Average Error: 4.0 → 2.8
Time: 31.0s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}
↓
\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3950840 = x;
        double r3950841 = y;
        double r3950842 = 2.0;
        double r3950843 = z;
        double r3950844 = t;
        double r3950845 = a;
        double r3950846 = r3950844 + r3950845;
        double r3950847 = sqrt(r3950846);
        double r3950848 = r3950843 * r3950847;
        double r3950849 = r3950848 / r3950844;
        double r3950850 = b;
        double r3950851 = c;
        double r3950852 = r3950850 - r3950851;
        double r3950853 = 5.0;
        double r3950854 = 6.0;
        double r3950855 = r3950853 / r3950854;
        double r3950856 = r3950845 + r3950855;
        double r3950857 = 3.0;
        double r3950858 = r3950844 * r3950857;
        double r3950859 = r3950842 / r3950858;
        double r3950860 = r3950856 - r3950859;
        double r3950861 = r3950852 * r3950860;
        double r3950862 = r3950849 - r3950861;
        double r3950863 = r3950842 * r3950862;
        double r3950864 = exp(r3950863);
        double r3950865 = r3950841 * r3950864;
        double r3950866 = r3950840 + r3950865;
        double r3950867 = r3950840 / r3950866;
        return r3950867;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3950868 = x;
        double r3950869 = y;
        double r3950870 = a;
        double r3950871 = t;
        double r3950872 = r3950870 + r3950871;
        double r3950873 = sqrt(r3950872);
        double r3950874 = cbrt(r3950871);
        double r3950875 = r3950873 / r3950874;
        double r3950876 = z;
        double r3950877 = r3950874 * r3950874;
        double r3950878 = r3950876 / r3950877;
        double r3950879 = r3950875 * r3950878;
        double r3950880 = 5.0;
        double r3950881 = 6.0;
        double r3950882 = r3950880 / r3950881;
        double r3950883 = r3950870 + r3950882;
        double r3950884 = 2.0;
        double r3950885 = 3.0;
        double r3950886 = r3950871 * r3950885;
        double r3950887 = r3950884 / r3950886;
        double r3950888 = r3950883 - r3950887;
        double r3950889 = b;
        double r3950890 = c;
        double r3950891 = r3950889 - r3950890;
        double r3950892 = r3950888 * r3950891;
        double r3950893 = r3950879 - r3950892;
        double r3950894 = r3950893 * r3950884;
        double r3950895 = exp(r3950894);
        double r3950896 = r3950869 * r3950895;
        double r3950897 = r3950868 + r3950896;
        double r3950898 = r3950868 / r3950897;
        return r3950898;
}

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

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.0

    \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt4.0

    \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

  4. Applied times-frac2.8

    \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

  5. Final simplification2.8

    \[\leadsto \frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))