Average Error: 1.9 → 1.1
Time: 35.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)} \cdot \left(x \cdot \frac{\sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}} \cdot \sqrt[3]{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r21139130 = x;
        double r21139131 = y;
        double r21139132 = z;
        double r21139133 = log(r21139132);
        double r21139134 = r21139131 * r21139133;
        double r21139135 = t;
        double r21139136 = 1.0;
        double r21139137 = r21139135 - r21139136;
        double r21139138 = a;
        double r21139139 = log(r21139138);
        double r21139140 = r21139137 * r21139139;
        double r21139141 = r21139134 + r21139140;
        double r21139142 = b;
        double r21139143 = r21139141 - r21139142;
        double r21139144 = exp(r21139143);
        double r21139145 = r21139130 * r21139144;
        double r21139146 = r21139145 / r21139131;
        return r21139146;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r21139147 = a;
        double r21139148 = log(r21139147);
        double r21139149 = t;
        double r21139150 = 1.0;
        double r21139151 = r21139149 - r21139150;
        double r21139152 = r21139148 * r21139151;
        double r21139153 = z;
        double r21139154 = log(r21139153);
        double r21139155 = y;
        double r21139156 = r21139154 * r21139155;
        double r21139157 = r21139152 + r21139156;
        double r21139158 = b;
        double r21139159 = r21139157 - r21139158;
        double r21139160 = exp(r21139159);
        double r21139161 = cbrt(r21139160);
        double r21139162 = cbrt(r21139155);
        double r21139163 = cbrt(r21139162);
        double r21139164 = r21139163 * r21139163;
        double r21139165 = r21139163 * r21139164;
        double r21139166 = r21139161 / r21139165;
        double r21139167 = x;
        double r21139168 = r21139161 * r21139161;
        double r21139169 = r21139162 * r21139162;
        double r21139170 = r21139168 / r21139169;
        double r21139171 = r21139167 * r21139170;
        double r21139172 = r21139166 * r21139171;
        return r21139172;
}

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
Target11.2
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

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 *-un-lft-identity1.9

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

  4. Applied times-frac2.1

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

  5. Simplified2.1

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

  7. Applied add-cube-cbrt2.1

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

  8. Applied add-cube-cbrt2.1

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

  9. Applied times-frac2.1

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

  10. Applied associate-*r*1.1

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

  12. Applied add-cube-cbrt1.1

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

  13. Final simplification1.1

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

Reproduce

herbie shell --seed 2019192 
(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))