Average Error: 4.1 → 2.9
Time: 23.3s
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 r58611 = x;
        double r58612 = y;
        double r58613 = 2.0;
        double r58614 = z;
        double r58615 = t;
        double r58616 = a;
        double r58617 = r58615 + r58616;
        double r58618 = sqrt(r58617);
        double r58619 = r58614 * r58618;
        double r58620 = r58619 / r58615;
        double r58621 = b;
        double r58622 = c;
        double r58623 = r58621 - r58622;
        double r58624 = 5.0;
        double r58625 = 6.0;
        double r58626 = r58624 / r58625;
        double r58627 = r58616 + r58626;
        double r58628 = 3.0;
        double r58629 = r58615 * r58628;
        double r58630 = r58613 / r58629;
        double r58631 = r58627 - r58630;
        double r58632 = r58623 * r58631;
        double r58633 = r58620 - r58632;
        double r58634 = r58613 * r58633;
        double r58635 = exp(r58634);
        double r58636 = r58612 * r58635;
        double r58637 = r58611 + r58636;
        double r58638 = r58611 / r58637;
        return r58638;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r58639 = x;
        double r58640 = y;
        double r58641 = 2.0;
        double r58642 = z;
        double r58643 = t;
        double r58644 = cbrt(r58643);
        double r58645 = r58644 * r58644;
        double r58646 = r58642 / r58645;
        double r58647 = a;
        double r58648 = r58643 + r58647;
        double r58649 = sqrt(r58648);
        double r58650 = r58649 / r58644;
        double r58651 = r58646 * r58650;
        double r58652 = b;
        double r58653 = c;
        double r58654 = r58652 - r58653;
        double r58655 = 5.0;
        double r58656 = 6.0;
        double r58657 = r58655 / r58656;
        double r58658 = r58647 + r58657;
        double r58659 = 3.0;
        double r58660 = r58643 * r58659;
        double r58661 = r58641 / r58660;
        double r58662 = r58658 - r58661;
        double r58663 = r58654 * r58662;
        double r58664 = r58651 - r58663;
        double r58665 = r58641 * r58664;
        double r58666 = exp(r58665);
        double r58667 = r58640 * r58666;
        double r58668 = r58639 + r58667;
        double r58669 = r58639 / r58668;
        return r58669;
}

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 4.1

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

  3. Applied add-cube-cbrt4.1

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

  4. Applied times-frac2.9

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

  5. Final simplification2.9

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

Reproduce

herbie shell --seed 2019325 
(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)))))))))))