Average Error: 3.8 → 3.8
Time: 10.9s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}\right)}}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \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 \log \left(e^{\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)}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r77672 = x;
        double r77673 = y;
        double r77674 = 2.0;
        double r77675 = z;
        double r77676 = t;
        double r77677 = a;
        double r77678 = r77676 + r77677;
        double r77679 = sqrt(r77678);
        double r77680 = r77675 * r77679;
        double r77681 = r77680 / r77676;
        double r77682 = b;
        double r77683 = c;
        double r77684 = r77682 - r77683;
        double r77685 = 5.0;
        double r77686 = 6.0;
        double r77687 = r77685 / r77686;
        double r77688 = r77677 + r77687;
        double r77689 = 3.0;
        double r77690 = r77676 * r77689;
        double r77691 = r77674 / r77690;
        double r77692 = r77688 - r77691;
        double r77693 = r77684 * r77692;
        double r77694 = r77681 - r77693;
        double r77695 = r77674 * r77694;
        double r77696 = exp(r77695);
        double r77697 = r77673 * r77696;
        double r77698 = r77672 + r77697;
        double r77699 = r77672 / r77698;
        return r77699;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r77700 = x;
        double r77701 = y;
        double r77702 = 2.0;
        double r77703 = z;
        double r77704 = t;
        double r77705 = a;
        double r77706 = r77704 + r77705;
        double r77707 = sqrt(r77706);
        double r77708 = r77703 * r77707;
        double r77709 = r77708 / r77704;
        double r77710 = b;
        double r77711 = c;
        double r77712 = r77710 - r77711;
        double r77713 = 5.0;
        double r77714 = 6.0;
        double r77715 = r77713 / r77714;
        double r77716 = r77705 + r77715;
        double r77717 = 3.0;
        double r77718 = r77704 * r77717;
        double r77719 = r77702 / r77718;
        double r77720 = r77716 - r77719;
        double r77721 = r77712 * r77720;
        double r77722 = r77709 - r77721;
        double r77723 = exp(r77722);
        double r77724 = log(r77723);
        double r77725 = r77702 * r77724;
        double r77726 = exp(r77725);
        double r77727 = r77701 * r77726;
        double r77728 = r77700 + r77727;
        double r77729 = r77700 / r77728;
        return r77729;
}

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 add-log-exp8.0

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

  4. Applied add-log-exp16.3

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

  5. Applied diff-log16.3

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

  6. Simplified3.8

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

  7. Final simplification3.8

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

Reproduce

herbie shell --seed 2020001 
(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)))))))))))