Average Error: 3.6 → 2.4
Time: 18.9s
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 r189109 = x;
        double r189110 = y;
        double r189111 = 2.0;
        double r189112 = z;
        double r189113 = t;
        double r189114 = a;
        double r189115 = r189113 + r189114;
        double r189116 = sqrt(r189115);
        double r189117 = r189112 * r189116;
        double r189118 = r189117 / r189113;
        double r189119 = b;
        double r189120 = c;
        double r189121 = r189119 - r189120;
        double r189122 = 5.0;
        double r189123 = 6.0;
        double r189124 = r189122 / r189123;
        double r189125 = r189114 + r189124;
        double r189126 = 3.0;
        double r189127 = r189113 * r189126;
        double r189128 = r189111 / r189127;
        double r189129 = r189125 - r189128;
        double r189130 = r189121 * r189129;
        double r189131 = r189118 - r189130;
        double r189132 = r189111 * r189131;
        double r189133 = exp(r189132);
        double r189134 = r189110 * r189133;
        double r189135 = r189109 + r189134;
        double r189136 = r189109 / r189135;
        return r189136;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r189137 = x;
        double r189138 = y;
        double r189139 = 2.0;
        double r189140 = z;
        double r189141 = t;
        double r189142 = cbrt(r189141);
        double r189143 = r189142 * r189142;
        double r189144 = r189140 / r189143;
        double r189145 = a;
        double r189146 = r189141 + r189145;
        double r189147 = sqrt(r189146);
        double r189148 = r189147 / r189142;
        double r189149 = r189144 * r189148;
        double r189150 = b;
        double r189151 = c;
        double r189152 = r189150 - r189151;
        double r189153 = 5.0;
        double r189154 = 6.0;
        double r189155 = r189153 / r189154;
        double r189156 = r189145 + r189155;
        double r189157 = 3.0;
        double r189158 = r189141 * r189157;
        double r189159 = r189139 / r189158;
        double r189160 = r189156 - r189159;
        double r189161 = r189152 * r189160;
        double r189162 = r189149 - r189161;
        double r189163 = r189139 * r189162;
        double r189164 = exp(r189163);
        double r189165 = r189138 * r189164;
        double r189166 = r189137 + r189165;
        double r189167 = r189137 / r189166;
        return r189167;
}

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 3.6

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

  3. Applied add-cube-cbrt3.6

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

  4. Applied times-frac2.4

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

  5. Final simplification2.4

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

Reproduce

herbie shell --seed 2020036 
(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)))))))))))