Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I

Percentage Accurate: 93.6% → 97.1%

Time: 20.6s

Alternatives: 14

Speedup: 0.7×

Specification

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

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)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 93.6% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

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)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{t + a}\\ \mathbf{if}\;\frac{z \cdot t\_1}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, t\_1, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{-x}, -1\right) \cdot \left(-x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (sqrt (+ t a))))
   (if (<=
        (+ (/ (* z t_1) t) (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))
        INFINITY)
     (/
      x
      (*
       (fma
        y
        (/
         (exp
          (*
           2.0
           (fma
            (/ z t)
            t_1
            (*
             (+ a (+ 0.8333333333333334 (/ -0.6666666666666666 t)))
             (- c b)))))
         (- x))
        -1.0)
       (- x)))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = sqrt((t + a));
	double tmp;
	if ((((z * t_1) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= ((double) INFINITY)) {
		tmp = x / (fma(y, (exp((2.0 * fma((z / t), t_1, ((a + (0.8333333333333334 + (-0.6666666666666666 / t))) * (c - b))))) / -x), -1.0) * -x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = sqrt(Float64(t + a))
	tmp = 0.0
	if (Float64(Float64(Float64(z * t_1) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0))))) <= Inf)
		tmp = Float64(x / Float64(fma(y, Float64(exp(Float64(2.0 * fma(Float64(z / t), t_1, Float64(Float64(a + Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t))) * Float64(c - b))))) / Float64(-x)), -1.0) * Float64(-x)));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(N[(z * t$95$1), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x / N[(N[(y * N[(N[Exp[N[(2.0 * N[(N[(z / t), $MachinePrecision] * t$95$1 + N[(N[(a + N[(0.8333333333333334 + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / (-x)), $MachinePrecision] + -1.0), $MachinePrecision] * (-x)), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 98.8%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 99.2%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   if +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 0.0%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 18.2%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 91.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{-x}, -1\right) \cdot \left(-x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\\ t_2 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ t_3 := 0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+284}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(2, t\_1, \left(b \cdot -1.3333333333333333\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot t\_1\right)\right), -1.6666666666666667 + a \cdot -2\right), 1\right), x\right)}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(c, 2 \cdot \mathsf{fma}\left(c, y \cdot \left(t\_3 \cdot t\_3\right), y \cdot t\_3\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (+ a 0.8333333333333334) (+ a 0.8333333333333334)))
        (t_2
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))
        (t_3 (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t)))))
   (if (<= t_2 -1e+52)
     1.0
     (if (<= t_2 5e+98)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (* c (+ a (+ 0.8333333333333334 (/ -0.6666666666666666 t)))))))))
       (if (<= t_2 4e+284)
         (/
          x
          (fma
           y
           (fma
            b
            (fma
             b
             (fma
              2.0
              t_1
              (* (* b -1.3333333333333333) (* (+ a 0.8333333333333334) t_1)))
             (+ -1.6666666666666667 (* a -2.0)))
            1.0)
           x))
         (if (<= t_2 INFINITY)
           (/ x (+ x (fma c (* 2.0 (fma c (* y (* t_3 t_3)) (* y t_3))) y)))
           1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a + 0.8333333333333334) * (a + 0.8333333333333334);
	double t_2 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double t_3 = 0.8333333333333334 + (a - (0.6666666666666666 / t));
	double tmp;
	if (t_2 <= -1e+52) {
		tmp = 1.0;
	} else if (t_2 <= 5e+98) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else if (t_2 <= 4e+284) {
		tmp = x / fma(y, fma(b, fma(b, fma(2.0, t_1, ((b * -1.3333333333333333) * ((a + 0.8333333333333334) * t_1))), (-1.6666666666666667 + (a * -2.0))), 1.0), x);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = x / (x + fma(c, (2.0 * fma(c, (y * (t_3 * t_3)), (y * t_3))), y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a + 0.8333333333333334) * Float64(a + 0.8333333333333334))
	t_2 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	t_3 = Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t)))
	tmp = 0.0
	if (t_2 <= -1e+52)
		tmp = 1.0;
	elseif (t_2 <= 5e+98)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t)))))))));
	elseif (t_2 <= 4e+284)
		tmp = Float64(x / fma(y, fma(b, fma(b, fma(2.0, t_1, Float64(Float64(b * -1.3333333333333333) * Float64(Float64(a + 0.8333333333333334) * t_1))), Float64(-1.6666666666666667 + Float64(a * -2.0))), 1.0), x));
	elseif (t_2 <= Inf)
		tmp = Float64(x / Float64(x + fma(c, Float64(2.0 * fma(c, Float64(y * Float64(t_3 * t_3)), Float64(y * t_3))), y)));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+52], 1.0, If[LessEqual[t$95$2, 5e+98], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(0.8333333333333334 + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+284], N[(x / N[(y * N[(b * N[(b * N[(2.0 * t$95$1 + N[(N[(b * -1.3333333333333333), $MachinePrecision] * N[(N[(a + 0.8333333333333334), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.6666666666666667 + N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(x / N[(x + N[(c * N[(2.0 * N[(c * N[(y * N[(t$95$3 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -9.9999999999999999e51 or +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 89.1%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 91.8%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.2%

      \[\leadsto \color{blue}{1} \]

   if -9.9999999999999999e51 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 4.9999999999999998e98

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 93.6

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 93.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   if 4.9999999999999998e98 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 4.00000000000000032e284

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 70.0

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 70.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in t around inf

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}, x\right)}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{\color{blue}{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{-2 \cdot \color{blue}{\left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      6. lower-+.f64 57.1

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \color{blue}{\left(0.8333333333333334 + a\right)}\right)}, x\right)} \]

   8. Applied rewrites 57.1%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \left(0.8333333333333334 + a\right)\right)}, x\right)}} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{1 + b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)}, x\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right) + 1}, x\right)} \]

       2. lower-fma.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(b, -2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right), 1\right)}, x\right)} \]

   11. Applied rewrites 75.8%

       \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(2, \left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right), \left(-1.3333333333333333 \cdot b\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right)\right)\right)\right), -1.6666666666666667 + -2 \cdot a\right), 1\right)}, x\right)} \]

   if 4.00000000000000032e284 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 97.1%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 66.0

