Average Error: 1.7 → 1.7
Time: 43.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)\right)\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}\right)} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}} \cdot \sqrt[3]{\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}{y}}}\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r3541636 = x;
        double r3541637 = y;
        double r3541638 = z;
        double r3541639 = log(r3541638);
        double r3541640 = r3541637 * r3541639;
        double r3541641 = t;
        double r3541642 = 1.0;
        double r3541643 = r3541641 - r3541642;
        double r3541644 = a;
        double r3541645 = log(r3541644);
        double r3541646 = r3541643 * r3541645;
        double r3541647 = r3541640 + r3541646;
        double r3541648 = b;
        double r3541649 = r3541647 - r3541648;
        double r3541650 = exp(r3541649);
        double r3541651 = r3541636 * r3541650;
        double r3541652 = r3541651 / r3541637;
        return r3541652;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3541653 = x;
        double r3541654 = exp(1.0);
        double r3541655 = a;
        double r3541656 = log(r3541655);
        double r3541657 = t;
        double r3541658 = 1.0;
        double r3541659 = r3541657 - r3541658;
        double r3541660 = r3541656 * r3541659;
        double r3541661 = z;
        double r3541662 = log(r3541661);
        double r3541663 = y;
        double r3541664 = r3541662 * r3541663;
        double r3541665 = r3541660 + r3541664;
        double r3541666 = b;
        double r3541667 = r3541665 - r3541666;
        double r3541668 = pow(r3541654, r3541667);
        double r3541669 = r3541653 * r3541668;
        double r3541670 = r3541669 / r3541663;
        double r3541671 = cbrt(r3541670);
        double r3541672 = exp(r3541667);
        double r3541673 = r3541653 * r3541672;
        double r3541674 = r3541673 / r3541663;
        double r3541675 = cbrt(r3541674);
        double r3541676 = r3541675 * r3541675;
        double r3541677 = r3541675 * r3541676;
        double r3541678 = cbrt(r3541677);
        double r3541679 = cbrt(r3541675);
        double r3541680 = r3541679 * r3541679;
        double r3541681 = r3541679 * r3541680;
        double r3541682 = r3541678 * r3541681;
        double r3541683 = r3541671 * r3541682;
        return r3541683;
}

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 1.7

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

  3. Applied add-cube-cbrt1.7

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

  5. Applied *-un-lft-identity1.7

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

  6. Applied exp-prod1.7

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

  7. Simplified1.7

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

  9. Applied add-cube-cbrt1.7

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

  11. Applied add-cbrt-cube1.7

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

  12. Final simplification1.7

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

Reproduce

herbie shell --seed 2019172 +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))