Average Error: 4.1 → 2.7
Time: 53.8s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.499850531274005 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{elif}\;t \le 9.422186440286068 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{x + e^{2.0 \cdot \frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(t \cdot 3.0\right) \cdot \left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) \cdot t}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \end{array}\]
\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.499850531274005 \cdot 10^{-14}:\\
\;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\

\mathbf{elif}\;t \le 9.422186440286068 \cdot 10^{-296}:\\
\;\;\;\;\frac{x}{x + e^{2.0 \cdot \frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(t \cdot 3.0\right) \cdot \left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) \cdot t}} \cdot y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1935143 = x;
        double r1935144 = y;
        double r1935145 = 2.0;
        double r1935146 = z;
        double r1935147 = t;
        double r1935148 = a;
        double r1935149 = r1935147 + r1935148;
        double r1935150 = sqrt(r1935149);
        double r1935151 = r1935146 * r1935150;
        double r1935152 = r1935151 / r1935147;
        double r1935153 = b;
        double r1935154 = c;
        double r1935155 = r1935153 - r1935154;
        double r1935156 = 5.0;
        double r1935157 = 6.0;
        double r1935158 = r1935156 / r1935157;
        double r1935159 = r1935148 + r1935158;
        double r1935160 = 3.0;
        double r1935161 = r1935147 * r1935160;
        double r1935162 = r1935145 / r1935161;
        double r1935163 = r1935159 - r1935162;
        double r1935164 = r1935155 * r1935163;
        double r1935165 = r1935152 - r1935164;
        double r1935166 = r1935145 * r1935165;
        double r1935167 = exp(r1935166);
        double r1935168 = r1935144 * r1935167;
        double r1935169 = r1935143 + r1935168;
        double r1935170 = r1935143 / r1935169;
        return r1935170;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1935171 = t;
        double r1935172 = -9.499850531274005e-14;
        bool r1935173 = r1935171 <= r1935172;
        double r1935174 = x;
        double r1935175 = z;
        double r1935176 = cbrt(r1935171);
        double r1935177 = r1935176 * r1935176;
        double r1935178 = r1935175 / r1935177;
        double r1935179 = a;
        double r1935180 = r1935171 + r1935179;
        double r1935181 = sqrt(r1935180);
        double r1935182 = r1935181 / r1935176;
        double r1935183 = r1935178 * r1935182;
        double r1935184 = 5.0;
        double r1935185 = 6.0;
        double r1935186 = r1935184 / r1935185;
        double r1935187 = r1935186 + r1935179;
        double r1935188 = 2.0;
        double r1935189 = 3.0;
        double r1935190 = r1935171 * r1935189;
        double r1935191 = r1935188 / r1935190;
        double r1935192 = r1935187 - r1935191;
        double r1935193 = b;
        double r1935194 = c;
        double r1935195 = r1935193 - r1935194;
        double r1935196 = r1935192 * r1935195;
        double r1935197 = r1935183 - r1935196;
        double r1935198 = r1935197 * r1935188;
        double r1935199 = exp(r1935198);
        double r1935200 = y;
        double r1935201 = r1935199 * r1935200;
        double r1935202 = r1935201 + r1935174;
        double r1935203 = r1935174 / r1935202;
        double r1935204 = 9.422186440286068e-296;
        bool r1935205 = r1935171 <= r1935204;
        double r1935206 = r1935181 * r1935175;
        double r1935207 = r1935179 - r1935186;
        double r1935208 = r1935207 * r1935190;
        double r1935209 = r1935206 * r1935208;
        double r1935210 = r1935179 * r1935179;
        double r1935211 = r1935186 * r1935186;
        double r1935212 = r1935210 - r1935211;
        double r1935213 = r1935190 * r1935212;
        double r1935214 = r1935207 * r1935188;
        double r1935215 = r1935213 - r1935214;
        double r1935216 = r1935195 * r1935215;
        double r1935217 = r1935171 * r1935216;
        double r1935218 = r1935209 - r1935217;
        double r1935219 = r1935208 * r1935171;
        double r1935220 = r1935218 / r1935219;
        double r1935221 = r1935188 * r1935220;
        double r1935222 = exp(r1935221);
        double r1935223 = r1935222 * r1935200;
        double r1935224 = r1935174 + r1935223;
        double r1935225 = r1935174 / r1935224;
        double r1935226 = r1935205 ? r1935225 : r1935203;
        double r1935227 = r1935173 ? r1935203 : r1935226;
        return r1935227;
}

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 < -9.499850531274005e-14 or 9.422186440286068e-296 < t

    1. Initial program 3.2

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt3.2

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

    4. Applied times-frac1.7

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

    if -9.499850531274005e-14 < t < 9.422186440286068e-296

    1. Initial program 7.7

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied flip-+9.7

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{blue}{\frac{a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}}{a - \frac{5.0}{6.0}}} - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

    4. Applied frac-sub9.7

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]

    5. Applied associate-*r/9.7

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]

    6. Applied frac-sub6.6

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.499850531274005 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{elif}\;t \le 9.422186440286068 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{x + e^{2.0 \cdot \frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(t \cdot 3.0\right) \cdot \left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) \cdot t}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 
(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)))))))))))