Average Error: 5.9 → 0.7
Time: 11.2s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -5.740477931683316 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.3953881520711723 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 6.0204975761929244 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 1.783795166746355 \cdot 10^{+210}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -5.740477931683316 \cdot 10^{+143}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -1.3953881520711723 \cdot 10^{-149}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 6.0204975761929244 \cdot 10^{-207}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 1.783795166746355 \cdot 10^{+210}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r32245742 = x;
        double r32245743 = y;
        double r32245744 = r32245742 * r32245743;
        double r32245745 = z;
        double r32245746 = r32245744 / r32245745;
        return r32245746;
}
↓
double f(double x, double y, double z) {
        double r32245747 = x;
        double r32245748 = y;
        double r32245749 = r32245747 * r32245748;
        double r32245750 = -5.740477931683316e+143;
        bool r32245751 = r32245749 <= r32245750;
        double r32245752 = z;
        double r32245753 = r32245752 / r32245748;
        double r32245754 = r32245747 / r32245753;
        double r32245755 = -1.3953881520711723e-149;
        bool r32245756 = r32245749 <= r32245755;
        double r32245757 = r32245749 / r32245752;
        double r32245758 = 6.0204975761929244e-207;
        bool r32245759 = r32245749 <= r32245758;
        double r32245760 = r32245748 / r32245752;
        double r32245761 = r32245760 * r32245747;
        double r32245762 = 1.783795166746355e+210;
        bool r32245763 = r32245749 <= r32245762;
        double r32245764 = r32245763 ? r32245757 : r32245754;
        double r32245765 = r32245759 ? r32245761 : r32245764;
        double r32245766 = r32245756 ? r32245757 : r32245765;
        double r32245767 = r32245751 ? r32245754 : r32245766;
        return r32245767;
}

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
Target5.6
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 3 regimes

  2. if (* x y) < -5.740477931683316e+143 or 1.783795166746355e+210 < (* x y)

    1. Initial program 20.4

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

    3. Applied associate-/l*1.8

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

    if -5.740477931683316e+143 < (* x y) < -1.3953881520711723e-149 or 6.0204975761929244e-207 < (* x y) < 1.783795166746355e+210

    1. Initial program 0.2

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

    if -1.3953881520711723e-149 < (* x y) < 6.0204975761929244e-207

    1. Initial program 9.5

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

    3. Applied *-un-lft-identity9.5

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -5.740477931683316 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -1.3953881520711723 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 6.0204975761929244 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 1.783795166746355 \cdot 10^{+210}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 +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))