Average Error: 3.4 → 2.4
Time: 25.8s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]
\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)}}
↓
\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1920107 = x;
        double r1920108 = y;
        double r1920109 = 2.0;
        double r1920110 = z;
        double r1920111 = t;
        double r1920112 = a;
        double r1920113 = r1920111 + r1920112;
        double r1920114 = sqrt(r1920113);
        double r1920115 = r1920110 * r1920114;
        double r1920116 = r1920115 / r1920111;
        double r1920117 = b;
        double r1920118 = c;
        double r1920119 = r1920117 - r1920118;
        double r1920120 = 5.0;
        double r1920121 = 6.0;
        double r1920122 = r1920120 / r1920121;
        double r1920123 = r1920112 + r1920122;
        double r1920124 = 3.0;
        double r1920125 = r1920111 * r1920124;
        double r1920126 = r1920109 / r1920125;
        double r1920127 = r1920123 - r1920126;
        double r1920128 = r1920119 * r1920127;
        double r1920129 = r1920116 - r1920128;
        double r1920130 = r1920109 * r1920129;
        double r1920131 = exp(r1920130);
        double r1920132 = r1920108 * r1920131;
        double r1920133 = r1920107 + r1920132;
        double r1920134 = r1920107 / r1920133;
        return r1920134;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1920135 = x;
        double r1920136 = y;
        double r1920137 = a;
        double r1920138 = t;
        double r1920139 = r1920137 + r1920138;
        double r1920140 = sqrt(r1920139);
        double r1920141 = cbrt(r1920138);
        double r1920142 = r1920140 / r1920141;
        double r1920143 = z;
        double r1920144 = r1920141 * r1920141;
        double r1920145 = r1920143 / r1920144;
        double r1920146 = r1920142 * r1920145;
        double r1920147 = 5.0;
        double r1920148 = 6.0;
        double r1920149 = r1920147 / r1920148;
        double r1920150 = r1920137 + r1920149;
        double r1920151 = 2.0;
        double r1920152 = 3.0;
        double r1920153 = r1920138 * r1920152;
        double r1920154 = r1920151 / r1920153;
        double r1920155 = r1920150 - r1920154;
        double r1920156 = b;
        double r1920157 = c;
        double r1920158 = r1920156 - r1920157;
        double r1920159 = r1920155 * r1920158;
        double r1920160 = r1920146 - r1920159;
        double r1920161 = r1920160 * r1920151;
        double r1920162 = exp(r1920161);
        double r1920163 = r1920136 * r1920162;
        double r1920164 = r1920135 + r1920163;
        double r1920165 = r1920135 / r1920164;
        return r1920165;
}

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 3.4

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

  3. Applied add-cube-cbrt3.4

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

  4. Applied times-frac2.4

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

  5. Final simplification2.4

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

Reproduce

herbie shell --seed 2019156 
(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)))))))))))