Average Error: 1.9 → 1.0
Time: 38.9s
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 r18573781 = x;
        double r18573782 = y;
        double r18573783 = z;
        double r18573784 = log(r18573783);
        double r18573785 = r18573782 * r18573784;
        double r18573786 = t;
        double r18573787 = 1.0;
        double r18573788 = r18573786 - r18573787;
        double r18573789 = a;
        double r18573790 = log(r18573789);
        double r18573791 = r18573788 * r18573790;
        double r18573792 = r18573785 + r18573791;
        double r18573793 = b;
        double r18573794 = r18573792 - r18573793;
        double r18573795 = exp(r18573794);
        double r18573796 = r18573781 * r18573795;
        double r18573797 = r18573796 / r18573782;
        return r18573797;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r18573798 = x;
        double r18573799 = y;
        double r18573800 = cbrt(r18573799);
        double r18573801 = r18573800 * r18573800;
        double r18573802 = a;
        double r18573803 = log(r18573802);
        double r18573804 = t;
        double r18573805 = 1.0;
        double r18573806 = r18573804 - r18573805;
        double r18573807 = r18573803 * r18573806;
        double r18573808 = z;
        double r18573809 = log(r18573808);
        double r18573810 = r18573809 * r18573799;
        double r18573811 = r18573807 + r18573810;
        double r18573812 = b;
        double r18573813 = r18573811 - r18573812;
        double r18573814 = exp(r18573813);
        double r18573815 = sqrt(r18573814);
        double r18573816 = r18573801 / r18573815;
        double r18573817 = r18573798 / r18573816;
        double r18573818 = cbrt(r18573800);
        double r18573819 = r18573818 * r18573818;
        double r18573820 = r18573818 * r18573819;
        double r18573821 = exp(1.0);
        double r18573822 = pow(r18573821, r18573813);
        double r18573823 = sqrt(r18573822);
        double r18573824 = r18573820 / r18573823;
        double r18573825 = r18573817 / r18573824;
        return r18573825;
}

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

Target

Original1.9
Target10.9
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

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, A"

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))