Average Error: 6.2 → 0.5
Time: 14.9s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -5.899145090483621243407591608868938844895 \cdot 10^{275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -4.740188247183417662311772579191743839341 \cdot 10^{-201}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \le 2.796489205112816623953257005668039638224 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 2.345913877288735097014094340963252524817 \cdot 10^{180}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -5.899145090483621243407591608868938844895 \cdot 10^{275}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le -4.740188247183417662311772579191743839341 \cdot 10^{-201}:\\
\;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\

\mathbf{elif}\;x \cdot y \le 2.796489205112816623953257005668039638224 \cdot 10^{-171}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le 2.345913877288735097014094340963252524817 \cdot 10^{180}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r28530127 = x;
        double r28530128 = y;
        double r28530129 = r28530127 * r28530128;
        double r28530130 = z;
        double r28530131 = r28530129 / r28530130;
        return r28530131;
}
↓
double f(double x, double y, double z) {
        double r28530132 = x;
        double r28530133 = y;
        double r28530134 = r28530132 * r28530133;
        double r28530135 = -5.899145090483621e+275;
        bool r28530136 = r28530134 <= r28530135;
        double r28530137 = z;
        double r28530138 = r28530133 / r28530137;
        double r28530139 = r28530132 * r28530138;
        double r28530140 = -4.740188247183418e-201;
        bool r28530141 = r28530134 <= r28530140;
        double r28530142 = 1.0;
        double r28530143 = r28530142 / r28530137;
        double r28530144 = r28530143 * r28530134;
        double r28530145 = 2.7964892051128166e-171;
        bool r28530146 = r28530134 <= r28530145;
        double r28530147 = r28530137 / r28530133;
        double r28530148 = r28530132 / r28530147;
        double r28530149 = 2.345913877288735e+180;
        bool r28530150 = r28530134 <= r28530149;
        double r28530151 = r28530134 / r28530137;
        double r28530152 = r28530150 ? r28530151 : r28530148;
        double r28530153 = r28530146 ? r28530148 : r28530152;
        double r28530154 = r28530141 ? r28530144 : r28530153;
        double r28530155 = r28530136 ? r28530139 : r28530154;
        return r28530155;
}

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
Target6.3
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* x y) < -5.899145090483621e+275

    1. Initial program 49.2

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

    3. Applied *-un-lft-identity49.2

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

    if -5.899145090483621e+275 < (* x y) < -4.740188247183418e-201

    1. Initial program 0.3

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

    3. Applied div-inv0.3

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

    if -4.740188247183418e-201 < (* x y) < 2.7964892051128166e-171 or 2.345913877288735e+180 < (* x y)

    1. Initial program 11.6

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

    3. Applied associate-/l*0.8

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

    if 2.7964892051128166e-171 < (* x y) < 2.345913877288735e+180

    1. Initial program 0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -5.899145090483621243407591608868938844895 \cdot 10^{275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le -4.740188247183417662311772579191743839341 \cdot 10^{-201}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \cdot y \le 2.796489205112816623953257005668039638224 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le 2.345913877288735097014094340963252524817 \cdot 10^{180}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 +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))