Average Error: 3.8 → 2.8
Time: 25.0s
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 r141419 = x;
        double r141420 = y;
        double r141421 = 2.0;
        double r141422 = z;
        double r141423 = t;
        double r141424 = a;
        double r141425 = r141423 + r141424;
        double r141426 = sqrt(r141425);
        double r141427 = r141422 * r141426;
        double r141428 = r141427 / r141423;
        double r141429 = b;
        double r141430 = c;
        double r141431 = r141429 - r141430;
        double r141432 = 5.0;
        double r141433 = 6.0;
        double r141434 = r141432 / r141433;
        double r141435 = r141424 + r141434;
        double r141436 = 3.0;
        double r141437 = r141423 * r141436;
        double r141438 = r141421 / r141437;
        double r141439 = r141435 - r141438;
        double r141440 = r141431 * r141439;
        double r141441 = r141428 - r141440;
        double r141442 = r141421 * r141441;
        double r141443 = exp(r141442);
        double r141444 = r141420 * r141443;
        double r141445 = r141419 + r141444;
        double r141446 = r141419 / r141445;
        return r141446;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r141447 = x;
        double r141448 = y;
        double r141449 = 2.0;
        double r141450 = z;
        double r141451 = t;
        double r141452 = cbrt(r141451);
        double r141453 = r141452 * r141452;
        double r141454 = r141450 / r141453;
        double r141455 = a;
        double r141456 = r141451 + r141455;
        double r141457 = sqrt(r141456);
        double r141458 = r141457 / r141452;
        double r141459 = r141454 * r141458;
        double r141460 = b;
        double r141461 = c;
        double r141462 = r141460 - r141461;
        double r141463 = 5.0;
        double r141464 = 6.0;
        double r141465 = r141463 / r141464;
        double r141466 = r141455 + r141465;
        double r141467 = 3.0;
        double r141468 = r141451 * r141467;
        double r141469 = r141449 / r141468;
        double r141470 = r141466 - r141469;
        double r141471 = r141462 * r141470;
        double r141472 = r141459 - r141471;
        double r141473 = r141449 * r141472;
        double r141474 = exp(r141473);
        double r141475 = r141448 * r141474;
        double r141476 = r141447 + r141475;
        double r141477 = r141447 / r141476;
        return r141477;
}

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 2020034 
(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)))))))))))