Average Error: 3.6 → 5.0
Time: 34.4s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 1.2987391929736296 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{\sqrt{t + a} \cdot z}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \left(\left(\frac{2.0}{t \cdot 3.0}\right)\right)\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \mathbf{elif}\;t \le 1.6282656461481258 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\left(\left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t}\right)\right) - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{\sqrt{t + a} \cdot z}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \left(\left(\frac{2.0}{t \cdot 3.0}\right)\right)\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \end{array}\]
\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)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le 1.2987391929736296 \cdot 10^{-301}:\\
\;\;\;\;\frac{x}{x + e^{\left(\frac{\sqrt{t + a} \cdot z}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \left(\left(\frac{2.0}{t \cdot 3.0}\right)\right)\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\

\mathbf{elif}\;t \le 1.6282656461481258 \cdot 10^{-106}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{\left(\left(\left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t}\right)\right) - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + e^{\left(\frac{\sqrt{t + a} \cdot z}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \left(\left(\frac{2.0}{t \cdot 3.0}\right)\right)\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3660094 = x;
        double r3660095 = y;
        double r3660096 = 2.0;
        double r3660097 = z;
        double r3660098 = t;
        double r3660099 = a;
        double r3660100 = r3660098 + r3660099;
        double r3660101 = sqrt(r3660100);
        double r3660102 = r3660097 * r3660101;
        double r3660103 = r3660102 / r3660098;
        double r3660104 = b;
        double r3660105 = c;
        double r3660106 = r3660104 - r3660105;
        double r3660107 = 5.0;
        double r3660108 = 6.0;
        double r3660109 = r3660107 / r3660108;
        double r3660110 = r3660099 + r3660109;
        double r3660111 = 3.0;
        double r3660112 = r3660098 * r3660111;
        double r3660113 = r3660096 / r3660112;
        double r3660114 = r3660110 - r3660113;
        double r3660115 = r3660106 * r3660114;
        double r3660116 = r3660103 - r3660115;
        double r3660117 = r3660096 * r3660116;
        double r3660118 = exp(r3660117);
        double r3660119 = r3660095 * r3660118;
        double r3660120 = r3660094 + r3660119;
        double r3660121 = r3660094 / r3660120;
        return r3660121;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3660122 = t;
        double r3660123 = 1.2987391929736296e-301;
        bool r3660124 = r3660122 <= r3660123;
        double r3660125 = x;
        double r3660126 = a;
        double r3660127 = r3660122 + r3660126;
        double r3660128 = sqrt(r3660127);
        double r3660129 = z;
        double r3660130 = r3660128 * r3660129;
        double r3660131 = r3660130 / r3660122;
        double r3660132 = 5.0;
        double r3660133 = 6.0;
        double r3660134 = r3660132 / r3660133;
        double r3660135 = r3660134 + r3660126;
        double r3660136 = 2.0;
        double r3660137 = 3.0;
        double r3660138 = r3660122 * r3660137;
        double r3660139 = r3660136 / r3660138;
        double r3660140 = /* ERROR: no posit support in C */;
        double r3660141 = /* ERROR: no posit support in C */;
        double r3660142 = r3660135 - r3660141;
        double r3660143 = b;
        double r3660144 = c;
        double r3660145 = r3660143 - r3660144;
        double r3660146 = r3660142 * r3660145;
        double r3660147 = r3660131 - r3660146;
        double r3660148 = r3660147 * r3660136;
        double r3660149 = exp(r3660148);
        double r3660150 = y;
        double r3660151 = r3660149 * r3660150;
        double r3660152 = r3660125 + r3660151;
        double r3660153 = r3660125 / r3660152;
        double r3660154 = 1.6282656461481258e-106;
        bool r3660155 = r3660122 <= r3660154;
        double r3660156 = /* ERROR: no posit support in C */;
        double r3660157 = /* ERROR: no posit support in C */;
        double r3660158 = r3660157 / r3660122;
        double r3660159 = /* ERROR: no posit support in C */;
        double r3660160 = /* ERROR: no posit support in C */;
        double r3660161 = r3660135 - r3660139;
        double r3660162 = r3660161 * r3660145;
        double r3660163 = r3660160 - r3660162;
        double r3660164 = r3660163 * r3660136;
        double r3660165 = exp(r3660164);
        double r3660166 = r3660150 * r3660165;
        double r3660167 = r3660125 + r3660166;
        double r3660168 = r3660125 / r3660167;
        double r3660169 = r3660155 ? r3660168 : r3660153;
        double r3660170 = r3660124 ? r3660153 : r3660169;
        return r3660170;
}

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

Derivation

  1. Split input into 2 regimes

  2. if t < 1.2987391929736296e-301 or 1.6282656461481258e-106 < t

    1. Initial program 2.9

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

    3. Applied insert-posit164.0

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

    if 1.2987391929736296e-301 < t < 1.6282656461481258e-106

    1. Initial program 6.3

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

    3. Applied insert-posit1612.6

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

    5. Applied insert-posit169.4

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(\left(\frac{\color{blue}{\left(\left(z \cdot \sqrt{t + a}\right)\right)}}{t}\right)\right) - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 1.2987391929736296 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{\sqrt{t + a} \cdot z}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \left(\left(\frac{2.0}{t \cdot 3.0}\right)\right)\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \mathbf{elif}\;t \le 1.6282656461481258 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\left(\left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t}\right)\right) - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{\sqrt{t + a} \cdot z}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \left(\left(\frac{2.0}{t \cdot 3.0}\right)\right)\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019138 
(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)))))))))))