Average Error: 2.0 → 2.4
Time: 14.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -4.56357796438428046 \cdot 10^{-228} \lor \neg \left(b \le 1.2486298280538037 \cdot 10^{-238}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b}} \cdot \frac{\frac{{\left(\frac{\sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}}}{y}\right)\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;b \le -4.56357796438428046 \cdot 10^{-228} \lor \neg \left(b \le 1.2486298280538037 \cdot 10^{-238}\right):\\
\;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(\frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b}} \cdot \frac{\frac{{\left(\frac{\sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}}}{y}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r83524 = x;
        double r83525 = y;
        double r83526 = z;
        double r83527 = log(r83526);
        double r83528 = r83525 * r83527;
        double r83529 = t;
        double r83530 = 1.0;
        double r83531 = r83529 - r83530;
        double r83532 = a;
        double r83533 = log(r83532);
        double r83534 = r83531 * r83533;
        double r83535 = r83528 + r83534;
        double r83536 = b;
        double r83537 = r83535 - r83536;
        double r83538 = exp(r83537);
        double r83539 = r83524 * r83538;
        double r83540 = r83539 / r83525;
        return r83540;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r83541 = b;
        double r83542 = -4.5635779643842805e-228;
        bool r83543 = r83541 <= r83542;
        double r83544 = 1.2486298280538037e-238;
        bool r83545 = r83541 <= r83544;
        double r83546 = !r83545;
        bool r83547 = r83543 || r83546;
        double r83548 = x;
        double r83549 = 1.0;
        double r83550 = a;
        double r83551 = r83549 / r83550;
        double r83552 = 1.0;
        double r83553 = pow(r83551, r83552);
        double r83554 = y;
        double r83555 = z;
        double r83556 = r83549 / r83555;
        double r83557 = log(r83556);
        double r83558 = r83554 * r83557;
        double r83559 = log(r83551);
        double r83560 = t;
        double r83561 = r83559 * r83560;
        double r83562 = r83561 + r83541;
        double r83563 = r83558 + r83562;
        double r83564 = exp(r83563);
        double r83565 = r83553 / r83564;
        double r83566 = r83548 * r83565;
        double r83567 = r83566 / r83554;
        double r83568 = cbrt(r83549);
        double r83569 = r83568 * r83568;
        double r83570 = sqrt(r83550);
        double r83571 = r83569 / r83570;
        double r83572 = pow(r83571, r83552);
        double r83573 = exp(r83562);
        double r83574 = r83572 / r83573;
        double r83575 = r83568 / r83570;
        double r83576 = pow(r83575, r83552);
        double r83577 = pow(r83556, r83554);
        double r83578 = r83576 / r83577;
        double r83579 = r83578 / r83554;
        double r83580 = r83574 * r83579;
        double r83581 = r83548 * r83580;
        double r83582 = r83547 ? r83567 : r83581;
        return r83582;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if b < -4.5635779643842805e-228 or 1.2486298280538037e-238 < b

    1. Initial program 1.7

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

    2. Taylor expanded around inf 1.7

      \[\leadsto \frac{x \cdot \color{blue}{e^{1 \cdot \log \left(\frac{1}{a}\right) - \left(y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)\right)}}}{y}\]

    3. Simplified1.1

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}\]

    if -4.5635779643842805e-228 < b < 1.2486298280538037e-238

    1. Initial program 3.8

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

    2. Taylor expanded around inf 3.8

      \[\leadsto \frac{x \cdot \color{blue}{e^{1 \cdot \log \left(\frac{1}{a}\right) - \left(y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)\right)}}}{y}\]

    3. Simplified2.5

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity2.5

      \[\leadsto \frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\color{blue}{1 \cdot y}}\]

    6. Applied times-frac2.8

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}}\]

    7. Simplified2.8

      \[\leadsto \color{blue}{x} \cdot \frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\]

    8. Simplified9.8

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b} \cdot {\left(\frac{1}{z}\right)}^{y}}}{y}}\]
    9. Using strategy rm

    10. Applied *-un-lft-identity9.8

      \[\leadsto x \cdot \frac{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b} \cdot {\left(\frac{1}{z}\right)}^{y}}}{\color{blue}{1 \cdot y}}\]

    11. Applied add-sqr-sqrt9.8

      \[\leadsto x \cdot \frac{\frac{{\left(\frac{1}{\color{blue}{\sqrt{a} \cdot \sqrt{a}}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b} \cdot {\left(\frac{1}{z}\right)}^{y}}}{1 \cdot y}\]

    12. Applied add-cube-cbrt9.8

      \[\leadsto x \cdot \frac{\frac{{\left(\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\sqrt{a} \cdot \sqrt{a}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b} \cdot {\left(\frac{1}{z}\right)}^{y}}}{1 \cdot y}\]

    13. Applied times-frac9.9

      \[\leadsto x \cdot \frac{\frac{{\color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}} \cdot \frac{\sqrt[3]{1}}{\sqrt{a}}\right)}}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b} \cdot {\left(\frac{1}{z}\right)}^{y}}}{1 \cdot y}\]

    14. Applied unpow-prod-down9.9

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}}\right)}^{1} \cdot {\left(\frac{\sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b} \cdot {\left(\frac{1}{z}\right)}^{y}}}{1 \cdot y}\]

    15. Applied times-frac9.9

      \[\leadsto x \cdot \frac{\color{blue}{\frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b}} \cdot \frac{{\left(\frac{\sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}}}}{1 \cdot y}\]

    16. Applied times-frac11.5

      \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b}}}{1} \cdot \frac{\frac{{\left(\frac{\sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}}}{y}\right)}\]

    17. Simplified11.5

      \[\leadsto x \cdot \left(\color{blue}{\frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b}}} \cdot \frac{\frac{{\left(\frac{\sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}}}{y}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.56357796438428046 \cdot 10^{-228} \lor \neg \left(b \le 1.2486298280538037 \cdot 10^{-238}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{e^{\log \left(\frac{1}{a}\right) \cdot t + b}} \cdot \frac{\frac{{\left(\frac{\sqrt[3]{1}}{\sqrt{a}}\right)}^{1}}{{\left(\frac{1}{z}\right)}^{y}}}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))