Average Error: 3.8 → 2.7
Time: 13.9s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\]
\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 \log \left(e^{\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 r68682 = x;
        double r68683 = y;
        double r68684 = 2.0;
        double r68685 = z;
        double r68686 = t;
        double r68687 = a;
        double r68688 = r68686 + r68687;
        double r68689 = sqrt(r68688);
        double r68690 = r68685 * r68689;
        double r68691 = r68690 / r68686;
        double r68692 = b;
        double r68693 = c;
        double r68694 = r68692 - r68693;
        double r68695 = 5.0;
        double r68696 = 6.0;
        double r68697 = r68695 / r68696;
        double r68698 = r68687 + r68697;
        double r68699 = 3.0;
        double r68700 = r68686 * r68699;
        double r68701 = r68684 / r68700;
        double r68702 = r68698 - r68701;
        double r68703 = r68694 * r68702;
        double r68704 = r68691 - r68703;
        double r68705 = r68684 * r68704;
        double r68706 = exp(r68705);
        double r68707 = r68683 * r68706;
        double r68708 = r68682 + r68707;
        double r68709 = r68682 / r68708;
        return r68709;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r68710 = x;
        double r68711 = y;
        double r68712 = 2.0;
        double r68713 = z;
        double r68714 = t;
        double r68715 = cbrt(r68714);
        double r68716 = r68715 * r68715;
        double r68717 = r68713 / r68716;
        double r68718 = a;
        double r68719 = r68714 + r68718;
        double r68720 = sqrt(r68719);
        double r68721 = r68720 / r68715;
        double r68722 = r68717 * r68721;
        double r68723 = b;
        double r68724 = c;
        double r68725 = r68723 - r68724;
        double r68726 = 5.0;
        double r68727 = 6.0;
        double r68728 = r68726 / r68727;
        double r68729 = r68718 + r68728;
        double r68730 = 3.0;
        double r68731 = r68714 * r68730;
        double r68732 = r68712 / r68731;
        double r68733 = r68729 - r68732;
        double r68734 = r68725 * r68733;
        double r68735 = r68722 - r68734;
        double r68736 = exp(r68735);
        double r68737 = log(r68736);
        double r68738 = r68712 * r68737;
        double r68739 = exp(r68738);
        double r68740 = r68711 * r68739;
        double r68741 = r68710 + r68740;
        double r68742 = r68710 / r68741;
        return r68742;
}

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-frac2.7

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

  6. Applied add-log-exp7.1

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

  7. Applied add-log-exp17.1

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

  8. Applied diff-log17.1

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

  9. Simplified2.7

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

  10. Final simplification2.7

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

Reproduce

herbie shell --seed 2019350 
(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)))))))))))