Average Error: 3.9 → 2.7
Time: 24.3s
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 r3058360 = x;
        double r3058361 = y;
        double r3058362 = 2.0;
        double r3058363 = z;
        double r3058364 = t;
        double r3058365 = a;
        double r3058366 = r3058364 + r3058365;
        double r3058367 = sqrt(r3058366);
        double r3058368 = r3058363 * r3058367;
        double r3058369 = r3058368 / r3058364;
        double r3058370 = b;
        double r3058371 = c;
        double r3058372 = r3058370 - r3058371;
        double r3058373 = 5.0;
        double r3058374 = 6.0;
        double r3058375 = r3058373 / r3058374;
        double r3058376 = r3058365 + r3058375;
        double r3058377 = 3.0;
        double r3058378 = r3058364 * r3058377;
        double r3058379 = r3058362 / r3058378;
        double r3058380 = r3058376 - r3058379;
        double r3058381 = r3058372 * r3058380;
        double r3058382 = r3058369 - r3058381;
        double r3058383 = r3058362 * r3058382;
        double r3058384 = exp(r3058383);
        double r3058385 = r3058361 * r3058384;
        double r3058386 = r3058360 + r3058385;
        double r3058387 = r3058360 / r3058386;
        return r3058387;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3058388 = x;
        double r3058389 = y;
        double r3058390 = a;
        double r3058391 = t;
        double r3058392 = r3058390 + r3058391;
        double r3058393 = sqrt(r3058392);
        double r3058394 = cbrt(r3058391);
        double r3058395 = r3058393 / r3058394;
        double r3058396 = z;
        double r3058397 = r3058394 * r3058394;
        double r3058398 = r3058396 / r3058397;
        double r3058399 = r3058395 * r3058398;
        double r3058400 = 5.0;
        double r3058401 = 6.0;
        double r3058402 = r3058400 / r3058401;
        double r3058403 = r3058390 + r3058402;
        double r3058404 = 2.0;
        double r3058405 = 3.0;
        double r3058406 = r3058391 * r3058405;
        double r3058407 = r3058404 / r3058406;
        double r3058408 = r3058403 - r3058407;
        double r3058409 = b;
        double r3058410 = c;
        double r3058411 = r3058409 - r3058410;
        double r3058412 = r3058408 * r3058411;
        double r3058413 = r3058399 - r3058412;
        double r3058414 = r3058413 * r3058404;
        double r3058415 = exp(r3058414);
        double r3058416 = r3058389 * r3058415;
        double r3058417 = r3058388 + r3058416;
        double r3058418 = r3058388 / r3058417;
        return r3058418;
}

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

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

  3. Applied add-cube-cbrt3.9

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

  4. Applied times-frac2.7

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

  5. Final simplification2.7

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

Reproduce

herbie shell --seed 2019171 
(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)))))))))))