Average Error: 3.8 → 2.8
Time: 27.4s
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 r108644 = x;
        double r108645 = y;
        double r108646 = 2.0;
        double r108647 = z;
        double r108648 = t;
        double r108649 = a;
        double r108650 = r108648 + r108649;
        double r108651 = sqrt(r108650);
        double r108652 = r108647 * r108651;
        double r108653 = r108652 / r108648;
        double r108654 = b;
        double r108655 = c;
        double r108656 = r108654 - r108655;
        double r108657 = 5.0;
        double r108658 = 6.0;
        double r108659 = r108657 / r108658;
        double r108660 = r108649 + r108659;
        double r108661 = 3.0;
        double r108662 = r108648 * r108661;
        double r108663 = r108646 / r108662;
        double r108664 = r108660 - r108663;
        double r108665 = r108656 * r108664;
        double r108666 = r108653 - r108665;
        double r108667 = r108646 * r108666;
        double r108668 = exp(r108667);
        double r108669 = r108645 * r108668;
        double r108670 = r108644 + r108669;
        double r108671 = r108644 / r108670;
        return r108671;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r108672 = x;
        double r108673 = y;
        double r108674 = 2.0;
        double r108675 = z;
        double r108676 = t;
        double r108677 = cbrt(r108676);
        double r108678 = r108677 * r108677;
        double r108679 = r108675 / r108678;
        double r108680 = a;
        double r108681 = r108676 + r108680;
        double r108682 = sqrt(r108681);
        double r108683 = r108682 / r108677;
        double r108684 = r108679 * r108683;
        double r108685 = b;
        double r108686 = c;
        double r108687 = r108685 - r108686;
        double r108688 = 5.0;
        double r108689 = 6.0;
        double r108690 = r108688 / r108689;
        double r108691 = r108680 + r108690;
        double r108692 = 3.0;
        double r108693 = r108676 * r108692;
        double r108694 = r108674 / r108693;
        double r108695 = r108691 - r108694;
        double r108696 = r108687 * r108695;
        double r108697 = r108684 - r108696;
        double r108698 = r108674 * r108697;
        double r108699 = exp(r108698);
        double r108700 = r108673 * r108699;
        double r108701 = r108672 + r108700;
        double r108702 = r108672 / r108701;
        return r108702;
}

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-frac2.8

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

  5. Final simplification2.8

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

Reproduce

herbie shell --seed 2019304 
(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)))))))))))