Average Error: 6.4 → 3.5
Time: 2.5s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -5.954942870390162170560614222042356335045 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le -5.954942870390162170560614222042356335045 \cdot 10^{-288}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r1265344 = x;
        double r1265345 = y;
        double r1265346 = r1265344 * r1265345;
        double r1265347 = z;
        double r1265348 = r1265346 / r1265347;
        return r1265348;
}
↓
double f(double x, double y, double z) {
        double r1265349 = x;
        double r1265350 = y;
        double r1265351 = r1265349 * r1265350;
        double r1265352 = z;
        double r1265353 = r1265351 / r1265352;
        double r1265354 = -inf.0;
        bool r1265355 = r1265353 <= r1265354;
        double r1265356 = r1265350 / r1265352;
        double r1265357 = r1265349 * r1265356;
        double r1265358 = -5.954942870390162e-288;
        bool r1265359 = r1265353 <= r1265358;
        double r1265360 = r1265352 / r1265350;
        double r1265361 = r1265349 / r1265360;
        double r1265362 = r1265359 ? r1265353 : r1265361;
        double r1265363 = r1265355 ? r1265357 : r1265362;
        return r1265363;
}

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
Target6.4
Herbie3.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x y) z) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity64.0

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

    if -inf.0 < (/ (* x y) z) < -5.954942870390162e-288

    1. Initial program 0.5

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

    3. Applied associate-/l*8.0

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

    5. Applied add-cube-cbrt9.0

      \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}}\]

    6. Applied *-un-lft-identity9.0

      \[\leadsto \frac{x}{\frac{\color{blue}{1 \cdot z}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

    7. Applied times-frac9.0

      \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}}}\]

    8. Applied associate-/r*2.7

      \[\leadsto \color{blue}{\frac{\frac{x}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}}{\frac{z}{\sqrt[3]{y}}}}\]

    9. Simplified2.7

      \[\leadsto \frac{\color{blue}{x \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)}}{\frac{z}{\sqrt[3]{y}}}\]

    10. Taylor expanded around 0 0.5

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

    if -5.954942870390162e-288 < (/ (* x y) z)

    1. Initial program 7.2

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

    3. Applied associate-/l*5.3

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -5.954942870390162170560614222042356335045 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019318 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.70421306606504721e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))