Average Error: 4.2 → 3.4
Time: 33.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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}{\frac{t}{\sqrt{t + a}}} - \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 r86835 = x;
        double r86836 = y;
        double r86837 = 2.0;
        double r86838 = z;
        double r86839 = t;
        double r86840 = a;
        double r86841 = r86839 + r86840;
        double r86842 = sqrt(r86841);
        double r86843 = r86838 * r86842;
        double r86844 = r86843 / r86839;
        double r86845 = b;
        double r86846 = c;
        double r86847 = r86845 - r86846;
        double r86848 = 5.0;
        double r86849 = 6.0;
        double r86850 = r86848 / r86849;
        double r86851 = r86840 + r86850;
        double r86852 = 3.0;
        double r86853 = r86839 * r86852;
        double r86854 = r86837 / r86853;
        double r86855 = r86851 - r86854;
        double r86856 = r86847 * r86855;
        double r86857 = r86844 - r86856;
        double r86858 = r86837 * r86857;
        double r86859 = exp(r86858);
        double r86860 = r86836 * r86859;
        double r86861 = r86835 + r86860;
        double r86862 = r86835 / r86861;
        return r86862;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r86863 = x;
        double r86864 = y;
        double r86865 = 2.0;
        double r86866 = z;
        double r86867 = t;
        double r86868 = a;
        double r86869 = r86867 + r86868;
        double r86870 = sqrt(r86869);
        double r86871 = r86867 / r86870;
        double r86872 = r86866 / r86871;
        double r86873 = b;
        double r86874 = c;
        double r86875 = r86873 - r86874;
        double r86876 = 5.0;
        double r86877 = 6.0;
        double r86878 = r86876 / r86877;
        double r86879 = r86868 + r86878;
        double r86880 = 3.0;
        double r86881 = r86867 * r86880;
        double r86882 = r86865 / r86881;
        double r86883 = r86879 - r86882;
        double r86884 = r86875 * r86883;
        double r86885 = r86872 - r86884;
        double r86886 = r86865 * r86885;
        double r86887 = exp(r86886);
        double r86888 = r86864 * r86887;
        double r86889 = r86863 + r86888;
        double r86890 = r86863 / r86889;
        return r86890;
}

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 associate-/l*3.4

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

  4. Final simplification3.4

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

Reproduce

herbie shell --seed 2019326 
(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)))))))))))