Average Error: 4.2 → 3.0
Time: 8.8s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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^{2 \cdot \left(\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)}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r88829 = x;
        double r88830 = y;
        double r88831 = 2.0;
        double r88832 = z;
        double r88833 = t;
        double r88834 = a;
        double r88835 = r88833 + r88834;
        double r88836 = sqrt(r88835);
        double r88837 = r88832 * r88836;
        double r88838 = r88837 / r88833;
        double r88839 = b;
        double r88840 = c;
        double r88841 = r88839 - r88840;
        double r88842 = 5.0;
        double r88843 = 6.0;
        double r88844 = r88842 / r88843;
        double r88845 = r88834 + r88844;
        double r88846 = 3.0;
        double r88847 = r88833 * r88846;
        double r88848 = r88831 / r88847;
        double r88849 = r88845 - r88848;
        double r88850 = r88841 * r88849;
        double r88851 = r88838 - r88850;
        double r88852 = r88831 * r88851;
        double r88853 = exp(r88852);
        double r88854 = r88830 * r88853;
        double r88855 = r88829 + r88854;
        double r88856 = r88829 / r88855;
        return r88856;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r88857 = x;
        double r88858 = y;
        double r88859 = 2.0;
        double r88860 = z;
        double r88861 = t;
        double r88862 = cbrt(r88861);
        double r88863 = r88862 * r88862;
        double r88864 = r88860 / r88863;
        double r88865 = a;
        double r88866 = r88861 + r88865;
        double r88867 = sqrt(r88866);
        double r88868 = r88867 / r88862;
        double r88869 = r88864 * r88868;
        double r88870 = b;
        double r88871 = c;
        double r88872 = r88870 - r88871;
        double r88873 = 5.0;
        double r88874 = 6.0;
        double r88875 = r88873 / r88874;
        double r88876 = r88865 + r88875;
        double r88877 = 3.0;
        double r88878 = r88861 * r88877;
        double r88879 = r88859 / r88878;
        double r88880 = r88876 - r88879;
        double r88881 = r88872 * r88880;
        double r88882 = r88869 - r88881;
        double r88883 = r88859 * r88882;
        double r88884 = exp(r88883);
        double r88885 = r88858 * r88884;
        double r88886 = r88857 + r88885;
        double r88887 = r88857 / r88886;
        return r88887;
}

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 4.2

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

  3. Applied add-cube-cbrt4.2

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

  4. Applied times-frac3.0

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

  5. Final simplification3.0

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))