Average Error: 3.8 → 2.8
Time: 11.0s
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 r100553 = x;
        double r100554 = y;
        double r100555 = 2.0;
        double r100556 = z;
        double r100557 = t;
        double r100558 = a;
        double r100559 = r100557 + r100558;
        double r100560 = sqrt(r100559);
        double r100561 = r100556 * r100560;
        double r100562 = r100561 / r100557;
        double r100563 = b;
        double r100564 = c;
        double r100565 = r100563 - r100564;
        double r100566 = 5.0;
        double r100567 = 6.0;
        double r100568 = r100566 / r100567;
        double r100569 = r100558 + r100568;
        double r100570 = 3.0;
        double r100571 = r100557 * r100570;
        double r100572 = r100555 / r100571;
        double r100573 = r100569 - r100572;
        double r100574 = r100565 * r100573;
        double r100575 = r100562 - r100574;
        double r100576 = r100555 * r100575;
        double r100577 = exp(r100576);
        double r100578 = r100554 * r100577;
        double r100579 = r100553 + r100578;
        double r100580 = r100553 / r100579;
        return r100580;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r100581 = x;
        double r100582 = y;
        double r100583 = 2.0;
        double r100584 = z;
        double r100585 = t;
        double r100586 = cbrt(r100585);
        double r100587 = r100586 * r100586;
        double r100588 = r100584 / r100587;
        double r100589 = a;
        double r100590 = r100585 + r100589;
        double r100591 = sqrt(r100590);
        double r100592 = r100591 / r100586;
        double r100593 = r100588 * r100592;
        double r100594 = b;
        double r100595 = c;
        double r100596 = r100594 - r100595;
        double r100597 = 5.0;
        double r100598 = 6.0;
        double r100599 = r100597 / r100598;
        double r100600 = r100589 + r100599;
        double r100601 = 3.0;
        double r100602 = r100585 * r100601;
        double r100603 = r100583 / r100602;
        double r100604 = r100600 - r100603;
        double r100605 = r100596 * r100604;
        double r100606 = r100593 - r100605;
        double r100607 = r100583 * r100606;
        double r100608 = exp(r100607);
        double r100609 = r100582 * r100608;
        double r100610 = r100581 + r100609;
        double r100611 = r100581 / r100610;
        return r100611;
}

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 2019318 
(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)))))))))))