Average Error: 3.8 → 3.0
Time: 23.7s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 2.108535095172928346218613549125577993008 \cdot 10^{241}:\\ \;\;\;\;\frac{x}{x + e^{\left(\left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right) + \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}}\right) \cdot 2} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(a \cdot \left(c - b\right) - b \cdot 0.8333333333333333703407674875052180141211\right) \cdot 2} + x}\\ \end{array}\]
\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}\;a \le 2.108535095172928346218613549125577993008 \cdot 10^{241}:\\
\;\;\;\;\frac{x}{x + e^{\left(\left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right) + \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}}\right) \cdot 2} \cdot y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{y \cdot e^{\left(a \cdot \left(c - b\right) - b \cdot 0.8333333333333333703407674875052180141211\right) \cdot 2} + x}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r60135 = x;
        double r60136 = y;
        double r60137 = 2.0;
        double r60138 = z;
        double r60139 = t;
        double r60140 = a;
        double r60141 = r60139 + r60140;
        double r60142 = sqrt(r60141);
        double r60143 = r60138 * r60142;
        double r60144 = r60143 / r60139;
        double r60145 = b;
        double r60146 = c;
        double r60147 = r60145 - r60146;
        double r60148 = 5.0;
        double r60149 = 6.0;
        double r60150 = r60148 / r60149;
        double r60151 = r60140 + r60150;
        double r60152 = 3.0;
        double r60153 = r60139 * r60152;
        double r60154 = r60137 / r60153;
        double r60155 = r60151 - r60154;
        double r60156 = r60147 * r60155;
        double r60157 = r60144 - r60156;
        double r60158 = r60137 * r60157;
        double r60159 = exp(r60158);
        double r60160 = r60136 * r60159;
        double r60161 = r60135 + r60160;
        double r60162 = r60135 / r60161;
        return r60162;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r60163 = a;
        double r60164 = 2.1085350951729283e+241;
        bool r60165 = r60163 <= r60164;
        double r60166 = x;
        double r60167 = c;
        double r60168 = b;
        double r60169 = r60167 - r60168;
        double r60170 = 0.6666666666666666;
        double r60171 = t;
        double r60172 = r60170 / r60171;
        double r60173 = r60163 - r60172;
        double r60174 = 5.0;
        double r60175 = 6.0;
        double r60176 = r60174 / r60175;
        double r60177 = r60173 + r60176;
        double r60178 = r60169 * r60177;
        double r60179 = z;
        double r60180 = cbrt(r60171);
        double r60181 = r60180 * r60180;
        double r60182 = r60179 / r60181;
        double r60183 = r60163 + r60171;
        double r60184 = sqrt(r60183);
        double r60185 = r60184 / r60180;
        double r60186 = r60182 * r60185;
        double r60187 = r60178 + r60186;
        double r60188 = 2.0;
        double r60189 = r60187 * r60188;
        double r60190 = exp(r60189);
        double r60191 = y;
        double r60192 = r60190 * r60191;
        double r60193 = r60166 + r60192;
        double r60194 = r60166 / r60193;
        double r60195 = r60163 * r60169;
        double r60196 = 0.8333333333333334;
        double r60197 = r60168 * r60196;
        double r60198 = r60195 - r60197;
        double r60199 = r60198 * r60188;
        double r60200 = exp(r60199);
        double r60201 = r60191 * r60200;
        double r60202 = r60201 + r60166;
        double r60203 = r60166 / r60202;
        double r60204 = r60165 ? r60194 : r60203;
        return r60204;
}

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 2 regimes

  2. if a < 2.1085350951729283e+241

    1. Initial program 3.3

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

    2. Simplified2.9

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

    4. Applied add-log-exp8.9

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

    5. Taylor expanded around 0 2.9

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{a + t}}{t} + \left(c - b\right) \cdot \left(\left(a - \color{blue}{\frac{0.6666666666666666296592325124947819858789}{t}}\right) + \frac{5}{6}\right)\right)} + x}\]
    6. Using strategy rm

    7. Applied add-cube-cbrt2.9

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{a + t}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} + \left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

    8. Applied *-un-lft-identity2.9

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\sqrt{\color{blue}{1 \cdot \left(a + t\right)}}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + \left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

    9. Applied sqrt-prod2.9

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \frac{\color{blue}{\sqrt{1} \cdot \sqrt{a + t}}}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}} + \left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

    10. Applied times-frac2.9

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(z \cdot \color{blue}{\left(\frac{\sqrt{1}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}}\right)} + \left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

    11. Applied associate-*r*2.5

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(\color{blue}{\left(z \cdot \frac{\sqrt{1}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}}} + \left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

    12. Simplified2.5

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}} + \left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right)\right)} + x}\]

    if 2.1085350951729283e+241 < a

    1. Initial program 8.3

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

    2. Simplified8.5

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

    4. Applied add-log-exp16.6

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

    5. Taylor expanded around inf 13.8

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \color{blue}{\left(a \cdot c - \left(a \cdot b + 0.8333333333333333703407674875052180141211 \cdot b\right)\right)}} + x}\]

    6. Simplified7.1

      \[\leadsto \frac{x}{y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right) - 0.8333333333333333703407674875052180141211 \cdot b\right)}} + x}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 2.108535095172928346218613549125577993008 \cdot 10^{241}:\\ \;\;\;\;\frac{x}{x + e^{\left(\left(c - b\right) \cdot \left(\left(a - \frac{0.6666666666666666296592325124947819858789}{t}\right) + \frac{5}{6}\right) + \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{a + t}}{\sqrt[3]{t}}\right) \cdot 2} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(a \cdot \left(c - b\right) - b \cdot 0.8333333333333333703407674875052180141211\right) \cdot 2} + x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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)))))))))))