Average Error: 6.5 → 0.7
Time: 2.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;{\left(\frac{x}{\frac{z}{y}}\right)}^{1}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -2.75403327231568085421125185005337842666 \cdot 10^{-316}:\\ \;\;\;\;{\left(\frac{x \cdot y}{z}\right)}^{1}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\ \;\;\;\;{\left(x \cdot \frac{y}{z}\right)}^{1}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.90915317948964794762777056224645120804 \cdot 10^{266}:\\ \;\;\;\;{\left(\frac{x \cdot y}{z}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;{\left(x \cdot \frac{y}{z}\right)}^{1}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\
\;\;\;\;{\left(\frac{x}{\frac{z}{y}}\right)}^{1}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le -2.75403327231568085421125185005337842666 \cdot 10^{-316}:\\
\;\;\;\;{\left(\frac{x \cdot y}{z}\right)}^{1}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\
\;\;\;\;{\left(x \cdot \frac{y}{z}\right)}^{1}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \le 3.90915317948964794762777056224645120804 \cdot 10^{266}:\\
\;\;\;\;{\left(\frac{x \cdot y}{z}\right)}^{1}\\

\mathbf{else}:\\
\;\;\;\;{\left(x \cdot \frac{y}{z}\right)}^{1}\\

\end{array}
double f(double x, double y, double z) {
        double r748317 = x;
        double r748318 = y;
        double r748319 = r748317 * r748318;
        double r748320 = z;
        double r748321 = r748319 / r748320;
        return r748321;
}
↓
double f(double x, double y, double z) {
        double r748322 = x;
        double r748323 = y;
        double r748324 = r748322 * r748323;
        double r748325 = z;
        double r748326 = r748324 / r748325;
        double r748327 = -inf.0;
        bool r748328 = r748326 <= r748327;
        double r748329 = r748325 / r748323;
        double r748330 = r748322 / r748329;
        double r748331 = 1.0;
        double r748332 = pow(r748330, r748331);
        double r748333 = -2.7540332723157e-316;
        bool r748334 = r748326 <= r748333;
        double r748335 = pow(r748326, r748331);
        double r748336 = 0.0;
        bool r748337 = r748326 <= r748336;
        double r748338 = r748323 / r748325;
        double r748339 = r748322 * r748338;
        double r748340 = pow(r748339, r748331);
        double r748341 = 3.909153179489648e+266;
        bool r748342 = r748326 <= r748341;
        double r748343 = r748342 ? r748335 : r748340;
        double r748344 = r748337 ? r748340 : r748343;
        double r748345 = r748334 ? r748335 : r748344;
        double r748346 = r748328 ? r748332 : r748345;
        return r748346;
}

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

Original6.5
Target6.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519428958560619200129306371776 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.704213066065047207696571404603247573308 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

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 add-cube-cbrt64.0

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

    4. Applied times-frac1.3

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied pow11.3

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

    7. Applied pow11.3

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

    8. Applied pow-prod-down1.3

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

    9. Simplified64.0

      \[\leadsto {\color{blue}{\left(\frac{x \cdot y}{z}\right)}}^{1}\]
    10. Using strategy rm

    11. Applied associate-/l*0.2

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

    if -inf.0 < (/ (* x y) z) < -2.7540332723157e-316 or 0.0 < (/ (* x y) z) < 3.909153179489648e+266

    1. Initial program 2.2

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

    3. Applied add-cube-cbrt3.2

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

    4. Applied times-frac6.4

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied pow16.4

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

    7. Applied pow16.4

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

    8. Applied pow-prod-down6.4

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

    9. Simplified2.2

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

    if -2.7540332723157e-316 < (/ (* x y) z) < 0.0 or 3.909153179489648e+266 < (/ (* x y) z)

    1. Initial program 18.8

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

    3. Applied add-cube-cbrt18.9

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

    4. Applied times-frac2.1

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{y}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied pow12.1

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

    7. Applied pow12.1

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

    8. Applied pow-prod-down2.1

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

    9. Simplified18.8

      \[\leadsto {\color{blue}{\left(\frac{x \cdot y}{z}\right)}}^{1}\]
    10. Using strategy rm

    11. Applied div-inv18.8

      \[\leadsto {\color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{z}\right)}}^{1}\]
    12. Using strategy rm

    13. Applied associate-*l*2.1

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

    14. Simplified2.1

      \[\leadsto {\left(x \cdot \color{blue}{\frac{y}{z}}\right)}^{1}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} = -\infty:\\ \;\;\;\;{\left(\frac{x}{\frac{z}{y}}\right)}^{1}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le -2.75403327231568085421125185005337842666 \cdot 10^{-316}:\\ \;\;\;\;{\left(\frac{x \cdot y}{z}\right)}^{1}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 0.0:\\ \;\;\;\;{\left(x \cdot \frac{y}{z}\right)}^{1}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \le 3.90915317948964794762777056224645120804 \cdot 10^{266}:\\ \;\;\;\;{\left(\frac{x \cdot y}{z}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;{\left(x \cdot \frac{y}{z}\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))