Average Error: 3.8 → 2.6
Time: 15.4s
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 r117637 = x;
        double r117638 = y;
        double r117639 = 2.0;
        double r117640 = z;
        double r117641 = t;
        double r117642 = a;
        double r117643 = r117641 + r117642;
        double r117644 = sqrt(r117643);
        double r117645 = r117640 * r117644;
        double r117646 = r117645 / r117641;
        double r117647 = b;
        double r117648 = c;
        double r117649 = r117647 - r117648;
        double r117650 = 5.0;
        double r117651 = 6.0;
        double r117652 = r117650 / r117651;
        double r117653 = r117642 + r117652;
        double r117654 = 3.0;
        double r117655 = r117641 * r117654;
        double r117656 = r117639 / r117655;
        double r117657 = r117653 - r117656;
        double r117658 = r117649 * r117657;
        double r117659 = r117646 - r117658;
        double r117660 = r117639 * r117659;
        double r117661 = exp(r117660);
        double r117662 = r117638 * r117661;
        double r117663 = r117637 + r117662;
        double r117664 = r117637 / r117663;
        return r117664;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r117665 = x;
        double r117666 = y;
        double r117667 = 2.0;
        double r117668 = z;
        double r117669 = t;
        double r117670 = cbrt(r117669);
        double r117671 = r117670 * r117670;
        double r117672 = r117668 / r117671;
        double r117673 = a;
        double r117674 = r117669 + r117673;
        double r117675 = sqrt(r117674);
        double r117676 = r117675 / r117670;
        double r117677 = r117672 * r117676;
        double r117678 = b;
        double r117679 = c;
        double r117680 = r117678 - r117679;
        double r117681 = 5.0;
        double r117682 = 6.0;
        double r117683 = r117681 / r117682;
        double r117684 = r117673 + r117683;
        double r117685 = 3.0;
        double r117686 = r117669 * r117685;
        double r117687 = r117667 / r117686;
        double r117688 = r117684 - r117687;
        double r117689 = r117680 * r117688;
        double r117690 = r117677 - r117689;
        double r117691 = r117667 * r117690;
        double r117692 = exp(r117691);
        double r117693 = r117666 * r117692;
        double r117694 = r117665 + r117693;
        double r117695 = r117665 / r117694;
        return r117695;
}

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 2020060 
(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)))))))))))