Average Error: 3.7 → 2.5
Time: 8.8s
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 r78940 = x;
        double r78941 = y;
        double r78942 = 2.0;
        double r78943 = z;
        double r78944 = t;
        double r78945 = a;
        double r78946 = r78944 + r78945;
        double r78947 = sqrt(r78946);
        double r78948 = r78943 * r78947;
        double r78949 = r78948 / r78944;
        double r78950 = b;
        double r78951 = c;
        double r78952 = r78950 - r78951;
        double r78953 = 5.0;
        double r78954 = 6.0;
        double r78955 = r78953 / r78954;
        double r78956 = r78945 + r78955;
        double r78957 = 3.0;
        double r78958 = r78944 * r78957;
        double r78959 = r78942 / r78958;
        double r78960 = r78956 - r78959;
        double r78961 = r78952 * r78960;
        double r78962 = r78949 - r78961;
        double r78963 = r78942 * r78962;
        double r78964 = exp(r78963);
        double r78965 = r78941 * r78964;
        double r78966 = r78940 + r78965;
        double r78967 = r78940 / r78966;
        return r78967;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r78968 = x;
        double r78969 = y;
        double r78970 = 2.0;
        double r78971 = z;
        double r78972 = t;
        double r78973 = cbrt(r78972);
        double r78974 = r78973 * r78973;
        double r78975 = r78971 / r78974;
        double r78976 = a;
        double r78977 = r78972 + r78976;
        double r78978 = sqrt(r78977);
        double r78979 = r78978 / r78973;
        double r78980 = r78975 * r78979;
        double r78981 = b;
        double r78982 = c;
        double r78983 = r78981 - r78982;
        double r78984 = 5.0;
        double r78985 = 6.0;
        double r78986 = r78984 / r78985;
        double r78987 = r78976 + r78986;
        double r78988 = 3.0;
        double r78989 = r78972 * r78988;
        double r78990 = r78970 / r78989;
        double r78991 = r78987 - r78990;
        double r78992 = r78983 * r78991;
        double r78993 = r78980 - r78992;
        double r78994 = r78970 * r78993;
        double r78995 = exp(r78994);
        double r78996 = r78969 * r78995;
        double r78997 = r78968 + r78996;
        double r78998 = r78968 / r78997;
        return r78998;
}

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 2020064 
(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)))))))))))