Average Error: 3.9 → 2.7
Time: 27.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]
\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^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r2935739 = x;
        double r2935740 = y;
        double r2935741 = 2.0;
        double r2935742 = z;
        double r2935743 = t;
        double r2935744 = a;
        double r2935745 = r2935743 + r2935744;
        double r2935746 = sqrt(r2935745);
        double r2935747 = r2935742 * r2935746;
        double r2935748 = r2935747 / r2935743;
        double r2935749 = b;
        double r2935750 = c;
        double r2935751 = r2935749 - r2935750;
        double r2935752 = 5.0;
        double r2935753 = 6.0;
        double r2935754 = r2935752 / r2935753;
        double r2935755 = r2935744 + r2935754;
        double r2935756 = 3.0;
        double r2935757 = r2935743 * r2935756;
        double r2935758 = r2935741 / r2935757;
        double r2935759 = r2935755 - r2935758;
        double r2935760 = r2935751 * r2935759;
        double r2935761 = r2935748 - r2935760;
        double r2935762 = r2935741 * r2935761;
        double r2935763 = exp(r2935762);
        double r2935764 = r2935740 * r2935763;
        double r2935765 = r2935739 + r2935764;
        double r2935766 = r2935739 / r2935765;
        return r2935766;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r2935767 = x;
        double r2935768 = y;
        double r2935769 = a;
        double r2935770 = t;
        double r2935771 = r2935769 + r2935770;
        double r2935772 = sqrt(r2935771);
        double r2935773 = cbrt(r2935770);
        double r2935774 = r2935772 / r2935773;
        double r2935775 = z;
        double r2935776 = r2935773 * r2935773;
        double r2935777 = r2935775 / r2935776;
        double r2935778 = r2935774 * r2935777;
        double r2935779 = 5.0;
        double r2935780 = 6.0;
        double r2935781 = r2935779 / r2935780;
        double r2935782 = r2935769 + r2935781;
        double r2935783 = 2.0;
        double r2935784 = 3.0;
        double r2935785 = r2935770 * r2935784;
        double r2935786 = r2935783 / r2935785;
        double r2935787 = r2935782 - r2935786;
        double r2935788 = b;
        double r2935789 = c;
        double r2935790 = r2935788 - r2935789;
        double r2935791 = r2935787 * r2935790;
        double r2935792 = r2935778 - r2935791;
        double r2935793 = r2935792 * r2935783;
        double r2935794 = exp(r2935793);
        double r2935795 = r2935768 * r2935794;
        double r2935796 = r2935767 + r2935795;
        double r2935797 = r2935767 / r2935796;
        return r2935797;
}

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

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

  3. Applied add-cube-cbrt3.9

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

  4. Applied times-frac2.7

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

  5. Final simplification2.7

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

Reproduce

herbie shell --seed 2019171 
(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)))))))))))