Average Error: 4.0 → 2.7
Time: 12.0s
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 r80691 = x;
        double r80692 = y;
        double r80693 = 2.0;
        double r80694 = z;
        double r80695 = t;
        double r80696 = a;
        double r80697 = r80695 + r80696;
        double r80698 = sqrt(r80697);
        double r80699 = r80694 * r80698;
        double r80700 = r80699 / r80695;
        double r80701 = b;
        double r80702 = c;
        double r80703 = r80701 - r80702;
        double r80704 = 5.0;
        double r80705 = 6.0;
        double r80706 = r80704 / r80705;
        double r80707 = r80696 + r80706;
        double r80708 = 3.0;
        double r80709 = r80695 * r80708;
        double r80710 = r80693 / r80709;
        double r80711 = r80707 - r80710;
        double r80712 = r80703 * r80711;
        double r80713 = r80700 - r80712;
        double r80714 = r80693 * r80713;
        double r80715 = exp(r80714);
        double r80716 = r80692 * r80715;
        double r80717 = r80691 + r80716;
        double r80718 = r80691 / r80717;
        return r80718;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r80719 = x;
        double r80720 = y;
        double r80721 = 2.0;
        double r80722 = z;
        double r80723 = t;
        double r80724 = cbrt(r80723);
        double r80725 = r80724 * r80724;
        double r80726 = r80722 / r80725;
        double r80727 = a;
        double r80728 = r80723 + r80727;
        double r80729 = sqrt(r80728);
        double r80730 = r80729 / r80724;
        double r80731 = r80726 * r80730;
        double r80732 = b;
        double r80733 = c;
        double r80734 = r80732 - r80733;
        double r80735 = 5.0;
        double r80736 = 6.0;
        double r80737 = r80735 / r80736;
        double r80738 = r80727 + r80737;
        double r80739 = 3.0;
        double r80740 = r80723 * r80739;
        double r80741 = r80721 / r80740;
        double r80742 = r80738 - r80741;
        double r80743 = r80734 * r80742;
        double r80744 = r80731 - r80743;
        double r80745 = r80721 * r80744;
        double r80746 = exp(r80745);
        double r80747 = r80720 * r80746;
        double r80748 = r80719 + r80747;
        double r80749 = r80719 / r80748;
        return r80749;
}

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-frac2.7

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

  5. Final simplification2.7

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

Reproduce

herbie shell --seed 2020047 
(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)))))))))))