Average Error: 3.8 → 2.6
Time: 16.6s
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 r100548 = x;
        double r100549 = y;
        double r100550 = 2.0;
        double r100551 = z;
        double r100552 = t;
        double r100553 = a;
        double r100554 = r100552 + r100553;
        double r100555 = sqrt(r100554);
        double r100556 = r100551 * r100555;
        double r100557 = r100556 / r100552;
        double r100558 = b;
        double r100559 = c;
        double r100560 = r100558 - r100559;
        double r100561 = 5.0;
        double r100562 = 6.0;
        double r100563 = r100561 / r100562;
        double r100564 = r100553 + r100563;
        double r100565 = 3.0;
        double r100566 = r100552 * r100565;
        double r100567 = r100550 / r100566;
        double r100568 = r100564 - r100567;
        double r100569 = r100560 * r100568;
        double r100570 = r100557 - r100569;
        double r100571 = r100550 * r100570;
        double r100572 = exp(r100571);
        double r100573 = r100549 * r100572;
        double r100574 = r100548 + r100573;
        double r100575 = r100548 / r100574;
        return r100575;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r100576 = x;
        double r100577 = y;
        double r100578 = 2.0;
        double r100579 = z;
        double r100580 = t;
        double r100581 = cbrt(r100580);
        double r100582 = r100581 * r100581;
        double r100583 = r100579 / r100582;
        double r100584 = a;
        double r100585 = r100580 + r100584;
        double r100586 = sqrt(r100585);
        double r100587 = r100586 / r100581;
        double r100588 = r100583 * r100587;
        double r100589 = b;
        double r100590 = c;
        double r100591 = r100589 - r100590;
        double r100592 = 5.0;
        double r100593 = 6.0;
        double r100594 = r100592 / r100593;
        double r100595 = r100584 + r100594;
        double r100596 = 3.0;
        double r100597 = r100580 * r100596;
        double r100598 = r100578 / r100597;
        double r100599 = r100595 - r100598;
        double r100600 = r100591 * r100599;
        double r100601 = r100588 - r100600;
        double r100602 = r100578 * r100601;
        double r100603 = exp(r100602);
        double r100604 = r100577 * r100603;
        double r100605 = r100576 + r100604;
        double r100606 = r100576 / r100605;
        return r100606;
}

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)))))))))))