Average Error: 3.9 → 2.5
Time: 12.6s
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 r85595 = x;
        double r85596 = y;
        double r85597 = 2.0;
        double r85598 = z;
        double r85599 = t;
        double r85600 = a;
        double r85601 = r85599 + r85600;
        double r85602 = sqrt(r85601);
        double r85603 = r85598 * r85602;
        double r85604 = r85603 / r85599;
        double r85605 = b;
        double r85606 = c;
        double r85607 = r85605 - r85606;
        double r85608 = 5.0;
        double r85609 = 6.0;
        double r85610 = r85608 / r85609;
        double r85611 = r85600 + r85610;
        double r85612 = 3.0;
        double r85613 = r85599 * r85612;
        double r85614 = r85597 / r85613;
        double r85615 = r85611 - r85614;
        double r85616 = r85607 * r85615;
        double r85617 = r85604 - r85616;
        double r85618 = r85597 * r85617;
        double r85619 = exp(r85618);
        double r85620 = r85596 * r85619;
        double r85621 = r85595 + r85620;
        double r85622 = r85595 / r85621;
        return r85622;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r85623 = x;
        double r85624 = y;
        double r85625 = 2.0;
        double r85626 = z;
        double r85627 = t;
        double r85628 = cbrt(r85627);
        double r85629 = r85628 * r85628;
        double r85630 = r85626 / r85629;
        double r85631 = a;
        double r85632 = r85627 + r85631;
        double r85633 = sqrt(r85632);
        double r85634 = r85633 / r85628;
        double r85635 = r85630 * r85634;
        double r85636 = b;
        double r85637 = c;
        double r85638 = r85636 - r85637;
        double r85639 = 5.0;
        double r85640 = 6.0;
        double r85641 = r85639 / r85640;
        double r85642 = r85631 + r85641;
        double r85643 = 3.0;
        double r85644 = r85627 * r85643;
        double r85645 = r85625 / r85644;
        double r85646 = r85642 - r85645;
        double r85647 = r85638 * r85646;
        double r85648 = r85635 - r85647;
        double r85649 = r85625 * r85648;
        double r85650 = exp(r85649);
        double r85651 = r85624 * r85650;
        double r85652 = r85623 + r85651;
        double r85653 = r85623 / r85652;
        return r85653;
}

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 3.9

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

  3. Applied add-cube-cbrt3.9

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

  4. Applied times-frac2.5

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

  5. Final simplification2.5

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

Reproduce

herbie shell --seed 2020018 
(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)))))))))))