Average Error: 1.9 → 1.0
Time: 42.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}}}{\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)}{\sqrt{{e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{x}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}}}{\frac{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)}{\sqrt{{e}^{\left(\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b\right)}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r3873592 = x;
        double r3873593 = y;
        double r3873594 = z;
        double r3873595 = log(r3873594);
        double r3873596 = r3873593 * r3873595;
        double r3873597 = t;
        double r3873598 = 1.0;
        double r3873599 = r3873597 - r3873598;
        double r3873600 = a;
        double r3873601 = log(r3873600);
        double r3873602 = r3873599 * r3873601;
        double r3873603 = r3873596 + r3873602;
        double r3873604 = b;
        double r3873605 = r3873603 - r3873604;
        double r3873606 = exp(r3873605);
        double r3873607 = r3873592 * r3873606;
        double r3873608 = r3873607 / r3873593;
        return r3873608;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r3873609 = x;
        double r3873610 = y;
        double r3873611 = cbrt(r3873610);
        double r3873612 = r3873611 * r3873611;
        double r3873613 = a;
        double r3873614 = log(r3873613);
        double r3873615 = t;
        double r3873616 = 1.0;
        double r3873617 = r3873615 - r3873616;
        double r3873618 = r3873614 * r3873617;
        double r3873619 = z;
        double r3873620 = log(r3873619);
        double r3873621 = r3873620 * r3873610;
        double r3873622 = r3873618 + r3873621;
        double r3873623 = b;
        double r3873624 = r3873622 - r3873623;
        double r3873625 = exp(r3873624);
        double r3873626 = sqrt(r3873625);
        double r3873627 = r3873612 / r3873626;
        double r3873628 = r3873609 / r3873627;
        double r3873629 = cbrt(r3873611);
        double r3873630 = r3873629 * r3873629;
        double r3873631 = r3873629 * r3873630;
        double r3873632 = exp(1.0);
        double r3873633 = pow(r3873632, r3873624);
        double r3873634 = sqrt(r3873633);
        double r3873635 = r3873631 / r3873634;
        double r3873636 = r3873628 / r3873635;
        return r3873636;
}

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

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

  3. Applied associate-/l*2.0

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

  5. Applied add-sqr-sqrt2.0

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

  6. Applied add-cube-cbrt2.0

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

  7. Applied times-frac2.0

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

  8. Applied associate-/r*1.0

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

  10. Applied *-un-lft-identity1.0

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

  11. Applied exp-prod1.0

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

  12. Simplified1.0

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

  14. Applied add-cube-cbrt1.0

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

  15. Final simplification1.0

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

Reproduce

herbie shell --seed 2019169 
(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))