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 66.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in c around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + c \cdot \left(2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + \left(y + c \cdot \left(2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + \color{blue}{\left(c \cdot \left(2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right) + y\right)}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(c, 2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right), y\right)}} \]

   8. Applied rewrites 79.6%

      \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(c, 2 \cdot \mathsf{fma}\left(c, y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -1 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 4 \cdot 10^{+284}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(2, \left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right), \left(b \cdot -1.3333333333333333\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right)\right)\right), -1.6666666666666667 + a \cdot -2\right), 1\right), x\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(c, 2 \cdot \mathsf{fma}\left(c, y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\\ t_2 := 0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\\ t_3 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}, x\right)}\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+284}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(2, t\_1, \left(b \cdot -1.3333333333333333\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot t\_1\right)\right), -1.6666666666666667 + a \cdot -2\right), 1\right), x\right)}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(c, 2 \cdot \mathsf{fma}\left(c, y \cdot \left(t\_2 \cdot t\_2\right), y \cdot t\_2\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (+ a 0.8333333333333334) (+ a 0.8333333333333334)))
        (t_2 (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t))))
        (t_3
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_3 -1e+52)
     1.0
     (if (<= t_3 5e+98)
       (/ x (fma y (exp (* 2.0 (* c (+ a 0.8333333333333334)))) x))
       (if (<= t_3 4e+284)
         (/
          x
          (fma
           y
           (fma
            b
            (fma
             b
             (fma
              2.0
              t_1
              (* (* b -1.3333333333333333) (* (+ a 0.8333333333333334) t_1)))
             (+ -1.6666666666666667 (* a -2.0)))
            1.0)
           x))
         (if (<= t_3 INFINITY)
           (/ x (+ x (fma c (* 2.0 (fma c (* y (* t_2 t_2)) (* y t_2))) y)))
           1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a + 0.8333333333333334) * (a + 0.8333333333333334);
	double t_2 = 0.8333333333333334 + (a - (0.6666666666666666 / t));
	double t_3 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_3 <= -1e+52) {
		tmp = 1.0;
	} else if (t_3 <= 5e+98) {
		tmp = x / fma(y, exp((2.0 * (c * (a + 0.8333333333333334)))), x);
	} else if (t_3 <= 4e+284) {
		tmp = x / fma(y, fma(b, fma(b, fma(2.0, t_1, ((b * -1.3333333333333333) * ((a + 0.8333333333333334) * t_1))), (-1.6666666666666667 + (a * -2.0))), 1.0), x);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = x / (x + fma(c, (2.0 * fma(c, (y * (t_2 * t_2)), (y * t_2))), y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a + 0.8333333333333334) * Float64(a + 0.8333333333333334))
	t_2 = Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t)))
	t_3 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_3 <= -1e+52)
		tmp = 1.0;
	elseif (t_3 <= 5e+98)
		tmp = Float64(x / fma(y, exp(Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334)))), x));
	elseif (t_3 <= 4e+284)
		tmp = Float64(x / fma(y, fma(b, fma(b, fma(2.0, t_1, Float64(Float64(b * -1.3333333333333333) * Float64(Float64(a + 0.8333333333333334) * t_1))), Float64(-1.6666666666666667 + Float64(a * -2.0))), 1.0), x));
	elseif (t_3 <= Inf)
		tmp = Float64(x / Float64(x + fma(c, Float64(2.0 * fma(c, Float64(y * Float64(t_2 * t_2)), Float64(y * t_2))), y)));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+52], 1.0, If[LessEqual[t$95$3, 5e+98], N[(x / N[(y * N[Exp[N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+284], N[(x / N[(y * N[(b * N[(b * N[(2.0 * t$95$1 + N[(N[(b * -1.3333333333333333), $MachinePrecision] * N[(N[(a + 0.8333333333333334), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.6666666666666667 + N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(x / N[(x + N[(c * N[(2.0 * N[(c * N[(y * N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -9.9999999999999999e51 or +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 89.1%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 91.8%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.2%

      \[\leadsto \color{blue}{1} \]

   if -9.9999999999999999e51 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 4.9999999999999998e98

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 93.6

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 93.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in t around inf

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}, x\right)}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{\color{blue}{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{2 \cdot \color{blue}{\left(c \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      6. lower-+.f64 85.0

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{2 \cdot \left(c \cdot \color{blue}{\left(0.8333333333333334 + a\right)}\right)}, x\right)} \]

   8. Applied rewrites 85.0%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}, x\right)}} \]

   if 4.9999999999999998e98 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 4.00000000000000032e284

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 70.0

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 70.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in t around inf

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}, x\right)}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{\color{blue}{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{-2 \cdot \color{blue}{\left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      6. lower-+.f64 57.1

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \color{blue}{\left(0.8333333333333334 + a\right)}\right)}, x\right)} \]

   8. Applied rewrites 57.1%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \left(0.8333333333333334 + a\right)\right)}, x\right)}} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{1 + b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)}, x\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right) + 1}, x\right)} \]

       2. lower-fma.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(b, -2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right), 1\right)}, x\right)} \]

   11. Applied rewrites 75.8%

       \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(2, \left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right), \left(-1.3333333333333333 \cdot b\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right)\right)\right)\right), -1.6666666666666667 + -2 \cdot a\right), 1\right)}, x\right)} \]

   if 4.00000000000000032e284 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 97.1%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 66.0

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 66.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in c around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + c \cdot \left(2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + \left(y + c \cdot \left(2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + \color{blue}{\left(c \cdot \left(2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right) + y\right)}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(c, 2 \cdot \left(c \cdot \left(y \cdot {\left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}^{2}\right)\right) + 2 \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right), y\right)}} \]

