Average Error: 1.9 → 1.9
Time: 1.0m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r4541631 = x;
        double r4541632 = y;
        double r4541633 = z;
        double r4541634 = log(r4541633);
        double r4541635 = r4541632 * r4541634;
        double r4541636 = t;
        double r4541637 = 1.0;
        double r4541638 = r4541636 - r4541637;
        double r4541639 = a;
        double r4541640 = log(r4541639);
        double r4541641 = r4541638 * r4541640;
        double r4541642 = r4541635 + r4541641;
        double r4541643 = b;
        double r4541644 = r4541642 - r4541643;
        double r4541645 = exp(r4541644);
        double r4541646 = r4541631 * r4541645;
        double r4541647 = r4541646 / r4541632;
        return r4541647;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r4541648 = x;
        double r4541649 = z;
        double r4541650 = cbrt(r4541649);
        double r4541651 = log(r4541650);
        double r4541652 = y;
        double r4541653 = r4541651 * r4541652;
        double r4541654 = r4541652 + r4541652;
        double r4541655 = r4541651 * r4541654;
        double r4541656 = r4541653 + r4541655;
        double r4541657 = t;
        double r4541658 = 1.0;
        double r4541659 = r4541657 - r4541658;
        double r4541660 = a;
        double r4541661 = log(r4541660);
        double r4541662 = r4541659 * r4541661;
        double r4541663 = r4541656 + r4541662;
        double r4541664 = b;
        double r4541665 = r4541663 - r4541664;
        double r4541666 = exp(r4541665);
        double r4541667 = r4541648 * r4541666;
        double r4541668 = cbrt(r4541652);
        double r4541669 = r4541668 * r4541668;
        double r4541670 = r4541667 / r4541669;
        double r4541671 = r4541670 / r4541668;
        double r4541672 = cbrt(r4541671);
        double r4541673 = r4541667 / r4541652;
        double r4541674 = cbrt(r4541673);
        double r4541675 = r4541672 * r4541674;
        double r4541676 = r4541672 * r4541675;
        return r4541676;
}

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. Initial program 1.9

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.9

    \[\leadsto \frac{x \cdot e^{\left(y \cdot \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]

  4. Applied log-prod1.9

    \[\leadsto \frac{x \cdot e^{\left(y \cdot \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)} + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]

  5. Applied distribute-lft-in1.9

    \[\leadsto \frac{x \cdot e^{\left(\color{blue}{\left(y \cdot \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)} + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]

  6. Simplified1.9

    \[\leadsto \frac{x \cdot e^{\left(\left(\color{blue}{\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)} + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt1.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt1.9

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}}\]

  11. Applied associate-/r*1.9

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\color{blue}{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt1.9

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}\]

  14. Applied associate-/r*1.9

    \[\leadsto \left(\sqrt[3]{\color{blue}{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}\]

  15. Final simplification1.9

    \[\leadsto \sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\frac{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\left(\log \left(\sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \left(y + y\right)\right) + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right)\]

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))