e+132 < (* x y)

    1. Initial program 16.0

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

    3. Applied *-un-lft-identity16.0

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

    4. Applied times-frac2.5

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

    5. Simplified2.5

      \[\leadsto \color{blue}{x} \cdot \frac{y}{z}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.833851608776524 \cdot 10^{+306}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.5178017273940387 \cdot 10^{-265}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le -0.0:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.93442146399531 \cdot 10^{+132}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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))