   8. Applied rewrites 79.6%

      \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(c, 2 \cdot \mathsf{fma}\left(c, y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -1 \cdot 10^{+52}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}, x\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 4 \cdot 10^{+284}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(2, \left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right), \left(b \cdot -1.3333333333333333\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right)\right)\right), -1.6666666666666667 + a \cdot -2\right), 1\right), x\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(c, 2 \cdot \mathsf{fma}\left(c, y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(2, \left(a + 0.8333333333333334\right) \cdot \left(c \cdot y\right), y\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(x - y\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \frac{c}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -4e+19)
     1.0
     (if (<= t_1 5e+48)
       (/ x (+ x (fma 2.0 (* (+ a 0.8333333333333334) (* c y)) y)))
       (if (<= t_1 2e+303)
         (* (- x y) (/ x (* (+ x y) (- x y))))
         (if (<= t_1 INFINITY)
           (/ x (* y (fma -1.3333333333333333 (/ c t) 1.0)))
           1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -4e+19) {
		tmp = 1.0;
	} else if (t_1 <= 5e+48) {
		tmp = x / (x + fma(2.0, ((a + 0.8333333333333334) * (c * y)), y));
	} else if (t_1 <= 2e+303) {
		tmp = (x - y) * (x / ((x + y) * (x - y)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x / (y * fma(-1.3333333333333333, (c / t), 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -4e+19)
		tmp = 1.0;
	elseif (t_1 <= 5e+48)
		tmp = Float64(x / Float64(x + fma(2.0, Float64(Float64(a + 0.8333333333333334) * Float64(c * y)), y)));
	elseif (t_1 <= 2e+303)
		tmp = Float64(Float64(x - y) * Float64(x / Float64(Float64(x + y) * Float64(x - y))));
	elseif (t_1 <= Inf)
		tmp = Float64(x / Float64(y * fma(-1.3333333333333333, Float64(c / t), 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+19], 1.0, If[LessEqual[t$95$1, 5e+48], N[(x / N[(x + N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c * y), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+303], N[(N[(x - y), $MachinePrecision] * N[(x / N[(N[(x + y), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(x / N[(y * N[(-1.3333333333333333 * N[(c / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -4e19 or +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 89.5%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.1%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.3%

      \[\leadsto \color{blue}{1} \]

   if -4e19 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 4.99999999999999973e48

   1. Initial program 99.9%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 94.8

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 94.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in c around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right) + y\right)}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(2, c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right), y\right)}} \]

      4. associate-*r* N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right)} \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right), y\right)} \]

      7. associate--l+ N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \color{blue}{\left(a - \frac{2}{3} \cdot \frac{1}{t}\right)}\right), y\right)} \]

      10. associate-*r/ N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right), y\right)} \]

      11. metadata-eval N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \frac{\color{blue}{\frac{2}{3}}}{t}\right)\right), y\right)} \]

      12. lower-/.f64 84.9

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \color{blue}{\frac{0.6666666666666666}{t}}\right)\right), y\right)} \]

   8. Applied rewrites 84.9%

      \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right), y\right)}} \]

   9. Taylor expanded in t around inf

      \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + a\right)}, y\right)} \]
   10. Step-by-step derivation

       1. lower-+.f64 84.9

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(0.8333333333333334 + a\right)}, y\right)} \]

   11. Applied rewrites 84.9%

       \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(0.8333333333333334 + a\right)}, y\right)} \]

   if 4.99999999999999973e48 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 2e303

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 61.7

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 61.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 18.4

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 18.4%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   9. Step-by-step derivation

      1. flip-+ N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{x \cdot x - y \cdot y}{x - y}}} \]

      2. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y}} \cdot \left(x - y\right) \]

      5. difference-of-squares N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \left(x - y\right)}} \cdot \left(x - y\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right)} \cdot \left(x - y\right)} \cdot \left(x - y\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \left(x - y\right)}} \cdot \left(x - y\right) \]

      8. lower--.f64 N/A

         \[\leadsto \frac{x}{\left(x + y\right) \cdot \color{blue}{\left(x - y\right)}} \cdot \left(x - y\right) \]

      9. lower--.f64 58.7

         \[\leadsto \frac{x}{\left(x + y\right) \cdot \left(x - y\right)} \cdot \color{blue}{\left(x - y\right)} \]

   10. Applied rewrites 58.7%

       \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x - y\right)} \cdot \left(x - y\right)} \]

   if 2e303 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 96.5%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 63.9

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 63.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in c around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right) + y\right)}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(2, c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right), y\right)}} \]

      4. associate-*r* N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right)} \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right), y\right)} \]

      7. associate--l+ N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \color{blue}{\left(a - \frac{2}{3} \cdot \frac{1}{t}\right)}\right), y\right)} \]

      10. associate-*r/ N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right), y\right)} \]

      11. metadata-eval N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \frac{\color{blue}{\frac{2}{3}}}{t}\right)\right), y\right)} \]

      12. lower-/.f64 59.2

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \color{blue}{\frac{0.6666666666666666}{t}}\right)\right), y\right)} \]

   8. Applied rewrites 59.2%

      \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right), y\right)}} \]

   9. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{\frac{-2}{3}}{t}}, y\right)} \]
   10. Step-by-step derivation

       1. lower-/.f64 53.8

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{-0.6666666666666666}{t}}, y\right)} \]

   11. Applied rewrites 53.8%

       \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{-0.6666666666666666}{t}}, y\right)} \]

   12. Taylor expanded in y around inf

       \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + \frac{-4}{3} \cdot \frac{c}{t}\right)}} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + \frac{-4}{3} \cdot \frac{c}{t}\right)}} \]

       2. +-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{\left(\frac{-4}{3} \cdot \frac{c}{t} + 1\right)}} \]

       3. lower-fma.f64 N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{\mathsf{fma}\left(\frac{-4}{3}, \frac{c}{t}, 1\right)}} \]

       4. lower-/.f64 65.8

          \[\leadsto \frac{x}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \color{blue}{\frac{c}{t}}, 1\right)} \]

