Average Error: 4.0 → 6.4
Time: 10.3s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.96807863435912862 \cdot 10^{-97} \lor \neg \left(t \le 4.7438821099503913 \cdot 10^{-240}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(b + c\right) + \left(-\left(t \cdot \left(b \cdot b - c \cdot c\right)\right) \cdot \left(a + \left(\frac{5}{6} - \frac{2}{t \cdot 3}\right)\right)\right)}{t \cdot \left(b + c\right)}}}\\ \end{array}\]
\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)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -6.96807863435912862 \cdot 10^{-97} \lor \neg \left(t \le 4.7438821099503913 \cdot 10^{-240}\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) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(b + c\right) + \left(-\left(t \cdot \left(b \cdot b - c \cdot c\right)\right) \cdot \left(a + \left(\frac{5}{6} - \frac{2}{t \cdot 3}\right)\right)\right)}{t \cdot \left(b + c\right)}}}\\

\end{array}
double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))))));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	double VAR;
	if (((t <= -6.968078634359129e-97) || !(t <= 4.7438821099503913e-240))) {
		VAR = (x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - cbrt(pow((2.0 / (t * 3.0)), 3.0))))))))));
	} else {
		VAR = (x / (x + (y * exp((2.0 * ((((z * sqrt((t + a))) * (b + c)) + -((t * ((b * b) - (c * c))) * (a + ((5.0 / 6.0) - (2.0 / (t * 3.0)))))) / (t * (b + c))))))));
	}
	return VAR;
}

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. Split input into 2 regimes

  2. if t < -6.968078634359129e-97 or 4.7438821099503913e-240 < t

    1. Initial program 2.7

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

    3. Applied add-cbrt-cube2.7

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

    4. Applied add-cbrt-cube4.8

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

    5. Applied cbrt-unprod4.8

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

    6. Applied add-cbrt-cube4.8

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

    7. Applied cbrt-undiv5.0

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

    8. Simplified5.0

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

    if -6.968078634359129e-97 < t < 4.7438821099503913e-240

    1. Initial program 9.3

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

    3. Applied add-cbrt-cube9.3

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

    4. Applied add-cbrt-cube16.2

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

    5. Applied cbrt-unprod16.2

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

    6. Applied add-cbrt-cube16.2

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

    7. Applied cbrt-undiv16.4

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

    8. Simplified16.4

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

    10. Applied flip--21.6

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

    11. Applied associate-*l/21.7

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

    12. Applied frac-sub20.6

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

    13. Simplified12.5

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

  4. Final simplification6.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.96807863435912862 \cdot 10^{-97} \lor \neg \left(t \le 4.7438821099503913 \cdot 10^{-240}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(b + c\right) + \left(-\left(t \cdot \left(b \cdot b - c \cdot c\right)\right) \cdot \left(a + \left(\frac{5}{6} - \frac{2}{t \cdot 3}\right)\right)\right)}{t \cdot \left(b + c\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 
(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)))))))))))