Average Error: 4.0 → 2.7
Time: 11.5s
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 r93220 = x;
        double r93221 = y;
        double r93222 = 2.0;
        double r93223 = z;
        double r93224 = t;
        double r93225 = a;
        double r93226 = r93224 + r93225;
        double r93227 = sqrt(r93226);
        double r93228 = r93223 * r93227;
        double r93229 = r93228 / r93224;
        double r93230 = b;
        double r93231 = c;
        double r93232 = r93230 - r93231;
        double r93233 = 5.0;
        double r93234 = 6.0;
        double r93235 = r93233 / r93234;
        double r93236 = r93225 + r93235;
        double r93237 = 3.0;
        double r93238 = r93224 * r93237;
        double r93239 = r93222 / r93238;
        double r93240 = r93236 - r93239;
        double r93241 = r93232 * r93240;
        double r93242 = r93229 - r93241;
        double r93243 = r93222 * r93242;
        double r93244 = exp(r93243);
        double r93245 = r93221 * r93244;
        double r93246 = r93220 + r93245;
        double r93247 = r93220 / r93246;
        return r93247;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r93248 = x;
        double r93249 = y;
        double r93250 = 2.0;
        double r93251 = z;
        double r93252 = t;
        double r93253 = cbrt(r93252);
        double r93254 = r93253 * r93253;
        double r93255 = r93251 / r93254;
        double r93256 = a;
        double r93257 = r93252 + r93256;
        double r93258 = sqrt(r93257);
        double r93259 = r93258 / r93253;
        double r93260 = r93255 * r93259;
        double r93261 = b;
        double r93262 = c;
        double r93263 = r93261 - r93262;
        double r93264 = 5.0;
        double r93265 = 6.0;
        double r93266 = r93264 / r93265;
        double r93267 = r93256 + r93266;
        double r93268 = 3.0;
        double r93269 = r93252 * r93268;
        double r93270 = r93250 / r93269;
        double r93271 = r93267 - r93270;
        double r93272 = r93263 * r93271;
        double r93273 = r93260 - r93272;
        double r93274 = r93250 * r93273;
        double r93275 = exp(r93274);
        double r93276 = r93249 * r93275;
        double r93277 = r93248 + r93276;
        double r93278 = r93248 / r93277;
        return r93278;
}

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

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

  3. Applied add-cube-cbrt4.0

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

  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

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

Reproduce

herbie shell --seed 2020047 
(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)))))))))))