   14. Applied rewrites 65.8%

       \[\leadsto \frac{x}{\color{blue}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \frac{c}{t}, 1\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(2, \left(a + 0.8333333333333334\right) \cdot \left(c \cdot y\right), y\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(x - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \frac{c}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(2, a \cdot c, 1\right)}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(x - y\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \frac{c}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -4e+19)
     1.0
     (if (<= t_1 5e+48)
       (/ x (+ x (* y (fma 2.0 (* a c) 1.0))))
       (if (<= t_1 2e+303)
         (* (- x y) (/ x (* (+ x y) (- x y))))
         (if (<= t_1 INFINITY)
           (/ x (* y (fma -1.3333333333333333 (/ c t) 1.0)))
           1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -4e+19) {
		tmp = 1.0;
	} else if (t_1 <= 5e+48) {
		tmp = x / (x + (y * fma(2.0, (a * c), 1.0)));
	} else if (t_1 <= 2e+303) {
		tmp = (x - y) * (x / ((x + y) * (x - y)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x / (y * fma(-1.3333333333333333, (c / t), 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -4e+19)
		tmp = 1.0;
	elseif (t_1 <= 5e+48)
		tmp = Float64(x / Float64(x + Float64(y * fma(2.0, Float64(a * c), 1.0))));
	elseif (t_1 <= 2e+303)
		tmp = Float64(Float64(x - y) * Float64(x / Float64(Float64(x + y) * Float64(x - y))));
	elseif (t_1 <= Inf)
		tmp = Float64(x / Float64(y * fma(-1.3333333333333333, Float64(c / t), 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+19], 1.0, If[LessEqual[t$95$1, 5e+48], N[(x / N[(x + N[(y * N[(2.0 * N[(a * c), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+303], N[(N[(x - y), $MachinePrecision] * N[(x / N[(N[(x + y), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(x / N[(y * N[(-1.3333333333333333 * N[(c / t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -4e19 or +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 89.5%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.1%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.3%

      \[\leadsto \color{blue}{1} \]

   if -4e19 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 4.99999999999999973e48

   1. Initial program 99.9%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 94.8

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 94.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{2 \cdot \left(a \cdot c\right)}}} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{2 \cdot \left(a \cdot c\right)}}} \]

      2. lower-*.f64 90.8

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot c\right)}}} \]

   8. Applied rewrites 90.8%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{2 \cdot \left(a \cdot c\right)}}} \]

   9. Taylor expanded in a around 0

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(a \cdot c\right)\right)}} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(2 \cdot \left(a \cdot c\right) + 1\right)}} \]

       2. lower-fma.f64 N/A

          \[\leadsto \frac{x}{x + y \cdot \color{blue}{\mathsf{fma}\left(2, a \cdot c, 1\right)}} \]

       3. lower-*.f64 84.9

          \[\leadsto \frac{x}{x + y \cdot \mathsf{fma}\left(2, \color{blue}{a \cdot c}, 1\right)} \]

   11. Applied rewrites 84.9%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\mathsf{fma}\left(2, a \cdot c, 1\right)}} \]

   if 4.99999999999999973e48 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 2e303

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 61.7

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 61.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 18.4

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 18.4%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   9. Step-by-step derivation

      1. flip-+ N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{x \cdot x - y \cdot y}{x - y}}} \]

      2. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y}} \cdot \left(x - y\right) \]

      5. difference-of-squares N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \left(x - y\right)}} \cdot \left(x - y\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right)} \cdot \left(x - y\right)} \cdot \left(x - y\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \left(x - y\right)}} \cdot \left(x - y\right) \]

      8. lower--.f64 N/A

         \[\leadsto \frac{x}{\left(x + y\right) \cdot \color{blue}{\left(x - y\right)}} \cdot \left(x - y\right) \]

      9. lower--.f64 58.7

         \[\leadsto \frac{x}{\left(x + y\right) \cdot \left(x - y\right)} \cdot \color{blue}{\left(x - y\right)} \]

   10. Applied rewrites 58.7%

       \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x - y\right)} \cdot \left(x - y\right)} \]

   if 2e303 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 96.5%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 63.9

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 63.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in c around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right) + y\right)}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(2, c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right), y\right)}} \]

      4. associate-*r* N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right)} \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right), y\right)} \]

      7. associate--l+ N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \color{blue}{\left(a - \frac{2}{3} \cdot \frac{1}{t}\right)}\right), y\right)} \]

      10. associate-*r/ N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right), y\right)} \]

      11. metadata-eval N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \frac{\color{blue}{\frac{2}{3}}}{t}\right)\right), y\right)} \]

      12. lower-/.f64 59.2

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \color{blue}{\frac{0.6666666666666666}{t}}\right)\right), y\right)} \]

   8. Applied rewrites 59.2%

      \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right), y\right)}} \]

   9. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{\frac{-2}{3}}{t}}, y\right)} \]
   10. Step-by-step derivation

       1. lower-/.f64 53.8

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{-0.6666666666666666}{t}}, y\right)} \]

   11. Applied rewrites 53.8%

       \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{-0.6666666666666666}{t}}, y\right)} \]

   12. Taylor expanded in y around inf

       \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + \frac{-4}{3} \cdot \frac{c}{t}\right)}} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + \frac{-4}{3} \cdot \frac{c}{t}\right)}} \]

       2. +-commutative N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{\left(\frac{-4}{3} \cdot \frac{c}{t} + 1\right)}} \]

       3. lower-fma.f64 N/A

          \[\leadsto \frac{x}{y \cdot \color{blue}{\mathsf{fma}\left(\frac{-4}{3}, \frac{c}{t}, 1\right)}} \]

       4. lower-/.f64 65.8

          \[\leadsto \frac{x}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \color{blue}{\frac{c}{t}}, 1\right)} \]

   14. Applied rewrites 65.8%

       \[\leadsto \frac{x}{\color{blue}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \frac{c}{t}, 1\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(2, a \cdot c, 1\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(x - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{y \cdot \mathsf{fma}\left(-1.3333333333333333, \frac{c}{t}, 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + 2 \cdot \left(a \cdot \left(c \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -4e+19)
     1.0
     (if (<= t_1 5e+101)
       (/ x (+ x y))
       (if (<= t_1 INFINITY) (/ x (+ x (* 2.0 (* a (* c y))))) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -4e+19) {
		tmp = 1.0;
	} else if (t_1 <= 5e+101) {
		tmp = x / (x + y);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (2.0 * (a * (c * y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -4e+19) {
		tmp = 1.0;
	} else if (t_1 <= 5e+101) {
		tmp = x / (x + y);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (2.0 * (a * (c * y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))
	tmp = 0
	if t_1 <= -4e+19:
		tmp = 1.0
	elif t_1 <= 5e+101:
		tmp = x / (x + y)
	elif t_1 <= math.inf:
		tmp = x / (x + (2.0 * (a * (c * y))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -4e+19)
		tmp = 1.0;
	elseif (t_1 <= 5e+101)
		tmp = Float64(x / Float64(x + y));
	elseif (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(2.0 * Float64(a * Float64(c * y)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	tmp = 0.0;
	if (t_1 <= -4e+19)
		tmp = 1.0;
	elseif (t_1 <= 5e+101)
		tmp = x / (x + y);
	elseif (t_1 <= Inf)
		tmp = x / (x + (2.0 * (a * (c * y))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+19], 1.0, If[LessEqual[t$95$1, 5e+101], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(2.0 * N[(a * N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -4e19 or +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 89.5%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.1%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.3%

      \[\leadsto \color{blue}{1} \]

   if -4e19 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 4.99999999999999989e101

