Average Error: 4.0 → 2.7
Time: 11.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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 r93145 = x;
        double r93146 = y;
        double r93147 = 2.0;
        double r93148 = z;
        double r93149 = t;
        double r93150 = a;
        double r93151 = r93149 + r93150;
        double r93152 = sqrt(r93151);
        double r93153 = r93148 * r93152;
        double r93154 = r93153 / r93149;
        double r93155 = b;
        double r93156 = c;
        double r93157 = r93155 - r93156;
        double r93158 = 5.0;
        double r93159 = 6.0;
        double r93160 = r93158 / r93159;
        double r93161 = r93150 + r93160;
        double r93162 = 3.0;
        double r93163 = r93149 * r93162;
        double r93164 = r93147 / r93163;
        double r93165 = r93161 - r93164;
        double r93166 = r93157 * r93165;
        double r93167 = r93154 - r93166;
        double r93168 = r93147 * r93167;
        double r93169 = exp(r93168);
        double r93170 = r93146 * r93169;
        double r93171 = r93145 + r93170;
        double r93172 = r93145 / r93171;
        return r93172;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r93173 = x;
        double r93174 = y;
        double r93175 = 2.0;
        double r93176 = z;
        double r93177 = t;
        double r93178 = cbrt(r93177);
        double r93179 = r93178 * r93178;
        double r93180 = r93176 / r93179;
        double r93181 = a;
        double r93182 = r93177 + r93181;
        double r93183 = sqrt(r93182);
        double r93184 = r93183 / r93178;
        double r93185 = r93180 * r93184;
        double r93186 = b;
        double r93187 = c;
        double r93188 = r93186 - r93187;
        double r93189 = 5.0;
        double r93190 = 6.0;
        double r93191 = r93189 / r93190;
        double r93192 = r93181 + r93191;
        double r93193 = 3.0;
        double r93194 = r93177 * r93193;
        double r93195 = r93175 / r93194;
        double r93196 = r93192 - r93195;
        double r93197 = r93188 * r93196;
        double r93198 = r93185 - r93197;
        double r93199 = r93175 * r93198;
        double r93200 = exp(r93199);
        double r93201 = r93174 * r93200;
        double r93202 = r93173 + r93201;
        double r93203 = r93173 / r93202;
        return r93203;
}

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 4.0

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

  3. Applied add-cube-cbrt4.0

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

  4. Applied times-frac2.7

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

  5. Final simplification2.7

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

Reproduce

herbie shell --seed 2020047 
(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)))))))))))