Average Error: 3.9 → 6.0
Time: 9.1s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.55405474180701056 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \log \left(e^{\frac{2}{t \cdot 3}}\right)\right)\right)}}\\ \mathbf{elif}\;t \le 1.379871604667855 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\sqrt[3]{t} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]
\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)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.55405474180701056 \cdot 10^{-127}:\\
\;\;\;\;\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) - \log \left(e^{\frac{2}{t \cdot 3}}\right)\right)\right)}}\\

\mathbf{elif}\;t \le 1.379871604667855 \cdot 10^{-48}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\sqrt[3]{t} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)} \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)}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r78177 = x;
        double r78178 = y;
        double r78179 = 2.0;
        double r78180 = z;
        double r78181 = t;
        double r78182 = a;
        double r78183 = r78181 + r78182;
        double r78184 = sqrt(r78183);
        double r78185 = r78180 * r78184;
        double r78186 = r78185 / r78181;
        double r78187 = b;
        double r78188 = c;
        double r78189 = r78187 - r78188;
        double r78190 = 5.0;
        double r78191 = 6.0;
        double r78192 = r78190 / r78191;
        double r78193 = r78182 + r78192;
        double r78194 = 3.0;
        double r78195 = r78181 * r78194;
        double r78196 = r78179 / r78195;
        double r78197 = r78193 - r78196;
        double r78198 = r78189 * r78197;
        double r78199 = r78186 - r78198;
        double r78200 = r78179 * r78199;
        double r78201 = exp(r78200);
        double r78202 = r78178 * r78201;
        double r78203 = r78177 + r78202;
        double r78204 = r78177 / r78203;
        return r78204;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r78205 = t;
        double r78206 = -3.5540547418070106e-127;
        bool r78207 = r78205 <= r78206;
        double r78208 = x;
        double r78209 = y;
        double r78210 = 2.0;
        double r78211 = z;
        double r78212 = a;
        double r78213 = r78205 + r78212;
        double r78214 = sqrt(r78213);
        double r78215 = r78211 * r78214;
        double r78216 = r78215 / r78205;
        double r78217 = b;
        double r78218 = c;
        double r78219 = r78217 - r78218;
        double r78220 = 5.0;
        double r78221 = 6.0;
        double r78222 = r78220 / r78221;
        double r78223 = r78212 + r78222;
        double r78224 = 3.0;
        double r78225 = r78205 * r78224;
        double r78226 = r78210 / r78225;
        double r78227 = exp(r78226);
        double r78228 = log(r78227);
        double r78229 = r78223 - r78228;
        double r78230 = r78219 * r78229;
        double r78231 = r78216 - r78230;
        double r78232 = r78210 * r78231;
        double r78233 = exp(r78232);
        double r78234 = r78209 * r78233;
        double r78235 = r78208 + r78234;
        double r78236 = r78208 / r78235;
        double r78237 = 1.379871604667855e-48;
        bool r78238 = r78205 <= r78237;
        double r78239 = cbrt(r78205);
        double r78240 = r78239 * r78239;
        double r78241 = r78211 / r78240;
        double r78242 = r78241 * r78214;
        double r78243 = r78212 - r78222;
        double r78244 = r78243 * r78225;
        double r78245 = r78242 * r78244;
        double r78246 = r78212 * r78212;
        double r78247 = r78222 * r78222;
        double r78248 = r78246 - r78247;
        double r78249 = r78248 * r78225;
        double r78250 = r78243 * r78210;
        double r78251 = r78249 - r78250;
        double r78252 = r78219 * r78251;
        double r78253 = r78239 * r78252;
        double r78254 = r78245 - r78253;
        double r78255 = r78239 * r78244;
        double r78256 = r78254 / r78255;
        double r78257 = r78210 * r78256;
        double r78258 = exp(r78257);
        double r78259 = r78209 * r78258;
        double r78260 = r78208 + r78259;
        double r78261 = r78208 / r78260;
        double r78262 = exp(r78239);
        double r78263 = log(r78262);
        double r78264 = r78239 * r78263;
        double r78265 = r78211 / r78264;
        double r78266 = r78214 / r78239;
        double r78267 = r78265 * r78266;
        double r78268 = r78223 - r78226;
        double r78269 = r78219 * r78268;
        double r78270 = r78267 - r78269;
        double r78271 = r78210 * r78270;
        double r78272 = exp(r78271);
        double r78273 = r78209 * r78272;
        double r78274 = r78208 + r78273;
        double r78275 = r78208 / r78274;
        double r78276 = r78238 ? r78261 : r78275;
        double r78277 = r78207 ? r78236 : r78276;
        return r78277;
}

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. Split input into 3 regimes

  2. if t < -3.5540547418070106e-127

    1. Initial program 2.9

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

    3. Applied add-log-exp7.7

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

    if -3.5540547418070106e-127 < t < 1.379871604667855e-48

    1. Initial program 6.1

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

    3. Applied add-cube-cbrt6.1

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

    4. Applied times-frac6.2

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

    6. Applied flip-+9.2

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

    7. Applied frac-sub9.2

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

    8. Applied associate-*r/9.2

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

    9. Applied associate-*r/9.2

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

    10. Applied frac-sub7.4

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

    if 1.379871604667855e-48 < t

    1. Initial program 2.5

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

    3. Applied add-cube-cbrt2.5

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

    4. Applied times-frac0.3

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

    6. Applied add-log-exp4.6

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

  4. Final simplification6.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.55405474180701056 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \log \left(e^{\frac{2}{t \cdot 3}}\right)\right)\right)}}\\ \mathbf{elif}\;t \le 1.379871604667855 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\sqrt[3]{t} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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)))))))))))