Average Error: 1.9 → 2.0
Time: 1.1m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{\sqrt[3]{y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right)\right)\right)}}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{{e}^{\left(\left(\log z \cdot y + \left(t - 1.0\right) \cdot \log a\right) - b\right)} \cdot x}{\sqrt[3]{y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}}}\right)\right)\right)}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r8583594 = x;
        double r8583595 = y;
        double r8583596 = z;
        double r8583597 = log(r8583596);
        double r8583598 = r8583595 * r8583597;
        double r8583599 = t;
        double r8583600 = 1.0;
        double r8583601 = r8583599 - r8583600;
        double r8583602 = a;
        double r8583603 = log(r8583602);
        double r8583604 = r8583601 * r8583603;
        double r8583605 = r8583598 + r8583604;
        double r8583606 = b;
        double r8583607 = r8583605 - r8583606;
        double r8583608 = exp(r8583607);
        double r8583609 = r8583594 * r8583608;
        double r8583610 = r8583609 / r8583595;
        return r8583610;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r8583611 = exp(1.0);
        double r8583612 = z;
        double r8583613 = log(r8583612);
        double r8583614 = y;
        double r8583615 = r8583613 * r8583614;
        double r8583616 = t;
        double r8583617 = 1.0;
        double r8583618 = r8583616 - r8583617;
        double r8583619 = a;
        double r8583620 = log(r8583619);
        double r8583621 = r8583618 * r8583620;
        double r8583622 = r8583615 + r8583621;
        double r8583623 = b;
        double r8583624 = r8583622 - r8583623;
        double r8583625 = pow(r8583611, r8583624);
        double r8583626 = x;
        double r8583627 = r8583625 * r8583626;
        double r8583628 = cbrt(r8583614);
        double r8583629 = cbrt(r8583628);
        double r8583630 = r8583629 * r8583629;
        double r8583631 = cbrt(r8583629);
        double r8583632 = r8583631 * r8583631;
        double r8583633 = r8583631 * r8583632;
        double r8583634 = r8583630 * r8583633;
        double r8583635 = r8583628 * r8583634;
        double r8583636 = r8583627 / r8583635;
        double r8583637 = r8583636 / r8583628;
        return r8583637;
}

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 *-un-lft-identity1.9

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

  4. Applied exp-prod2.0

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

  5. Simplified2.0

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

  7. Applied add-cube-cbrt2.0

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

  8. Applied associate-/r*2.0

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

  10. Applied add-cube-cbrt2.0

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

  12. Applied add-cube-cbrt2.0

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

  13. Final simplification2.0

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

Reproduce

herbie shell --seed 2019104 
(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))