Average Error: 6.4 → 0.9
Time: 40.8s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.075244188619026 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.8786363330310987 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.803402612881974 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.5781588091808662 \cdot 10^{+198}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.075244188619026 \cdot 10^{+301}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -1.8786363330310987 \cdot 10^{-77}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 3.803402612881974 \cdot 10^{-254}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 1.5781588091808662 \cdot 10^{+198}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r30714807 = x;
        double r30714808 = y;
        double r30714809 = r30714807 * r30714808;
        double r30714810 = z;
        double r30714811 = r30714809 / r30714810;
        return r30714811;
}
↓
double f(double x, double y, double z) {
        double r30714812 = x;
        double r30714813 = y;
        double r30714814 = r30714812 * r30714813;
        double r30714815 = -1.075244188619026e+301;
        bool r30714816 = r30714814 <= r30714815;
        double r30714817 = z;
        double r30714818 = r30714813 / r30714817;
        double r30714819 = r30714812 * r30714818;
        double r30714820 = -1.8786363330310987e-77;
        bool r30714821 = r30714814 <= r30714820;
        double r30714822 = r30714814 / r30714817;
        double r30714823 = 3.803402612881974e-254;
        bool r30714824 = r30714814 <= r30714823;
        double r30714825 = r30714817 / r30714813;
        double r30714826 = r30714812 / r30714825;
        double r30714827 = 1.5781588091808662e+198;
        bool r30714828 = r30714814 <= r30714827;
        double r30714829 = r30714828 ? r30714822 : r30714819;
        double r30714830 = r30714824 ? r30714826 : r30714829;
        double r30714831 = r30714821 ? r30714822 : r30714830;
        double r30714832 = r30714816 ? r30714819 : r30714831;
        return r30714832;
}

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

Original6.4
Target6.2
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -1.075244188619026e+301 or 1.5781588091808662e+198 < (* x y)

    1. Initial program 37.7

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

    3. Applied *-un-lft-identity37.7

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

    if -1.075244188619026e+301 < (* x y) < -1.8786363330310987e-77 or 3.803402612881974e-254 < (* x y) < 1.5781588091808662e+198

    1. Initial program 0.2

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

    if -1.8786363330310987e-77 < (* x y) < 3.803402612881974e-254

    1. Initial program 8.6

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

    3. Applied associate-/l*2.1

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.075244188619026 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -1.8786363330310987 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.803402612881974 \cdot 10^{-254}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 1.5781588091808662 \cdot 10^{+198}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(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))