Average Error: 4.0 → 3.3
Time: 49.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)} + x}\]
\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}{y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{a + t}}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)} + x}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3104721 = x;
        double r3104722 = y;
        double r3104723 = 2.0;
        double r3104724 = z;
        double r3104725 = t;
        double r3104726 = a;
        double r3104727 = r3104725 + r3104726;
        double r3104728 = sqrt(r3104727);
        double r3104729 = r3104724 * r3104728;
        double r3104730 = r3104729 / r3104725;
        double r3104731 = b;
        double r3104732 = c;
        double r3104733 = r3104731 - r3104732;
        double r3104734 = 5.0;
        double r3104735 = 6.0;
        double r3104736 = r3104734 / r3104735;
        double r3104737 = r3104726 + r3104736;
        double r3104738 = 3.0;
        double r3104739 = r3104725 * r3104738;
        double r3104740 = r3104723 / r3104739;
        double r3104741 = r3104737 - r3104740;
        double r3104742 = r3104733 * r3104741;
        double r3104743 = r3104730 - r3104742;
        double r3104744 = r3104723 * r3104743;
        double r3104745 = exp(r3104744);
        double r3104746 = r3104722 * r3104745;
        double r3104747 = r3104721 + r3104746;
        double r3104748 = r3104721 / r3104747;
        return r3104748;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r3104749 = x;
        double r3104750 = y;
        double r3104751 = 2.0;
        double r3104752 = z;
        double r3104753 = t;
        double r3104754 = a;
        double r3104755 = r3104754 + r3104753;
        double r3104756 = sqrt(r3104755);
        double r3104757 = r3104753 / r3104756;
        double r3104758 = r3104752 / r3104757;
        double r3104759 = 5.0;
        double r3104760 = 6.0;
        double r3104761 = r3104759 / r3104760;
        double r3104762 = r3104761 + r3104754;
        double r3104763 = 3.0;
        double r3104764 = r3104753 * r3104763;
        double r3104765 = r3104751 / r3104764;
        double r3104766 = r3104762 - r3104765;
        double r3104767 = b;
        double r3104768 = c;
        double r3104769 = r3104767 - r3104768;
        double r3104770 = r3104766 * r3104769;
        double r3104771 = r3104758 - r3104770;
        double r3104772 = r3104751 * r3104771;
        double r3104773 = exp(r3104772);
        double r3104774 = r3104750 * r3104773;
        double r3104775 = r3104774 + r3104749;
        double r3104776 = r3104749 / r3104775;
        return r3104776;
}

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 4.0

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

  3. Applied associate-/l*3.3

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

  4. Final simplification3.3

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

Reproduce

herbie shell --seed 2019144 
(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)))))))))))