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 73.0

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 73.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 64.0

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 64.0%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   if 4.99999999999999989e101 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 98.2%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 64.4

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 64.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in c around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right) + y\right)}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(2, c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right), y\right)}} \]

      4. associate-*r* N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right)} \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right), y\right)} \]

      7. associate--l+ N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \color{blue}{\left(a - \frac{2}{3} \cdot \frac{1}{t}\right)}\right), y\right)} \]

      10. associate-*r/ N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right), y\right)} \]

      11. metadata-eval N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \frac{\color{blue}{\frac{2}{3}}}{t}\right)\right), y\right)} \]

      12. lower-/.f64 53.5

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \color{blue}{\frac{0.6666666666666666}{t}}\right)\right), y\right)} \]

   8. Applied rewrites 53.5%

      \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right), y\right)}} \]

   9. Taylor expanded in a around inf

      \[\leadsto \frac{x}{x + \color{blue}{2 \cdot \left(a \cdot \left(c \cdot y\right)\right)}} \]
   10. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \color{blue}{2 \cdot \left(a \cdot \left(c \cdot y\right)\right)}} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + 2 \cdot \color{blue}{\left(a \cdot \left(c \cdot y\right)\right)}} \]

       3. lower-*.f64 45.7

          \[\leadsto \frac{x}{x + 2 \cdot \left(a \cdot \color{blue}{\left(c \cdot y\right)}\right)} \]

   11. Applied rewrites 45.7%

       \[\leadsto \frac{x}{x + \color{blue}{2 \cdot \left(a \cdot \left(c \cdot y\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + 2 \cdot \left(a \cdot \left(c \cdot y\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 10^{+115}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;-0.75 \cdot \left(t \cdot \frac{x}{c \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -4e+19)
     1.0
     (if (<= t_1 1e+115)
       (/ x (+ x y))
       (if (<= t_1 INFINITY) (* -0.75 (* t (/ x (* c y)))) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -4e+19) {
		tmp = 1.0;
	} else if (t_1 <= 1e+115) {
		tmp = x / (x + y);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = -0.75 * (t * (x / (c * y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -4e+19) {
		tmp = 1.0;
	} else if (t_1 <= 1e+115) {
		tmp = x / (x + y);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = -0.75 * (t * (x / (c * y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))
	tmp = 0
	if t_1 <= -4e+19:
		tmp = 1.0
	elif t_1 <= 1e+115:
		tmp = x / (x + y)
	elif t_1 <= math.inf:
		tmp = -0.75 * (t * (x / (c * y)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -4e+19)
		tmp = 1.0;
	elseif (t_1 <= 1e+115)
		tmp = Float64(x / Float64(x + y));
	elseif (t_1 <= Inf)
		tmp = Float64(-0.75 * Float64(t * Float64(x / Float64(c * y))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	tmp = 0.0;
	if (t_1 <= -4e+19)
		tmp = 1.0;
	elseif (t_1 <= 1e+115)
		tmp = x / (x + y);
	elseif (t_1 <= Inf)
		tmp = -0.75 * (t * (x / (c * y)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+19], 1.0, If[LessEqual[t$95$1, 1e+115], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(-0.75 * N[(t * N[(x / N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -4e19 or +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 89.5%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.1%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.3%

      \[\leadsto \color{blue}{1} \]

   if -4e19 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 1e115

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 74.6

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 74.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 63.3

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 63.3%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   if 1e115 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 98.2%

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

   3. Taylor expanded in c around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + \frac{5}{6}\right)} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}} \]

      3. associate--l+ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      4. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \color{blue}{\left(a + \left(\frac{5}{6} - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}} \]

      5. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      6. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \color{blue}{\left(\frac{5}{6} + \left(\mathsf{neg}\left(\frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)}\right)\right)}} \]

      7. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{5}{6} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right)\right)\right)\right)}} \]

      8. metadata-eval N/A

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

      9. distribute-neg-frac N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 64.6

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \color{blue}{\frac{-0.6666666666666666}{t}}\right)\right)\right)}} \]

   5. Applied rewrites 64.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}} \]

   6. Taylor expanded in c around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{x + \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)\right) + y\right)}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(2, c \cdot \left(y \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right), y\right)}} \]

      4. associate-*r* N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)}, y\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \color{blue}{\left(c \cdot y\right)} \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right), y\right)} \]

      7. associate--l+ N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\left(\frac{5}{6} + \left(a - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}, y\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \color{blue}{\left(a - \frac{2}{3} \cdot \frac{1}{t}\right)}\right), y\right)} \]

      10. associate-*r/ N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \color{blue}{\frac{\frac{2}{3} \cdot 1}{t}}\right)\right), y\right)} \]

      11. metadata-eval N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(\frac{5}{6} + \left(a - \frac{\color{blue}{\frac{2}{3}}}{t}\right)\right), y\right)} \]

      12. lower-/.f64 53.6

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \color{blue}{\frac{0.6666666666666666}{t}}\right)\right), y\right)} \]

   8. Applied rewrites 53.6%

      \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right), y\right)}} \]

   9. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{\frac{-2}{3}}{t}}, y\right)} \]
   10. Step-by-step derivation

       1. lower-/.f64 48.4

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{-0.6666666666666666}{t}}, y\right)} \]

   11. Applied rewrites 48.4%

       \[\leadsto \frac{x}{x + \mathsf{fma}\left(2, \left(c \cdot y\right) \cdot \color{blue}{\frac{-0.6666666666666666}{t}}, y\right)} \]

   12. Taylor expanded in c around inf

       \[\leadsto \color{blue}{\frac{-3}{4} \cdot \frac{t \cdot x}{c \cdot y}} \]
   13. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{-3}{4} \cdot \frac{t \cdot x}{c \cdot y}} \]

