Average Error: 3.7 → 2.5
Time: 9.6s
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 r71911 = x;
        double r71912 = y;
        double r71913 = 2.0;
        double r71914 = z;
        double r71915 = t;
        double r71916 = a;
        double r71917 = r71915 + r71916;
        double r71918 = sqrt(r71917);
        double r71919 = r71914 * r71918;
        double r71920 = r71919 / r71915;
        double r71921 = b;
        double r71922 = c;
        double r71923 = r71921 - r71922;
        double r71924 = 5.0;
        double r71925 = 6.0;
        double r71926 = r71924 / r71925;
        double r71927 = r71916 + r71926;
        double r71928 = 3.0;
        double r71929 = r71915 * r71928;
        double r71930 = r71913 / r71929;
        double r71931 = r71927 - r71930;
        double r71932 = r71923 * r71931;
        double r71933 = r71920 - r71932;
        double r71934 = r71913 * r71933;
        double r71935 = exp(r71934);
        double r71936 = r71912 * r71935;
        double r71937 = r71911 + r71936;
        double r71938 = r71911 / r71937;
        return r71938;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r71939 = x;
        double r71940 = y;
        double r71941 = 2.0;
        double r71942 = z;
        double r71943 = t;
        double r71944 = cbrt(r71943);
        double r71945 = r71944 * r71944;
        double r71946 = r71942 / r71945;
        double r71947 = a;
        double r71948 = r71943 + r71947;
        double r71949 = sqrt(r71948);
        double r71950 = r71949 / r71944;
        double r71951 = r71946 * r71950;
        double r71952 = b;
        double r71953 = c;
        double r71954 = r71952 - r71953;
        double r71955 = 5.0;
        double r71956 = 6.0;
        double r71957 = r71955 / r71956;
        double r71958 = r71947 + r71957;
        double r71959 = 3.0;
        double r71960 = r71943 * r71959;
        double r71961 = r71941 / r71960;
        double r71962 = r71958 - r71961;
        double r71963 = r71954 * r71962;
        double r71964 = r71951 - r71963;
        double r71965 = r71941 * r71964;
        double r71966 = exp(r71965);
        double r71967 = r71940 * r71966;
        double r71968 = r71939 + r71967;
        double r71969 = r71939 / r71968;
        return r71969;
}

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 3.7

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

  3. Applied add-cube-cbrt3.7

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

  4. Applied times-frac2.5

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

  5. Final simplification2.5

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

Reproduce

herbie shell --seed 2020081 
(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)))))))))))