Average Error: 1.8 → 1.8
Time: 53.9s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\left(\sqrt[3]{\frac{x \cdot \left(\sqrt{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{\left(\sqrt{{\left(\sqrt{e}\right)}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot x}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot \left(\sqrt{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}}\]
\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{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}} \cdot \sqrt[3]{\frac{\left(\sqrt{{\left(\sqrt{e}\right)}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot {\left(\sqrt{e}\right)}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right) \cdot x}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot \left(\sqrt{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)}} \cdot \sqrt{e^{\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r2231711 = x;
        double r2231712 = y;
        double r2231713 = z;
        double r2231714 = log(r2231713);
        double r2231715 = r2231712 * r2231714;
        double r2231716 = t;
        double r2231717 = 1.0;
        double r2231718 = r2231716 - r2231717;
        double r2231719 = a;
        double r2231720 = log(r2231719);
        double r2231721 = r2231718 * r2231720;
        double r2231722 = r2231715 + r2231721;
        double r2231723 = b;
        double r2231724 = r2231722 - r2231723;
        double r2231725 = exp(r2231724);
        double r2231726 = r2231711 * r2231725;
        double r2231727 = r2231726 / r2231712;
        return r2231727;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r2231728 = x;
        double r2231729 = exp(1.0);
        double r2231730 = z;
        double r2231731 = log(r2231730);
        double r2231732 = y;
        double r2231733 = r2231731 * r2231732;
        double r2231734 = t;
        double r2231735 = 1.0;
        double r2231736 = r2231734 - r2231735;
        double r2231737 = a;
        double r2231738 = log(r2231737);
        double r2231739 = r2231736 * r2231738;
        double r2231740 = r2231733 + r2231739;
        double r2231741 = b;
        double r2231742 = r2231740 - r2231741;
        double r2231743 = pow(r2231729, r2231742);
        double r2231744 = sqrt(r2231743);
        double r2231745 = exp(r2231742);
        double r2231746 = sqrt(r2231745);
        double r2231747 = r2231744 * r2231746;
        double r2231748 = r2231728 * r2231747;
        double r2231749 = r2231748 / r2231732;
        double r2231750 = cbrt(r2231749);
        double r2231751 = sqrt(r2231729);
        double r2231752 = pow(r2231751, r2231742);
        double r2231753 = r2231752 * r2231752;
        double r2231754 = sqrt(r2231753);
        double r2231755 = r2231754 * r2231746;
        double r2231756 = r2231755 * r2231728;
        double r2231757 = r2231756 / r2231732;
        double r2231758 = cbrt(r2231757);
        double r2231759 = r2231750 * r2231758;
        double r2231760 = r2231759 * r2231750;
        return r2231760;
}

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-sqr-sqrt1.8

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

  5. Applied *-un-lft-identity1.8

    \[\leadsto \frac{x \cdot \left(\sqrt{e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}\]

  6. Applied exp-prod1.8

    \[\leadsto \frac{x \cdot \left(\sqrt{\color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}\]

  7. Simplified1.8

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

  9. Applied add-cube-cbrt1.8

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

  11. Applied add-sqr-sqrt1.8

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

  12. Applied unpow-prod-down1.8

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

  13. Final simplification1.8

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

Reproduce

herbie shell --seed 2019130 +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))