Average Error: 3.9 → 2.6
Time: 2.2m
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2.0 \cdot \log \left(e^{\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)}\right)}}\]
\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^{2.0 \cdot \log \left(e^{\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)}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r20005440 = x;
        double r20005441 = y;
        double r20005442 = 2.0;
        double r20005443 = z;
        double r20005444 = t;
        double r20005445 = a;
        double r20005446 = r20005444 + r20005445;
        double r20005447 = sqrt(r20005446);
        double r20005448 = r20005443 * r20005447;
        double r20005449 = r20005448 / r20005444;
        double r20005450 = b;
        double r20005451 = c;
        double r20005452 = r20005450 - r20005451;
        double r20005453 = 5.0;
        double r20005454 = 6.0;
        double r20005455 = r20005453 / r20005454;
        double r20005456 = r20005445 + r20005455;
        double r20005457 = 3.0;
        double r20005458 = r20005444 * r20005457;
        double r20005459 = r20005442 / r20005458;
        double r20005460 = r20005456 - r20005459;
        double r20005461 = r20005452 * r20005460;
        double r20005462 = r20005449 - r20005461;
        double r20005463 = r20005442 * r20005462;
        double r20005464 = exp(r20005463);
        double r20005465 = r20005441 * r20005464;
        double r20005466 = r20005440 + r20005465;
        double r20005467 = r20005440 / r20005466;
        return r20005467;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r20005468 = x;
        double r20005469 = y;
        double r20005470 = 2.0;
        double r20005471 = a;
        double r20005472 = t;
        double r20005473 = r20005471 + r20005472;
        double r20005474 = sqrt(r20005473);
        double r20005475 = cbrt(r20005472);
        double r20005476 = r20005474 / r20005475;
        double r20005477 = z;
        double r20005478 = r20005475 * r20005475;
        double r20005479 = r20005477 / r20005478;
        double r20005480 = r20005476 * r20005479;
        double r20005481 = 5.0;
        double r20005482 = 6.0;
        double r20005483 = r20005481 / r20005482;
        double r20005484 = r20005471 + r20005483;
        double r20005485 = 3.0;
        double r20005486 = r20005472 * r20005485;
        double r20005487 = r20005470 / r20005486;
        double r20005488 = r20005484 - r20005487;
        double r20005489 = b;
        double r20005490 = c;
        double r20005491 = r20005489 - r20005490;
        double r20005492 = r20005488 * r20005491;
        double r20005493 = r20005480 - r20005492;
        double r20005494 = exp(r20005493);
        double r20005495 = log(r20005494);
        double r20005496 = r20005470 * r20005495;
        double r20005497 = exp(r20005496);
        double r20005498 = r20005469 * r20005497;
        double r20005499 = r20005468 + r20005498;
        double r20005500 = r20005468 / r20005499;
        return r20005500;
}

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

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

  3. Applied add-cube-cbrt3.9

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

  4. Applied times-frac2.6

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

  6. Applied add-log-exp2.6

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

  7. Final simplification2.6

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

Reproduce

herbie shell --seed 2019119 
(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)))))))))))