Average Error: 3.8 → 2.8
Time: 45.3s
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 r124888 = x;
        double r124889 = y;
        double r124890 = 2.0;
        double r124891 = z;
        double r124892 = t;
        double r124893 = a;
        double r124894 = r124892 + r124893;
        double r124895 = sqrt(r124894);
        double r124896 = r124891 * r124895;
        double r124897 = r124896 / r124892;
        double r124898 = b;
        double r124899 = c;
        double r124900 = r124898 - r124899;
        double r124901 = 5.0;
        double r124902 = 6.0;
        double r124903 = r124901 / r124902;
        double r124904 = r124893 + r124903;
        double r124905 = 3.0;
        double r124906 = r124892 * r124905;
        double r124907 = r124890 / r124906;
        double r124908 = r124904 - r124907;
        double r124909 = r124900 * r124908;
        double r124910 = r124897 - r124909;
        double r124911 = r124890 * r124910;
        double r124912 = exp(r124911);
        double r124913 = r124889 * r124912;
        double r124914 = r124888 + r124913;
        double r124915 = r124888 / r124914;
        return r124915;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r124916 = x;
        double r124917 = y;
        double r124918 = 2.0;
        double r124919 = z;
        double r124920 = t;
        double r124921 = cbrt(r124920);
        double r124922 = r124921 * r124921;
        double r124923 = r124919 / r124922;
        double r124924 = a;
        double r124925 = r124920 + r124924;
        double r124926 = sqrt(r124925);
        double r124927 = r124926 / r124921;
        double r124928 = r124923 * r124927;
        double r124929 = b;
        double r124930 = c;
        double r124931 = r124929 - r124930;
        double r124932 = 5.0;
        double r124933 = 6.0;
        double r124934 = r124932 / r124933;
        double r124935 = r124924 + r124934;
        double r124936 = 3.0;
        double r124937 = r124920 * r124936;
        double r124938 = r124918 / r124937;
        double r124939 = r124935 - r124938;
        double r124940 = r124931 * r124939;
        double r124941 = r124928 - r124940;
        double r124942 = r124918 * r124941;
        double r124943 = exp(r124942);
        double r124944 = r124917 * r124943;
        double r124945 = r124916 + r124944;
        double r124946 = r124916 / r124945;
        return r124946;
}

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. Using strategy rm

  3. Applied add-cube-cbrt3.8

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

  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

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

Reproduce

herbie shell --seed 2019298 
(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)))))))))))