Average Error: 1.8 → 1.9
Time: 57.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\sqrt[3]{\frac{x \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)\right)}{y}}\right) \cdot \sqrt[3]{\frac{\left(\sqrt[3]{{\left(e^{\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)\right) \cdot x}{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\left(\sqrt[3]{\frac{x \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)\right)}{y}}\right) \cdot \sqrt[3]{\frac{\left(\sqrt[3]{{\left(e^{\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b} \cdot \sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)}^{\left(\sqrt[3]{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}\right)}} \cdot \left(\sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}\right)\right) \cdot x}{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3824707 = x;
        double r3824708 = y;
        double r3824709 = z;
        double r3824710 = log(r3824709);
        double r3824711 = r3824708 * r3824710;
        double r3824712 = t;
        double r3824713 = 1.0;
        double r3824714 = r3824712 - r3824713;
        double r3824715 = a;
        double r3824716 = log(r3824715);
        double r3824717 = r3824714 * r3824716;
        double r3824718 = r3824711 + r3824717;
        double r3824719 = b;
        double r3824720 = r3824718 - r3824719;
        double r3824721 = exp(r3824720);
        double r3824722 = r3824707 * r3824721;
        double r3824723 = r3824722 / r3824708;
        return r3824723;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3824724 = x;
        double r3824725 = a;
        double r3824726 = log(r3824725);
        double r3824727 = t;
        double r3824728 = 1.0;
        double r3824729 = r3824727 - r3824728;
        double r3824730 = r3824726 * r3824729;
        double r3824731 = z;
        double r3824732 = log(r3824731);
        double r3824733 = y;
        double r3824734 = r3824732 * r3824733;
        double r3824735 = r3824730 + r3824734;
        double r3824736 = b;
        double r3824737 = r3824735 - r3824736;
        double r3824738 = exp(r3824737);
        double r3824739 = cbrt(r3824738);
        double r3824740 = r3824739 * r3824739;
        double r3824741 = r3824739 * r3824740;
        double r3824742 = r3824724 * r3824741;
        double r3824743 = r3824742 / r3824733;
        double r3824744 = cbrt(r3824743);
        double r3824745 = r3824744 * r3824744;
        double r3824746 = cbrt(r3824737);
        double r3824747 = r3824746 * r3824746;
        double r3824748 = exp(r3824747);
        double r3824749 = pow(r3824748, r3824746);
        double r3824750 = cbrt(r3824749);
        double r3824751 = r3824750 * r3824740;
        double r3824752 = r3824751 * r3824724;
        double r3824753 = r3824752 / r3824733;
        double r3824754 = cbrt(r3824753);
        double r3824755 = r3824745 * r3824754;
        return r3824755;
}

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 1.8

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

  3. Applied add-cube-cbrt1.8

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

  5. Applied add-cube-cbrt1.8

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

  7. Applied add-cube-cbrt1.9

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

  8. Applied exp-prod1.9

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

  9. Final simplification1.9

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

Reproduce

herbie shell --seed 2019144 
(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))