Average Error: 3.9 → 3.2
Time: 29.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{e^{2.0 \cdot \log \left(e^{\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(b - c\right) \cdot \left(\left(a - \frac{\frac{2.0}{t}}{3.0}\right) + \frac{5.0}{6.0}\right)}\right)} \cdot y + x}\]
\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}
↓
\frac{x}{e^{2.0 \cdot \log \left(e^{\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(b - c\right) \cdot \left(\left(a - \frac{\frac{2.0}{t}}{3.0}\right) + \frac{5.0}{6.0}\right)}\right)} \cdot y + x}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3977877 = x;
        double r3977878 = y;
        double r3977879 = 2.0;
        double r3977880 = z;
        double r3977881 = t;
        double r3977882 = a;
        double r3977883 = r3977881 + r3977882;
        double r3977884 = sqrt(r3977883);
        double r3977885 = r3977880 * r3977884;
        double r3977886 = r3977885 / r3977881;
        double r3977887 = b;
        double r3977888 = c;
        double r3977889 = r3977887 - r3977888;
        double r3977890 = 5.0;
        double r3977891 = 6.0;
        double r3977892 = r3977890 / r3977891;
        double r3977893 = r3977882 + r3977892;
        double r3977894 = 3.0;
        double r3977895 = r3977881 * r3977894;
        double r3977896 = r3977879 / r3977895;
        double r3977897 = r3977893 - r3977896;
        double r3977898 = r3977889 * r3977897;
        double r3977899 = r3977886 - r3977898;
        double r3977900 = r3977879 * r3977899;
        double r3977901 = exp(r3977900);
        double r3977902 = r3977878 * r3977901;
        double r3977903 = r3977877 + r3977902;
        double r3977904 = r3977877 / r3977903;
        return r3977904;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3977905 = x;
        double r3977906 = 2.0;
        double r3977907 = z;
        double r3977908 = t;
        double r3977909 = a;
        double r3977910 = r3977909 + r3977908;
        double r3977911 = sqrt(r3977910);
        double r3977912 = r3977908 / r3977911;
        double r3977913 = r3977907 / r3977912;
        double r3977914 = b;
        double r3977915 = c;
        double r3977916 = r3977914 - r3977915;
        double r3977917 = r3977906 / r3977908;
        double r3977918 = 3.0;
        double r3977919 = r3977917 / r3977918;
        double r3977920 = r3977909 - r3977919;
        double r3977921 = 5.0;
        double r3977922 = 6.0;
        double r3977923 = r3977921 / r3977922;
        double r3977924 = r3977920 + r3977923;
        double r3977925 = r3977916 * r3977924;
        double r3977926 = r3977913 - r3977925;
        double r3977927 = exp(r3977926);
        double r3977928 = log(r3977927);
        double r3977929 = r3977906 * r3977928;
        double r3977930 = exp(r3977929);
        double r3977931 = y;
        double r3977932 = r3977930 * r3977931;
        double r3977933 = r3977932 + r3977905;
        double r3977934 = r3977905 / r3977933;
        return r3977934;
}

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 3.9

    \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
  2. Using strategy rm

  3. Applied add-log-exp8.4

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}\right)}}\]

  4. Applied add-log-exp16.7

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\log \left(e^{\frac{z \cdot \sqrt{t + a}}{t}}\right)} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)\right)}}\]

  5. Applied diff-log16.7

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}}\right)}}}\]

  6. Simplified3.2

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \log \color{blue}{\left(e^{\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)}\right)}}}\]

  7. Final simplification3.2

    \[\leadsto \frac{x}{e^{2.0 \cdot \log \left(e^{\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(b - c\right) \cdot \left(\left(a - \frac{\frac{2.0}{t}}{3.0}\right) + \frac{5.0}{6.0}\right)}\right)} \cdot y + x}\]

Reproduce

herbie shell --seed 2019165 
(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)))))))))))