Average Error: 3.7 → 2.6
Time: 18.9s
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 r62257 = x;
        double r62258 = y;
        double r62259 = 2.0;
        double r62260 = z;
        double r62261 = t;
        double r62262 = a;
        double r62263 = r62261 + r62262;
        double r62264 = sqrt(r62263);
        double r62265 = r62260 * r62264;
        double r62266 = r62265 / r62261;
        double r62267 = b;
        double r62268 = c;
        double r62269 = r62267 - r62268;
        double r62270 = 5.0;
        double r62271 = 6.0;
        double r62272 = r62270 / r62271;
        double r62273 = r62262 + r62272;
        double r62274 = 3.0;
        double r62275 = r62261 * r62274;
        double r62276 = r62259 / r62275;
        double r62277 = r62273 - r62276;
        double r62278 = r62269 * r62277;
        double r62279 = r62266 - r62278;
        double r62280 = r62259 * r62279;
        double r62281 = exp(r62280);
        double r62282 = r62258 * r62281;
        double r62283 = r62257 + r62282;
        double r62284 = r62257 / r62283;
        return r62284;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r62285 = x;
        double r62286 = y;
        double r62287 = 2.0;
        double r62288 = z;
        double r62289 = t;
        double r62290 = cbrt(r62289);
        double r62291 = r62290 * r62290;
        double r62292 = r62288 / r62291;
        double r62293 = a;
        double r62294 = r62289 + r62293;
        double r62295 = sqrt(r62294);
        double r62296 = r62295 / r62290;
        double r62297 = r62292 * r62296;
        double r62298 = b;
        double r62299 = c;
        double r62300 = r62298 - r62299;
        double r62301 = 5.0;
        double r62302 = 6.0;
        double r62303 = r62301 / r62302;
        double r62304 = r62293 + r62303;
        double r62305 = 3.0;
        double r62306 = r62289 * r62305;
        double r62307 = r62287 / r62306;
        double r62308 = r62304 - r62307;
        double r62309 = r62300 * r62308;
        double r62310 = r62297 - r62309;
        double r62311 = r62287 * r62310;
        double r62312 = exp(r62311);
        double r62313 = r62286 * r62312;
        double r62314 = r62285 + r62313;
        double r62315 = r62285 / r62314;
        return r62315;
}

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 2019209 
(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)))))))))))