Average Error: 3.6 → 2.4
Time: 28.9s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]
\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\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{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4565442 = x;
        double r4565443 = y;
        double r4565444 = 2.0;
        double r4565445 = z;
        double r4565446 = t;
        double r4565447 = a;
        double r4565448 = r4565446 + r4565447;
        double r4565449 = sqrt(r4565448);
        double r4565450 = r4565445 * r4565449;
        double r4565451 = r4565450 / r4565446;
        double r4565452 = b;
        double r4565453 = c;
        double r4565454 = r4565452 - r4565453;
        double r4565455 = 5.0;
        double r4565456 = 6.0;
        double r4565457 = r4565455 / r4565456;
        double r4565458 = r4565447 + r4565457;
        double r4565459 = 3.0;
        double r4565460 = r4565446 * r4565459;
        double r4565461 = r4565444 / r4565460;
        double r4565462 = r4565458 - r4565461;
        double r4565463 = r4565454 * r4565462;
        double r4565464 = r4565451 - r4565463;
        double r4565465 = r4565444 * r4565464;
        double r4565466 = exp(r4565465);
        double r4565467 = r4565443 * r4565466;
        double r4565468 = r4565442 + r4565467;
        double r4565469 = r4565442 / r4565468;
        return r4565469;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4565470 = x;
        double r4565471 = y;
        double r4565472 = a;
        double r4565473 = t;
        double r4565474 = r4565472 + r4565473;
        double r4565475 = sqrt(r4565474);
        double r4565476 = cbrt(r4565473);
        double r4565477 = r4565475 / r4565476;
        double r4565478 = z;
        double r4565479 = r4565476 * r4565476;
        double r4565480 = r4565478 / r4565479;
        double r4565481 = r4565477 * r4565480;
        double r4565482 = 5.0;
        double r4565483 = 6.0;
        double r4565484 = r4565482 / r4565483;
        double r4565485 = r4565472 + r4565484;
        double r4565486 = 2.0;
        double r4565487 = 3.0;
        double r4565488 = r4565473 * r4565487;
        double r4565489 = r4565486 / r4565488;
        double r4565490 = r4565485 - r4565489;
        double r4565491 = b;
        double r4565492 = c;
        double r4565493 = r4565491 - r4565492;
        double r4565494 = r4565490 * r4565493;
        double r4565495 = r4565481 - r4565494;
        double r4565496 = r4565495 * r4565486;
        double r4565497 = exp(r4565496);
        double r4565498 = r4565471 * r4565497;
        double r4565499 = r4565470 + r4565498;
        double r4565500 = r4565470 / r4565499;
        return r4565500;
}

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 3.6

    \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt3.6

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  4. Applied times-frac2.4

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  5. Final simplification2.4

    \[\leadsto \frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]

Reproduce

herbie shell --seed 2019163 
(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)))))))))))