Average Error: 4.0 → 2.9
Time: 2.3m
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 r19738266 = x;
        double r19738267 = y;
        double r19738268 = 2.0;
        double r19738269 = z;
        double r19738270 = t;
        double r19738271 = a;
        double r19738272 = r19738270 + r19738271;
        double r19738273 = sqrt(r19738272);
        double r19738274 = r19738269 * r19738273;
        double r19738275 = r19738274 / r19738270;
        double r19738276 = b;
        double r19738277 = c;
        double r19738278 = r19738276 - r19738277;
        double r19738279 = 5.0;
        double r19738280 = 6.0;
        double r19738281 = r19738279 / r19738280;
        double r19738282 = r19738271 + r19738281;
        double r19738283 = 3.0;
        double r19738284 = r19738270 * r19738283;
        double r19738285 = r19738268 / r19738284;
        double r19738286 = r19738282 - r19738285;
        double r19738287 = r19738278 * r19738286;
        double r19738288 = r19738275 - r19738287;
        double r19738289 = r19738268 * r19738288;
        double r19738290 = exp(r19738289);
        double r19738291 = r19738267 * r19738290;
        double r19738292 = r19738266 + r19738291;
        double r19738293 = r19738266 / r19738292;
        return r19738293;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r19738294 = x;
        double r19738295 = y;
        double r19738296 = a;
        double r19738297 = t;
        double r19738298 = r19738296 + r19738297;
        double r19738299 = sqrt(r19738298);
        double r19738300 = cbrt(r19738297);
        double r19738301 = r19738299 / r19738300;
        double r19738302 = z;
        double r19738303 = r19738300 * r19738300;
        double r19738304 = r19738302 / r19738303;
        double r19738305 = r19738301 * r19738304;
        double r19738306 = 5.0;
        double r19738307 = 6.0;
        double r19738308 = r19738306 / r19738307;
        double r19738309 = r19738296 + r19738308;
        double r19738310 = 2.0;
        double r19738311 = 3.0;
        double r19738312 = r19738297 * r19738311;
        double r19738313 = r19738310 / r19738312;
        double r19738314 = r19738309 - r19738313;
        double r19738315 = b;
        double r19738316 = c;
        double r19738317 = r19738315 - r19738316;
        double r19738318 = r19738314 * r19738317;
        double r19738319 = r19738305 - r19738318;
        double r19738320 = r19738319 * r19738310;
        double r19738321 = exp(r19738320);
        double r19738322 = r19738295 * r19738321;
        double r19738323 = r19738294 + r19738322;
        double r19738324 = r19738294 / r19738323;
        return r19738324;
}

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 4.0

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

  3. Applied add-cube-cbrt4.0

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

  4. Applied times-frac2.9

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

  5. Final simplification2.9

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

Reproduce

herbie shell --seed 2019124 
(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)))))))))))