Average Error: 3.8 → 2.6
Time: 43.0s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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 r137747 = x;
        double r137748 = y;
        double r137749 = 2.0;
        double r137750 = z;
        double r137751 = t;
        double r137752 = a;
        double r137753 = r137751 + r137752;
        double r137754 = sqrt(r137753);
        double r137755 = r137750 * r137754;
        double r137756 = r137755 / r137751;
        double r137757 = b;
        double r137758 = c;
        double r137759 = r137757 - r137758;
        double r137760 = 5.0;
        double r137761 = 6.0;
        double r137762 = r137760 / r137761;
        double r137763 = r137752 + r137762;
        double r137764 = 3.0;
        double r137765 = r137751 * r137764;
        double r137766 = r137749 / r137765;
        double r137767 = r137763 - r137766;
        double r137768 = r137759 * r137767;
        double r137769 = r137756 - r137768;
        double r137770 = r137749 * r137769;
        double r137771 = exp(r137770);
        double r137772 = r137748 * r137771;
        double r137773 = r137747 + r137772;
        double r137774 = r137747 / r137773;
        return r137774;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r137775 = x;
        double r137776 = y;
        double r137777 = 2.0;
        double r137778 = z;
        double r137779 = t;
        double r137780 = cbrt(r137779);
        double r137781 = r137780 * r137780;
        double r137782 = r137778 / r137781;
        double r137783 = a;
        double r137784 = r137779 + r137783;
        double r137785 = sqrt(r137784);
        double r137786 = r137785 / r137780;
        double r137787 = r137782 * r137786;
        double r137788 = b;
        double r137789 = c;
        double r137790 = r137788 - r137789;
        double r137791 = 5.0;
        double r137792 = 6.0;
        double r137793 = r137791 / r137792;
        double r137794 = r137783 + r137793;
        double r137795 = 3.0;
        double r137796 = r137779 * r137795;
        double r137797 = r137777 / r137796;
        double r137798 = r137794 - r137797;
        double r137799 = r137790 * r137798;
        double r137800 = r137787 - r137799;
        double r137801 = r137777 * r137800;
        double r137802 = exp(r137801);
        double r137803 = r137776 * r137802;
        double r137804 = r137775 + r137803;
        double r137805 = r137775 / r137804;
        return r137805;
}

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-frac2.6

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

  5. Final simplification2.6

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

Reproduce

herbie shell --seed 2019347 
(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)))))))))))