Average Error: 4.2 → 3.6
Time: 36.8s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \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(z \cdot \frac{\sqrt{t + a}}{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 r86488 = x;
        double r86489 = y;
        double r86490 = 2.0;
        double r86491 = z;
        double r86492 = t;
        double r86493 = a;
        double r86494 = r86492 + r86493;
        double r86495 = sqrt(r86494);
        double r86496 = r86491 * r86495;
        double r86497 = r86496 / r86492;
        double r86498 = b;
        double r86499 = c;
        double r86500 = r86498 - r86499;
        double r86501 = 5.0;
        double r86502 = 6.0;
        double r86503 = r86501 / r86502;
        double r86504 = r86493 + r86503;
        double r86505 = 3.0;
        double r86506 = r86492 * r86505;
        double r86507 = r86490 / r86506;
        double r86508 = r86504 - r86507;
        double r86509 = r86500 * r86508;
        double r86510 = r86497 - r86509;
        double r86511 = r86490 * r86510;
        double r86512 = exp(r86511);
        double r86513 = r86489 * r86512;
        double r86514 = r86488 + r86513;
        double r86515 = r86488 / r86514;
        return r86515;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r86516 = x;
        double r86517 = y;
        double r86518 = 2.0;
        double r86519 = z;
        double r86520 = t;
        double r86521 = a;
        double r86522 = r86520 + r86521;
        double r86523 = sqrt(r86522);
        double r86524 = r86523 / r86520;
        double r86525 = r86519 * r86524;
        double r86526 = b;
        double r86527 = c;
        double r86528 = r86526 - r86527;
        double r86529 = 5.0;
        double r86530 = 6.0;
        double r86531 = r86529 / r86530;
        double r86532 = r86521 + r86531;
        double r86533 = 3.0;
        double r86534 = r86520 * r86533;
        double r86535 = r86518 / r86534;
        double r86536 = r86532 - r86535;
        double r86537 = r86528 * r86536;
        double r86538 = r86525 - r86537;
        double r86539 = r86518 * r86538;
        double r86540 = exp(r86539);
        double r86541 = r86517 * r86540;
        double r86542 = r86516 + r86541;
        double r86543 = r86516 / r86542;
        return r86543;
}

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 4.2

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

  3. Applied *-un-lft-identity4.2

    \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{1 \cdot t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

  4. Applied times-frac3.6

    \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{1} \cdot \frac{\sqrt{t + a}}{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

  5. Simplified3.6

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

  6. Final simplification3.6

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

Reproduce

herbie shell --seed 2019326 
(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)))))))))))