Average Error: 4.1 → 2.9
Time: 23.1s
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 r57619 = x;
        double r57620 = y;
        double r57621 = 2.0;
        double r57622 = z;
        double r57623 = t;
        double r57624 = a;
        double r57625 = r57623 + r57624;
        double r57626 = sqrt(r57625);
        double r57627 = r57622 * r57626;
        double r57628 = r57627 / r57623;
        double r57629 = b;
        double r57630 = c;
        double r57631 = r57629 - r57630;
        double r57632 = 5.0;
        double r57633 = 6.0;
        double r57634 = r57632 / r57633;
        double r57635 = r57624 + r57634;
        double r57636 = 3.0;
        double r57637 = r57623 * r57636;
        double r57638 = r57621 / r57637;
        double r57639 = r57635 - r57638;
        double r57640 = r57631 * r57639;
        double r57641 = r57628 - r57640;
        double r57642 = r57621 * r57641;
        double r57643 = exp(r57642);
        double r57644 = r57620 * r57643;
        double r57645 = r57619 + r57644;
        double r57646 = r57619 / r57645;
        return r57646;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r57647 = x;
        double r57648 = y;
        double r57649 = 2.0;
        double r57650 = z;
        double r57651 = t;
        double r57652 = cbrt(r57651);
        double r57653 = r57652 * r57652;
        double r57654 = r57650 / r57653;
        double r57655 = a;
        double r57656 = r57651 + r57655;
        double r57657 = sqrt(r57656);
        double r57658 = r57657 / r57652;
        double r57659 = r57654 * r57658;
        double r57660 = b;
        double r57661 = c;
        double r57662 = r57660 - r57661;
        double r57663 = 5.0;
        double r57664 = 6.0;
        double r57665 = r57663 / r57664;
        double r57666 = r57655 + r57665;
        double r57667 = 3.0;
        double r57668 = r57651 * r57667;
        double r57669 = r57649 / r57668;
        double r57670 = r57666 - r57669;
        double r57671 = r57662 * r57670;
        double r57672 = r57659 - r57671;
        double r57673 = r57649 * r57672;
        double r57674 = exp(r57673);
        double r57675 = r57648 * r57674;
        double r57676 = r57647 + r57675;
        double r57677 = r57647 / r57676;
        return r57677;
}

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)))))))))))