Average Error: 3.9 → 1.6
Time: 53.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.863752365364698602827271216718095908021 \cdot 10^{-196} \lor \neg \left(t \le 1.377649032039963197338721484104213014264 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + e^{2 \cdot \frac{\left(\left(t \cdot 3\right) \cdot \left(\sqrt{t + a} \cdot z\right)\right) \cdot \left(a - \frac{5}{6}\right) - \left(t \cdot \left(b - c\right)\right) \cdot \left(\left(t \cdot \left(\left(a - \frac{5}{6}\right) \cdot 3\right)\right) \cdot \left(\frac{5}{6} + a\right) - 2 \cdot \left(a - \frac{5}{6}\right)\right)}{\left(t \cdot 3\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot t\right)}} \cdot y}\\ \end{array}\]
\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 -1.863752365364698602827271216718095908021 \cdot 10^{-196} \lor \neg \left(t \le 1.377649032039963197338721484104213014264 \cdot 10^{-82}\right):\\
\;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r134041 = x;
        double r134042 = y;
        double r134043 = 2.0;
        double r134044 = z;
        double r134045 = t;
        double r134046 = a;
        double r134047 = r134045 + r134046;
        double r134048 = sqrt(r134047);
        double r134049 = r134044 * r134048;
        double r134050 = r134049 / r134045;
        double r134051 = b;
        double r134052 = c;
        double r134053 = r134051 - r134052;
        double r134054 = 5.0;
        double r134055 = 6.0;
        double r134056 = r134054 / r134055;
        double r134057 = r134046 + r134056;
        double r134058 = 3.0;
        double r134059 = r134045 * r134058;
        double r134060 = r134043 / r134059;
        double r134061 = r134057 - r134060;
        double r134062 = r134053 * r134061;
        double r134063 = r134050 - r134062;
        double r134064 = r134043 * r134063;
        double r134065 = exp(r134064);
        double r134066 = r134042 * r134065;
        double r134067 = r134041 + r134066;
        double r134068 = r134041 / r134067;
        return r134068;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r134069 = t;
        double r134070 = -1.8637523653646986e-196;
        bool r134071 = r134069 <= r134070;
        double r134072 = 1.3776490320399632e-82;
        bool r134073 = r134069 <= r134072;
        double r134074 = !r134073;
        bool r134075 = r134071 || r134074;
        double r134076 = x;
        double r134077 = z;
        double r134078 = cbrt(r134069);
        double r134079 = r134078 * r134078;
        double r134080 = r134077 / r134079;
        double r134081 = a;
        double r134082 = r134069 + r134081;
        double r134083 = sqrt(r134082);
        double r134084 = r134083 / r134078;
        double r134085 = r134080 * r134084;
        double r134086 = 5.0;
        double r134087 = 6.0;
        double r134088 = r134086 / r134087;
        double r134089 = r134088 + r134081;
        double r134090 = 2.0;
        double r134091 = 3.0;
        double r134092 = r134069 * r134091;
        double r134093 = r134090 / r134092;
        double r134094 = r134089 - r134093;
        double r134095 = b;
        double r134096 = c;
        double r134097 = r134095 - r134096;
        double r134098 = r134094 * r134097;
        double r134099 = r134085 - r134098;
        double r134100 = r134099 * r134090;
        double r134101 = exp(r134100);
        double r134102 = y;
        double r134103 = r134101 * r134102;
        double r134104 = r134103 + r134076;
        double r134105 = r134076 / r134104;
        double r134106 = r134083 * r134077;
        double r134107 = r134092 * r134106;
        double r134108 = r134081 - r134088;
        double r134109 = r134107 * r134108;
        double r134110 = r134069 * r134097;
        double r134111 = r134108 * r134091;
        double r134112 = r134069 * r134111;
        double r134113 = r134112 * r134089;
        double r134114 = r134090 * r134108;
        double r134115 = r134113 - r134114;
        double r134116 = r134110 * r134115;
        double r134117 = r134109 - r134116;
        double r134118 = r134108 * r134069;
        double r134119 = r134092 * r134118;
        double r134120 = r134117 / r134119;
        double r134121 = r134090 * r134120;
        double r134122 = exp(r134121);
        double r134123 = r134122 * r134102;
        double r134124 = r134076 + r134123;
        double r134125 = r134076 / r134124;
        double r134126 = r134075 ? r134105 : r134125;
        return r134126;
}

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 t < -1.8637523653646986e-196 or 1.3776490320399632e-82 < t

    1. Initial program 2.7

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

    3. Applied add-cube-cbrt2.7

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

    4. Applied times-frac0.9

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

    if -1.8637523653646986e-196 < t < 1.3776490320399632e-82

    1. Initial program 6.5

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

    3. Applied flip-+10.0

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

    4. Applied frac-sub10.0

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

    5. Applied associate-*r/10.0

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

    6. Applied frac-sub7.1

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

    7. Simplified3.4

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

    8. Simplified3.4

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.863752365364698602827271216718095908021 \cdot 10^{-196} \lor \neg \left(t \le 1.377649032039963197338721484104213014264 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + e^{2 \cdot \frac{\left(\left(t \cdot 3\right) \cdot \left(\sqrt{t + a} \cdot z\right)\right) \cdot \left(a - \frac{5}{6}\right) - \left(t \cdot \left(b - c\right)\right) \cdot \left(\left(t \cdot \left(\left(a - \frac{5}{6}\right) \cdot 3\right)\right) \cdot \left(\frac{5}{6} + a\right) - 2 \cdot \left(a - \frac{5}{6}\right)\right)}{\left(t \cdot 3\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot t\right)}} \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(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)))))))))))