Average Error: 4.0 → 2.8
Time: 32.7s
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 r3989672 = x;
        double r3989673 = y;
        double r3989674 = 2.0;
        double r3989675 = z;
        double r3989676 = t;
        double r3989677 = a;
        double r3989678 = r3989676 + r3989677;
        double r3989679 = sqrt(r3989678);
        double r3989680 = r3989675 * r3989679;
        double r3989681 = r3989680 / r3989676;
        double r3989682 = b;
        double r3989683 = c;
        double r3989684 = r3989682 - r3989683;
        double r3989685 = 5.0;
        double r3989686 = 6.0;
        double r3989687 = r3989685 / r3989686;
        double r3989688 = r3989677 + r3989687;
        double r3989689 = 3.0;
        double r3989690 = r3989676 * r3989689;
        double r3989691 = r3989674 / r3989690;
        double r3989692 = r3989688 - r3989691;
        double r3989693 = r3989684 * r3989692;
        double r3989694 = r3989681 - r3989693;
        double r3989695 = r3989674 * r3989694;
        double r3989696 = exp(r3989695);
        double r3989697 = r3989673 * r3989696;
        double r3989698 = r3989672 + r3989697;
        double r3989699 = r3989672 / r3989698;
        return r3989699;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3989700 = x;
        double r3989701 = y;
        double r3989702 = a;
        double r3989703 = t;
        double r3989704 = r3989702 + r3989703;
        double r3989705 = sqrt(r3989704);
        double r3989706 = cbrt(r3989703);
        double r3989707 = r3989705 / r3989706;
        double r3989708 = z;
        double r3989709 = r3989706 * r3989706;
        double r3989710 = r3989708 / r3989709;
        double r3989711 = r3989707 * r3989710;
        double r3989712 = 5.0;
        double r3989713 = 6.0;
        double r3989714 = r3989712 / r3989713;
        double r3989715 = r3989702 + r3989714;
        double r3989716 = 2.0;
        double r3989717 = 3.0;
        double r3989718 = r3989703 * r3989717;
        double r3989719 = r3989716 / r3989718;
        double r3989720 = r3989715 - r3989719;
        double r3989721 = b;
        double r3989722 = c;
        double r3989723 = r3989721 - r3989722;
        double r3989724 = r3989720 * r3989723;
        double r3989725 = r3989711 - r3989724;
        double r3989726 = r3989725 * r3989716;
        double r3989727 = exp(r3989726);
        double r3989728 = r3989701 * r3989727;
        double r3989729 = r3989700 + r3989728;
        double r3989730 = r3989700 / r3989729;
        return r3989730;
}

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 4.0

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

  3. Applied add-cube-cbrt4.0

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

  4. Applied times-frac2.8

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

  5. Final simplification2.8

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

Reproduce

herbie shell --seed 2019172 
(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)))))))))))