Average Error: 3.9 → 2.6
Time: 25.1s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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 r152142 = x;
        double r152143 = y;
        double r152144 = 2.0;
        double r152145 = z;
        double r152146 = t;
        double r152147 = a;
        double r152148 = r152146 + r152147;
        double r152149 = sqrt(r152148);
        double r152150 = r152145 * r152149;
        double r152151 = r152150 / r152146;
        double r152152 = b;
        double r152153 = c;
        double r152154 = r152152 - r152153;
        double r152155 = 5.0;
        double r152156 = 6.0;
        double r152157 = r152155 / r152156;
        double r152158 = r152147 + r152157;
        double r152159 = 3.0;
        double r152160 = r152146 * r152159;
        double r152161 = r152144 / r152160;
        double r152162 = r152158 - r152161;
        double r152163 = r152154 * r152162;
        double r152164 = r152151 - r152163;
        double r152165 = r152144 * r152164;
        double r152166 = exp(r152165);
        double r152167 = r152143 * r152166;
        double r152168 = r152142 + r152167;
        double r152169 = r152142 / r152168;
        return r152169;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r152170 = x;
        double r152171 = y;
        double r152172 = 2.0;
        double r152173 = z;
        double r152174 = t;
        double r152175 = cbrt(r152174);
        double r152176 = r152175 * r152175;
        double r152177 = r152173 / r152176;
        double r152178 = a;
        double r152179 = r152174 + r152178;
        double r152180 = sqrt(r152179);
        double r152181 = r152180 / r152175;
        double r152182 = r152177 * r152181;
        double r152183 = b;
        double r152184 = c;
        double r152185 = r152183 - r152184;
        double r152186 = 5.0;
        double r152187 = 6.0;
        double r152188 = r152186 / r152187;
        double r152189 = r152178 + r152188;
        double r152190 = 3.0;
        double r152191 = r152174 * r152190;
        double r152192 = r152172 / r152191;
        double r152193 = r152189 - r152192;
        double r152194 = r152185 * r152193;
        double r152195 = r152182 - r152194;
        double r152196 = r152172 * r152195;
        double r152197 = exp(r152196);
        double r152198 = r152171 * r152197;
        double r152199 = r152170 + r152198;
        double r152200 = r152170 / r152199;
        return r152200;
}

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 3.9

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

  3. Applied add-cube-cbrt3.9

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

  4. Applied times-frac2.6

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

  5. Final simplification2.6

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

Reproduce

herbie shell --seed 2019352 
(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)))))))))))