       2. associate-/l* N/A

          \[\leadsto \frac{-3}{4} \cdot \color{blue}{\left(t \cdot \frac{x}{c \cdot y}\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \frac{-3}{4} \cdot \color{blue}{\left(t \cdot \frac{x}{c \cdot y}\right)} \]

       4. lower-/.f64 N/A

          \[\leadsto \frac{-3}{4} \cdot \left(t \cdot \color{blue}{\frac{x}{c \cdot y}}\right) \]

       5. *-commutative N/A

          \[\leadsto \frac{-3}{4} \cdot \left(t \cdot \frac{x}{\color{blue}{y \cdot c}}\right) \]

       6. lower-*.f64 45.4

          \[\leadsto -0.75 \cdot \left(t \cdot \frac{x}{\color{blue}{y \cdot c}}\right) \]

   14. Applied rewrites 45.4%

       \[\leadsto \color{blue}{-0.75 \cdot \left(t \cdot \frac{x}{y \cdot c}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -4 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 10^{+115}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;-0.75 \cdot \left(t \cdot \frac{x}{c \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(b \cdot 2, \left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right), -1.6666666666666667 + a \cdot -2\right), 1\right), x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      2e-36)
   (/
    x
    (fma
     y
     (fma
      b
      (fma
       (* b 2.0)
       (* (+ a 0.8333333333333334) (+ a 0.8333333333333334))
       (+ -1.6666666666666667 (* a -2.0)))
      1.0)
     x))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = x / fma(y, fma(b, fma((b * 2.0), ((a + 0.8333333333333334) * (a + 0.8333333333333334)), (-1.6666666666666667 + (a * -2.0))), 1.0), x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 2e-36)
		tmp = Float64(x / fma(y, fma(b, fma(Float64(b * 2.0), Float64(Float64(a + 0.8333333333333334) * Float64(a + 0.8333333333333334)), Float64(-1.6666666666666667 + Float64(a * -2.0))), 1.0), x));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-36], N[(x / N[(y * N[(b * N[(N[(b * 2.0), $MachinePrecision] * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision] + N[(-1.6666666666666667 + N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 1.9999999999999999e-36

   1. Initial program 98.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 66.1

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 66.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in t around inf

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}, x\right)}} \]

      3. lower-exp.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{e^{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{\color{blue}{-2 \cdot \left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{-2 \cdot \color{blue}{\left(b \cdot \left(\frac{5}{6} + a\right)\right)}}, x\right)} \]

      6. lower-+.f64 54.6

         \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \color{blue}{\left(0.8333333333333334 + a\right)}\right)}, x\right)} \]

   8. Applied rewrites 54.6%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{-2 \cdot \left(b \cdot \left(0.8333333333333334 + a\right)\right)}, x\right)}} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{1 + b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + 2 \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)}, x\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + 2 \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right) + 1}, x\right)} \]

       2. lower-fma.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(b, -2 \cdot \left(\frac{5}{6} + a\right) + 2 \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2}\right), 1\right)}, x\right)} \]

       3. +-commutative N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \color{blue}{2 \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2}\right) + -2 \cdot \left(\frac{5}{6} + a\right)}, 1\right), x\right)} \]

       4. associate-*r* N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \color{blue}{\left(2 \cdot b\right) \cdot {\left(\frac{5}{6} + a\right)}^{2}} + -2 \cdot \left(\frac{5}{6} + a\right), 1\right), x\right)} \]

       5. lower-fma.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(2 \cdot b, {\left(\frac{5}{6} + a\right)}^{2}, -2 \cdot \left(\frac{5}{6} + a\right)\right)}, 1\right), x\right)} \]

       6. lower-*.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(\color{blue}{2 \cdot b}, {\left(\frac{5}{6} + a\right)}^{2}, -2 \cdot \left(\frac{5}{6} + a\right)\right), 1\right), x\right)} \]

       7. unpow2 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \color{blue}{\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)}, -2 \cdot \left(\frac{5}{6} + a\right)\right), 1\right), x\right)} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \color{blue}{\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)}, -2 \cdot \left(\frac{5}{6} + a\right)\right), 1\right), x\right)} \]

       9. lower-+.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \color{blue}{\left(\frac{5}{6} + a\right)} \cdot \left(\frac{5}{6} + a\right), -2 \cdot \left(\frac{5}{6} + a\right)\right), 1\right), x\right)} \]

       10. lower-+.f64 N/A

           \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \left(\frac{5}{6} + a\right) \cdot \color{blue}{\left(\frac{5}{6} + a\right)}, -2 \cdot \left(\frac{5}{6} + a\right)\right), 1\right), x\right)} \]

       11. distribute-lft-in N/A

           \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right), \color{blue}{-2 \cdot \frac{5}{6} + -2 \cdot a}\right), 1\right), x\right)} \]

       12. metadata-eval N/A

           \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right), \color{blue}{\frac{-5}{3}} + -2 \cdot a\right), 1\right), x\right)} \]

       13. lower-+.f64 N/A

           \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right), \color{blue}{\frac{-5}{3} + -2 \cdot a}\right), 1\right), x\right)} \]

       14. lower-*.f64 68.4

           \[\leadsto \frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right), -1.6666666666666667 + \color{blue}{-2 \cdot a}\right), 1\right), x\right)} \]

   11. Applied rewrites 68.4%

       \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(2 \cdot b, \left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right), -1.6666666666666667 + -2 \cdot a\right), 1\right)}, x\right)} \]

   if 1.9999999999999999e-36 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 90.2%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.6%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \mathsf{fma}\left(b, \mathsf{fma}\left(b \cdot 2, \left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right), -1.6666666666666667 + a \cdot -2\right), 1\right), x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(a, \left(a \cdot 2\right) \cdot \left(y \cdot \left(b \cdot b\right)\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      2e-36)
   (/ x (+ x (fma a (* (* a 2.0) (* y (* b b))) y)))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = x / (x + fma(a, ((a * 2.0) * (y * (b * b))), y));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 2e-36)
		tmp = Float64(x / Float64(x + fma(a, Float64(Float64(a * 2.0) * Float64(y * Float64(b * b))), y)));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-36], N[(x / N[(x + N[(a * N[(N[(a * 2.0), $MachinePrecision] * N[(y * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 1.9999999999999999e-36

