Average Error: 4.2 → 2.8
Time: 8.1s
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 r74122 = x;
        double r74123 = y;
        double r74124 = 2.0;
        double r74125 = z;
        double r74126 = t;
        double r74127 = a;
        double r74128 = r74126 + r74127;
        double r74129 = sqrt(r74128);
        double r74130 = r74125 * r74129;
        double r74131 = r74130 / r74126;
        double r74132 = b;
        double r74133 = c;
        double r74134 = r74132 - r74133;
        double r74135 = 5.0;
        double r74136 = 6.0;
        double r74137 = r74135 / r74136;
        double r74138 = r74127 + r74137;
        double r74139 = 3.0;
        double r74140 = r74126 * r74139;
        double r74141 = r74124 / r74140;
        double r74142 = r74138 - r74141;
        double r74143 = r74134 * r74142;
        double r74144 = r74131 - r74143;
        double r74145 = r74124 * r74144;
        double r74146 = exp(r74145);
        double r74147 = r74123 * r74146;
        double r74148 = r74122 + r74147;
        double r74149 = r74122 / r74148;
        return r74149;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r74150 = x;
        double r74151 = y;
        double r74152 = 2.0;
        double r74153 = z;
        double r74154 = t;
        double r74155 = cbrt(r74154);
        double r74156 = r74155 * r74155;
        double r74157 = r74153 / r74156;
        double r74158 = a;
        double r74159 = r74154 + r74158;
        double r74160 = sqrt(r74159);
        double r74161 = r74160 / r74155;
        double r74162 = r74157 * r74161;
        double r74163 = b;
        double r74164 = c;
        double r74165 = r74163 - r74164;
        double r74166 = 5.0;
        double r74167 = 6.0;
        double r74168 = r74166 / r74167;
        double r74169 = r74158 + r74168;
        double r74170 = 3.0;
        double r74171 = r74154 * r74170;
        double r74172 = r74152 / r74171;
        double r74173 = r74169 - r74172;
        double r74174 = r74165 * r74173;
        double r74175 = r74162 - r74174;
        double r74176 = r74152 * r74175;
        double r74177 = exp(r74176);
        double r74178 = r74151 * r74177;
        double r74179 = r74150 + r74178;
        double r74180 = r74150 / r74179;
        return r74180;
}

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 4.2

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

  3. Applied add-cube-cbrt4.2

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

  4. Applied times-frac2.8

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

  5. Final simplification2.8

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

Reproduce

herbie shell --seed 2020083 
(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)))))))))))