Average Error: 3.5 → 2.4
Time: 1.3m
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 r271 = x;
        double r272 = y;
        double r273 = 2.0;
        double r274 = z;
        double r275 = t;
        double r276 = a;
        double r277 = r275 + r276;
        double r278 = sqrt(r277);
        double r279 = r274 * r278;
        double r280 = r279 / r275;
        double r281 = b;
        double r282 = c;
        double r283 = r281 - r282;
        double r284 = 5.0;
        double r285 = 6.0;
        double r286 = r284 / r285;
        double r287 = r276 + r286;
        double r288 = 3.0;
        double r289 = r275 * r288;
        double r290 = r273 / r289;
        double r291 = r287 - r290;
        double r292 = r283 * r291;
        double r293 = r280 - r292;
        double r294 = r273 * r293;
        double r295 = exp(r294);
        double r296 = r272 * r295;
        double r297 = r271 + r296;
        double r298 = r271 / r297;
        return r298;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r299 = x;
        double r300 = y;
        double r301 = 2.0;
        double r302 = z;
        double r303 = t;
        double r304 = cbrt(r303);
        double r305 = r304 * r304;
        double r306 = r302 / r305;
        double r307 = a;
        double r308 = r303 + r307;
        double r309 = sqrt(r308);
        double r310 = r309 / r304;
        double r311 = r306 * r310;
        double r312 = b;
        double r313 = c;
        double r314 = r312 - r313;
        double r315 = 5.0;
        double r316 = 6.0;
        double r317 = r315 / r316;
        double r318 = r307 + r317;
        double r319 = 3.0;
        double r320 = r303 * r319;
        double r321 = r301 / r320;
        double r322 = r318 - r321;
        double r323 = r314 * r322;
        double r324 = r311 - r323;
        double r325 = r301 * r324;
        double r326 = exp(r325);
        double r327 = r300 * r326;
        double r328 = r299 + r327;
        double r329 = r299 / r328;
        return r329;
}

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 3.5

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

  3. Applied add-cube-cbrt3.5

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

  4. Applied times-frac2.4

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

  5. Final simplification2.4

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

Reproduce

herbie shell --seed 2020025 
(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)))))))))))