Average Error: 3.8 → 2.8
Time: 39.1s
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 r95475 = x;
        double r95476 = y;
        double r95477 = 2.0;
        double r95478 = z;
        double r95479 = t;
        double r95480 = a;
        double r95481 = r95479 + r95480;
        double r95482 = sqrt(r95481);
        double r95483 = r95478 * r95482;
        double r95484 = r95483 / r95479;
        double r95485 = b;
        double r95486 = c;
        double r95487 = r95485 - r95486;
        double r95488 = 5.0;
        double r95489 = 6.0;
        double r95490 = r95488 / r95489;
        double r95491 = r95480 + r95490;
        double r95492 = 3.0;
        double r95493 = r95479 * r95492;
        double r95494 = r95477 / r95493;
        double r95495 = r95491 - r95494;
        double r95496 = r95487 * r95495;
        double r95497 = r95484 - r95496;
        double r95498 = r95477 * r95497;
        double r95499 = exp(r95498);
        double r95500 = r95476 * r95499;
        double r95501 = r95475 + r95500;
        double r95502 = r95475 / r95501;
        return r95502;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r95503 = x;
        double r95504 = y;
        double r95505 = 2.0;
        double r95506 = z;
        double r95507 = t;
        double r95508 = cbrt(r95507);
        double r95509 = r95508 * r95508;
        double r95510 = r95506 / r95509;
        double r95511 = a;
        double r95512 = r95507 + r95511;
        double r95513 = sqrt(r95512);
        double r95514 = r95513 / r95508;
        double r95515 = r95510 * r95514;
        double r95516 = b;
        double r95517 = c;
        double r95518 = r95516 - r95517;
        double r95519 = 5.0;
        double r95520 = 6.0;
        double r95521 = r95519 / r95520;
        double r95522 = r95511 + r95521;
        double r95523 = 3.0;
        double r95524 = r95507 * r95523;
        double r95525 = r95505 / r95524;
        double r95526 = r95522 - r95525;
        double r95527 = r95518 * r95526;
        double r95528 = r95515 - r95527;
        double r95529 = r95505 * r95528;
        double r95530 = exp(r95529);
        double r95531 = r95504 * r95530;
        double r95532 = r95503 + r95531;
        double r95533 = r95503 / r95532;
        return r95533;
}

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)))))))))))