   1. Initial program 98.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 66.1

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 66.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in a around inf

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{-2 \cdot \left(a \cdot b\right)}}} \]
   7. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{-2 \cdot \left(a \cdot b\right)}}} \]

      2. lower-*.f64 43.4

         \[\leadsto \frac{x}{x + y \cdot e^{-2 \cdot \color{blue}{\left(a \cdot b\right)}}} \]

   8. Applied rewrites 43.4%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{-2 \cdot \left(a \cdot b\right)}}} \]

   9. Taylor expanded in a around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + a \cdot \left(-2 \cdot \left(b \cdot y\right) + 2 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{x + \left(y + a \cdot \left(-2 \cdot \left(b \cdot y\right) + 2 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)\right)\right)}} \]

       2. +-commutative N/A

          \[\leadsto \frac{x}{x + \color{blue}{\left(a \cdot \left(-2 \cdot \left(b \cdot y\right) + 2 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)\right) + y\right)}} \]

       3. lower-fma.f64 N/A

          \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(a, -2 \cdot \left(b \cdot y\right) + 2 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right), y\right)}} \]

       4. lower-fma.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \color{blue}{\mathsf{fma}\left(-2, b \cdot y, 2 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)\right)}, y\right)} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, \color{blue}{b \cdot y}, 2 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)\right), y\right)} \]

       6. associate-*r* N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, b \cdot y, \color{blue}{\left(2 \cdot a\right) \cdot \left({b}^{2} \cdot y\right)}\right), y\right)} \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, b \cdot y, \color{blue}{\left(2 \cdot a\right) \cdot \left({b}^{2} \cdot y\right)}\right), y\right)} \]

       8. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, b \cdot y, \color{blue}{\left(2 \cdot a\right)} \cdot \left({b}^{2} \cdot y\right)\right), y\right)} \]

       9. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, b \cdot y, \left(2 \cdot a\right) \cdot \color{blue}{\left({b}^{2} \cdot y\right)}\right), y\right)} \]

       10. unpow2 N/A

           \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, b \cdot y, \left(2 \cdot a\right) \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)\right), y\right)} \]

       11. lower-*.f64 57.2

           \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, b \cdot y, \left(2 \cdot a\right) \cdot \left(\color{blue}{\left(b \cdot b\right)} \cdot y\right)\right), y\right)} \]

   11. Applied rewrites 57.2%

       \[\leadsto \frac{x}{\color{blue}{x + \mathsf{fma}\left(a, \mathsf{fma}\left(-2, b \cdot y, \left(2 \cdot a\right) \cdot \left(\left(b \cdot b\right) \cdot y\right)\right), y\right)}} \]

   12. Taylor expanded in b around inf

       \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \color{blue}{2 \cdot \left(a \cdot \left({b}^{2} \cdot y\right)\right)}, y\right)} \]
   13. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \color{blue}{\left(2 \cdot a\right) \cdot \left({b}^{2} \cdot y\right)}, y\right)} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \color{blue}{\left(2 \cdot a\right) \cdot \left({b}^{2} \cdot y\right)}, y\right)} \]

       3. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \color{blue}{\left(2 \cdot a\right)} \cdot \left({b}^{2} \cdot y\right), y\right)} \]

       4. *-commutative N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \left(2 \cdot a\right) \cdot \color{blue}{\left(y \cdot {b}^{2}\right)}, y\right)} \]

       5. lower-*.f64 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \left(2 \cdot a\right) \cdot \color{blue}{\left(y \cdot {b}^{2}\right)}, y\right)} \]

       6. unpow2 N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \left(2 \cdot a\right) \cdot \left(y \cdot \color{blue}{\left(b \cdot b\right)}\right), y\right)} \]

       7. lower-*.f64 63.2

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \left(2 \cdot a\right) \cdot \left(y \cdot \color{blue}{\left(b \cdot b\right)}\right), y\right)} \]

   14. Applied rewrites 63.2%

       \[\leadsto \frac{x}{x + \mathsf{fma}\left(a, \color{blue}{\left(2 \cdot a\right) \cdot \left(y \cdot \left(b \cdot b\right)\right)}, y\right)} \]

   if 1.9999999999999999e-36 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 90.2%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.6%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + \mathsf{fma}\left(a, \left(a \cdot 2\right) \cdot \left(y \cdot \left(b \cdot b\right)\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(x - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      2e-36)
   (* (- x y) (/ x (* (+ x y) (- x y))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = (x - y) * (x / ((x + y) * (x - y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 2d-36) then
        tmp = (x - y) * (x / ((x + y) * (x - y)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = (x - y) * (x / ((x + y) * (x - y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36:
		tmp = (x - y) * (x / ((x + y) * (x - y)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 2e-36)
		tmp = Float64(Float64(x - y) * Float64(x / Float64(Float64(x + y) * Float64(x - y))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36)
		tmp = (x - y) * (x / ((x + y) * (x - y)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-36], N[(N[(x - y), $MachinePrecision] * N[(x / N[(N[(x + y), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 1.9999999999999999e-36

   1. Initial program 98.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 66.1

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 66.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 27.6

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 27.6%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   9. Step-by-step derivation

      1. flip-+ N/A

         \[\leadsto \frac{x}{\color{blue}{\frac{x \cdot x - y \cdot y}{x - y}}} \]

      2. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{x \cdot x - y \cdot y}} \cdot \left(x - y\right) \]

      5. difference-of-squares N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \left(x - y\right)}} \cdot \left(x - y\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right)} \cdot \left(x - y\right)} \cdot \left(x - y\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \left(x - y\right)}} \cdot \left(x - y\right) \]

      8. lower--.f64 N/A

         \[\leadsto \frac{x}{\left(x + y\right) \cdot \color{blue}{\left(x - y\right)}} \cdot \left(x - y\right) \]

      9. lower--.f64 54.9

         \[\leadsto \frac{x}{\left(x + y\right) \cdot \left(x - y\right)} \cdot \color{blue}{\left(x - y\right)} \]

