Average Error: 3.8 → 3.1
Time: 32.9s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\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 r89800 = x;
        double r89801 = y;
        double r89802 = 2.0;
        double r89803 = z;
        double r89804 = t;
        double r89805 = a;
        double r89806 = r89804 + r89805;
        double r89807 = sqrt(r89806);
        double r89808 = r89803 * r89807;
        double r89809 = r89808 / r89804;
        double r89810 = b;
        double r89811 = c;
        double r89812 = r89810 - r89811;
        double r89813 = 5.0;
        double r89814 = 6.0;
        double r89815 = r89813 / r89814;
        double r89816 = r89805 + r89815;
        double r89817 = 3.0;
        double r89818 = r89804 * r89817;
        double r89819 = r89802 / r89818;
        double r89820 = r89816 - r89819;
        double r89821 = r89812 * r89820;
        double r89822 = r89809 - r89821;
        double r89823 = r89802 * r89822;
        double r89824 = exp(r89823);
        double r89825 = r89801 * r89824;
        double r89826 = r89800 + r89825;
        double r89827 = r89800 / r89826;
        return r89827;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r89828 = x;
        double r89829 = y;
        double r89830 = 2.0;
        double r89831 = z;
        double r89832 = t;
        double r89833 = a;
        double r89834 = r89832 + r89833;
        double r89835 = sqrt(r89834);
        double r89836 = r89832 / r89835;
        double r89837 = r89831 / r89836;
        double r89838 = b;
        double r89839 = c;
        double r89840 = r89838 - r89839;
        double r89841 = 5.0;
        double r89842 = 6.0;
        double r89843 = r89841 / r89842;
        double r89844 = r89833 + r89843;
        double r89845 = 3.0;
        double r89846 = r89832 * r89845;
        double r89847 = r89830 / r89846;
        double r89848 = r89844 - r89847;
        double r89849 = r89840 * r89848;
        double r89850 = r89837 - r89849;
        double r89851 = r89830 * r89850;
        double r89852 = exp(r89851);
        double r89853 = r89829 * r89852;
        double r89854 = r89828 + r89853;
        double r89855 = r89828 / r89854;
        return r89855;
}

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 3.8

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

  3. Applied associate-/l*3.1

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

  4. Final simplification3.1

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

Reproduce

herbie shell --seed 2019305 
(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)))))))))))