Average Error: 3.8 → 3.1
Time: 18.0s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{y \cdot e^{2 \cdot \left(\frac{\sqrt{t + a}}{t} \cdot z + \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right) \cdot \left(c - b\right)\right)} + x}\]
\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}{y \cdot e^{2 \cdot \left(\frac{\sqrt{t + a}}{t} \cdot z + \left(\left(a - \frac{\frac{2}{3}}{t}\right) + \frac{5}{6}\right) \cdot \left(c - b\right)\right)} + x}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r69819 = x;
        double r69820 = y;
        double r69821 = 2.0;
        double r69822 = z;
        double r69823 = t;
        double r69824 = a;
        double r69825 = r69823 + r69824;
        double r69826 = sqrt(r69825);
        double r69827 = r69822 * r69826;
        double r69828 = r69827 / r69823;
        double r69829 = b;
        double r69830 = c;
        double r69831 = r69829 - r69830;
        double r69832 = 5.0;
        double r69833 = 6.0;
        double r69834 = r69832 / r69833;
        double r69835 = r69824 + r69834;
        double r69836 = 3.0;
        double r69837 = r69823 * r69836;
        double r69838 = r69821 / r69837;
        double r69839 = r69835 - r69838;
        double r69840 = r69831 * r69839;
        double r69841 = r69828 - r69840;
        double r69842 = r69821 * r69841;
        double r69843 = exp(r69842);
        double r69844 = r69820 * r69843;
        double r69845 = r69819 + r69844;
        double r69846 = r69819 / r69845;
        return r69846;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r69847 = x;
        double r69848 = y;
        double r69849 = 2.0;
        double r69850 = t;
        double r69851 = a;
        double r69852 = r69850 + r69851;
        double r69853 = sqrt(r69852);
        double r69854 = r69853 / r69850;
        double r69855 = z;
        double r69856 = r69854 * r69855;
        double r69857 = 3.0;
        double r69858 = r69849 / r69857;
        double r69859 = r69858 / r69850;
        double r69860 = r69851 - r69859;
        double r69861 = 5.0;
        double r69862 = 6.0;
        double r69863 = r69861 / r69862;
        double r69864 = r69860 + r69863;
        double r69865 = c;
        double r69866 = b;
        double r69867 = r69865 - r69866;
        double r69868 = r69864 * r69867;
        double r69869 = r69856 + r69868;
        double r69870 = r69849 * r69869;
        double r69871 = exp(r69870);
        double r69872 = r69848 * r69871;
        double r69873 = r69872 + r69847;
        double r69874 = r69847 / r69873;
        return r69874;
}

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 3.8

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

  2. Simplified3.1

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

  3. Final simplification3.1

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

Reproduce

herbie shell --seed 2019195 
(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)))))))))))