   10. Applied rewrites 54.9%

       \[\leadsto \color{blue}{\frac{x}{\left(x + y\right) \cdot \left(x - y\right)} \cdot \left(x - y\right)} \]

   if 1.9999999999999999e-36 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 90.2%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.6%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(x - y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{1}{\frac{x + y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      2e-36)
   (/ 1.0 (/ (+ x y) x))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = 1.0 / ((x + y) / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 2d-36) then
        tmp = 1.0d0 / ((x + y) / x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = 1.0 / ((x + y) / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36:
		tmp = 1.0 / ((x + y) / x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 2e-36)
		tmp = Float64(1.0 / Float64(Float64(x + y) / x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36)
		tmp = 1.0 / ((x + y) / x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-36], N[(1.0 / N[(N[(x + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 1.9999999999999999e-36

   1. Initial program 98.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 66.1

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 66.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 27.6

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 27.6%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   9. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

      2. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x}}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x}}} \]

      4. lower-/.f64 28.4

         \[\leadsto \frac{1}{\color{blue}{\frac{x + y}{x}}} \]

   10. Applied rewrites 28.4%

       \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x}}} \]

   if 1.9999999999999999e-36 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 90.2%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.6%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{1}{\frac{x + y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      2e-36)
   (/ x (+ x y))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 2d-36) then
        tmp = x / (x + y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36:
		tmp = x / (x + y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 2e-36)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36)
		tmp = x / (x + y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-36], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 1.9999999999999999e-36

   1. Initial program 98.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 66.1

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 66.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 27.6

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 27.6%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   if 1.9999999999999999e-36 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 90.2%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.6%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      2e-36)
   (/ x y)
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 2d-36) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 2e-36)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 2e-36)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-36], N[(x / y), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 1.9999999999999999e-36

   1. Initial program 98.5%

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

   3. Taylor expanded in b around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}}} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)}} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} - \left(\frac{5}{6} + a\right)\right)\right)}} \]

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 66.1

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   5. Applied rewrites 66.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   6. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 27.6

         \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   8. Applied rewrites 27.6%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   10. Step-by-step derivation

       1. lower-/.f64 27.2

          \[\leadsto \color{blue}{\frac{x}{y}} \]

   11. Applied rewrites 27.2%

       \[\leadsto \color{blue}{\frac{x}{y}} \]

   if 1.9999999999999999e-36 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 90.2%

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

   3. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   5. Applied rewrites 92.6%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.5% accurate, 198.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 1.0)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return 1.0;
}

Python

def code(x, y, z, t, a, b, c):
	return 1.0

Julia

function code(x, y, z, t, a, b, c)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := 1.0

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in x around -inf

   \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

5. Applied rewrites 95.7%

   \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, -\frac{e^{2 \cdot \mathsf{fma}\left(\frac{z}{t}, \sqrt{t + a}, \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)}}{x}, -1\right) \cdot \left(-x\right)}} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
7. Step-by-step derivation

8. Applied rewrites 49.3%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Developer Target 1: 95.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ t_2 := a - \frac{5}{6}\\ \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{t\_1 \cdot \left(\left(3 \cdot t\right) \cdot t\_2\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(t\_2 \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot t\_2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{t\_1}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (sqrt (+ t a)))) (t_2 (- a (/ 5.0 6.0))))
   (if (< t -2.118326644891581e-50)
     (/
      x
      (+
       x
       (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b)))))))
     (if (< t 5.196588770651547e-123)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (/
             (-
              (* t_1 (* (* 3.0 t) t_2))
              (*
               (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0)
               (* t_2 (* (- b c) t))))
             (* (* (* t t) 3.0) t_2)))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (/ t_1 t)
             (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * sqrt((t + a))
    t_2 = a - (5.0d0 / 6.0d0)
    if (t < (-2.118326644891581d-50)) then
        tmp = x / (x + (y * exp((2.0d0 * (((a * c) + (0.8333333333333334d0 * c)) - (a * b))))))
    else if (t < 5.196588770651547d-123) then
        tmp = x / (x + (y * exp((2.0d0 * (((t_1 * ((3.0d0 * t) * t_2)) - (((((5.0d0 / 6.0d0) + a) * (3.0d0 * t)) - 2.0d0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0d0) * t_2))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((t_1 / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * Math.sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * Math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * Math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * math.sqrt((t + a))
	t_2 = a - (5.0 / 6.0)
	tmp = 0
	if t < -2.118326644891581e-50:
		tmp = x / (x + (y * math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))))
	elif t < 5.196588770651547e-123:
		tmp = x / (x + (y * math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * sqrt(Float64(t + a)))
	t_2 = Float64(a - Float64(5.0 / 6.0))
	tmp = 0.0
	if (t < -2.118326644891581e-50)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(a * c) + Float64(0.8333333333333334 * c)) - Float64(a * b)))))));
	elseif (t < 5.196588770651547e-123)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(t_1 * Float64(Float64(3.0 * t) * t_2)) - Float64(Float64(Float64(Float64(Float64(5.0 / 6.0) + a) * Float64(3.0 * t)) - 2.0) * Float64(t_2 * Float64(Float64(b - c) * t)))) / Float64(Float64(Float64(t * t) * 3.0) * t_2)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(t_1 / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * sqrt((t + a));
	t_2 = a - (5.0 / 6.0);
	tmp = 0.0;
	if (t < -2.118326644891581e-50)
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	elseif (t < 5.196588770651547e-123)
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -2.118326644891581e-50], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(a * c), $MachinePrecision] + N[(0.8333333333333334 * c), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[t, 5.196588770651547e-123], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(t$95$1 * N[(N[(3.0 * t), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(5.0 / 6.0), $MachinePrecision] + a), $MachinePrecision] * N[(3.0 * t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision] * N[(t$95$2 * N[(N[(b - c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * t), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(t$95$1 / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -2118326644891581/100000000000000000000000000000000000000000000000000000000000000000) (/ x (+ x (* y (exp (* 2 (- (+ (* a c) (* 4166666666666667/5000000000000000 c)) (* a b))))))) (if (< t 5196588770651547/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (+ x (* y (exp (* 2 (/ (- (* (* z (sqrt (+ t a))) (* (* 3 t) (- a (/ 5 6)))) (* (- (* (+ (/ 5 6) a) (* 3 t)) 2) (* (- a (/ 5 6)) (* (- b c) t)))) (* (* (* t t) 3) (- a (/ 5 6))))))))) (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))