Average Error: 3.9 → 2.8
Time: 33.6s
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 r107399 = x;
        double r107400 = y;
        double r107401 = 2.0;
        double r107402 = z;
        double r107403 = t;
        double r107404 = a;
        double r107405 = r107403 + r107404;
        double r107406 = sqrt(r107405);
        double r107407 = r107402 * r107406;
        double r107408 = r107407 / r107403;
        double r107409 = b;
        double r107410 = c;
        double r107411 = r107409 - r107410;
        double r107412 = 5.0;
        double r107413 = 6.0;
        double r107414 = r107412 / r107413;
        double r107415 = r107404 + r107414;
        double r107416 = 3.0;
        double r107417 = r107403 * r107416;
        double r107418 = r107401 / r107417;
        double r107419 = r107415 - r107418;
        double r107420 = r107411 * r107419;
        double r107421 = r107408 - r107420;
        double r107422 = r107401 * r107421;
        double r107423 = exp(r107422);
        double r107424 = r107400 * r107423;
        double r107425 = r107399 + r107424;
        double r107426 = r107399 / r107425;
        return r107426;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r107427 = x;
        double r107428 = y;
        double r107429 = 2.0;
        double r107430 = z;
        double r107431 = t;
        double r107432 = cbrt(r107431);
        double r107433 = r107432 * r107432;
        double r107434 = r107430 / r107433;
        double r107435 = a;
        double r107436 = r107431 + r107435;
        double r107437 = sqrt(r107436);
        double r107438 = r107437 / r107432;
        double r107439 = r107434 * r107438;
        double r107440 = b;
        double r107441 = c;
        double r107442 = r107440 - r107441;
        double r107443 = 5.0;
        double r107444 = 6.0;
        double r107445 = r107443 / r107444;
        double r107446 = r107435 + r107445;
        double r107447 = 3.0;
        double r107448 = r107431 * r107447;
        double r107449 = r107429 / r107448;
        double r107450 = r107446 - r107449;
        double r107451 = r107442 * r107450;
        double r107452 = r107439 - r107451;
        double r107453 = r107429 * r107452;
        double r107454 = exp(r107453);
        double r107455 = r107428 * r107454;
        double r107456 = r107427 + r107455;
        double r107457 = r107427 / r107456;
        return r107457;
}

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 3.9

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

  3. Applied add-cube-cbrt3.9

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

  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 2019294 
(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)))))))))))