Average Error: 4.0 → 2.8
Time: 29.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}\]
\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^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3605390 = x;
        double r3605391 = y;
        double r3605392 = 2.0;
        double r3605393 = z;
        double r3605394 = t;
        double r3605395 = a;
        double r3605396 = r3605394 + r3605395;
        double r3605397 = sqrt(r3605396);
        double r3605398 = r3605393 * r3605397;
        double r3605399 = r3605398 / r3605394;
        double r3605400 = b;
        double r3605401 = c;
        double r3605402 = r3605400 - r3605401;
        double r3605403 = 5.0;
        double r3605404 = 6.0;
        double r3605405 = r3605403 / r3605404;
        double r3605406 = r3605395 + r3605405;
        double r3605407 = 3.0;
        double r3605408 = r3605394 * r3605407;
        double r3605409 = r3605392 / r3605408;
        double r3605410 = r3605406 - r3605409;
        double r3605411 = r3605402 * r3605410;
        double r3605412 = r3605399 - r3605411;
        double r3605413 = r3605392 * r3605412;
        double r3605414 = exp(r3605413);
        double r3605415 = r3605391 * r3605414;
        double r3605416 = r3605390 + r3605415;
        double r3605417 = r3605390 / r3605416;
        return r3605417;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3605418 = x;
        double r3605419 = y;
        double r3605420 = a;
        double r3605421 = t;
        double r3605422 = r3605420 + r3605421;
        double r3605423 = sqrt(r3605422);
        double r3605424 = cbrt(r3605421);
        double r3605425 = r3605423 / r3605424;
        double r3605426 = z;
        double r3605427 = r3605424 * r3605424;
        double r3605428 = r3605426 / r3605427;
        double r3605429 = r3605425 * r3605428;
        double r3605430 = 5.0;
        double r3605431 = 6.0;
        double r3605432 = r3605430 / r3605431;
        double r3605433 = r3605420 + r3605432;
        double r3605434 = 2.0;
        double r3605435 = 3.0;
        double r3605436 = r3605421 * r3605435;
        double r3605437 = r3605434 / r3605436;
        double r3605438 = r3605433 - r3605437;
        double r3605439 = b;
        double r3605440 = c;
        double r3605441 = r3605439 - r3605440;
        double r3605442 = r3605438 * r3605441;
        double r3605443 = r3605429 - r3605442;
        double r3605444 = r3605443 * r3605434;
        double r3605445 = exp(r3605444);
        double r3605446 = r3605419 * r3605445;
        double r3605447 = r3605418 + r3605446;
        double r3605448 = r3605418 / r3605447;
        return r3605448;
}

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 4.0

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

  3. Applied add-cube-cbrt4.0

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

  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

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))