Average Error: 3.7 → 2.6
Time: 41.3s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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(\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)}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r82263 = x;
        double r82264 = y;
        double r82265 = 2.0;
        double r82266 = z;
        double r82267 = t;
        double r82268 = a;
        double r82269 = r82267 + r82268;
        double r82270 = sqrt(r82269);
        double r82271 = r82266 * r82270;
        double r82272 = r82271 / r82267;
        double r82273 = b;
        double r82274 = c;
        double r82275 = r82273 - r82274;
        double r82276 = 5.0;
        double r82277 = 6.0;
        double r82278 = r82276 / r82277;
        double r82279 = r82268 + r82278;
        double r82280 = 3.0;
        double r82281 = r82267 * r82280;
        double r82282 = r82265 / r82281;
        double r82283 = r82279 - r82282;
        double r82284 = r82275 * r82283;
        double r82285 = r82272 - r82284;
        double r82286 = r82265 * r82285;
        double r82287 = exp(r82286);
        double r82288 = r82264 * r82287;
        double r82289 = r82263 + r82288;
        double r82290 = r82263 / r82289;
        return r82290;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r82291 = x;
        double r82292 = y;
        double r82293 = 2.0;
        double r82294 = z;
        double r82295 = t;
        double r82296 = cbrt(r82295);
        double r82297 = r82296 * r82296;
        double r82298 = r82294 / r82297;
        double r82299 = a;
        double r82300 = r82295 + r82299;
        double r82301 = sqrt(r82300);
        double r82302 = r82301 / r82296;
        double r82303 = r82298 * r82302;
        double r82304 = b;
        double r82305 = c;
        double r82306 = r82304 - r82305;
        double r82307 = 5.0;
        double r82308 = 6.0;
        double r82309 = r82307 / r82308;
        double r82310 = r82299 + r82309;
        double r82311 = 3.0;
        double r82312 = r82295 * r82311;
        double r82313 = r82293 / r82312;
        double r82314 = r82310 - r82313;
        double r82315 = r82306 * r82314;
        double r82316 = r82303 - r82315;
        double r82317 = r82293 * r82316;
        double r82318 = exp(r82317);
        double r82319 = r82292 * r82318;
        double r82320 = r82291 + r82319;
        double r82321 = r82291 / r82320;
        return r82321;
}

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 3.7

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

  3. Applied add-cube-cbrt3.7

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

  4. Applied times-frac2.6

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

  5. Final simplification2.6

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

Reproduce

herbie shell --seed 2019199 
(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)))))))))))