Average Error: 3.6 → 2.6
Time: 14.9s
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 r100811 = x;
        double r100812 = y;
        double r100813 = 2.0;
        double r100814 = z;
        double r100815 = t;
        double r100816 = a;
        double r100817 = r100815 + r100816;
        double r100818 = sqrt(r100817);
        double r100819 = r100814 * r100818;
        double r100820 = r100819 / r100815;
        double r100821 = b;
        double r100822 = c;
        double r100823 = r100821 - r100822;
        double r100824 = 5.0;
        double r100825 = 6.0;
        double r100826 = r100824 / r100825;
        double r100827 = r100816 + r100826;
        double r100828 = 3.0;
        double r100829 = r100815 * r100828;
        double r100830 = r100813 / r100829;
        double r100831 = r100827 - r100830;
        double r100832 = r100823 * r100831;
        double r100833 = r100820 - r100832;
        double r100834 = r100813 * r100833;
        double r100835 = exp(r100834);
        double r100836 = r100812 * r100835;
        double r100837 = r100811 + r100836;
        double r100838 = r100811 / r100837;
        return r100838;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r100839 = x;
        double r100840 = y;
        double r100841 = 2.0;
        double r100842 = z;
        double r100843 = t;
        double r100844 = cbrt(r100843);
        double r100845 = r100844 * r100844;
        double r100846 = r100842 / r100845;
        double r100847 = a;
        double r100848 = r100843 + r100847;
        double r100849 = sqrt(r100848);
        double r100850 = r100849 / r100844;
        double r100851 = r100846 * r100850;
        double r100852 = b;
        double r100853 = c;
        double r100854 = r100852 - r100853;
        double r100855 = 5.0;
        double r100856 = 6.0;
        double r100857 = r100855 / r100856;
        double r100858 = r100847 + r100857;
        double r100859 = 3.0;
        double r100860 = r100843 * r100859;
        double r100861 = r100841 / r100860;
        double r100862 = r100858 - r100861;
        double r100863 = r100854 * r100862;
        double r100864 = r100851 - r100863;
        double r100865 = r100841 * r100864;
        double r100866 = exp(r100865);
        double r100867 = r100840 * r100866;
        double r100868 = r100839 + r100867;
        double r100869 = r100839 / r100868;
        return r100869;
}

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 3.6

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

  3. Applied add-cube-cbrt3.6

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

  4. Applied times-frac2.6

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

  5. Final simplification2.6

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

Reproduce

herbie shell --seed 2020056 
(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)))))))))))