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

Percentage Accurate: 94.1% → 96.9%

Time: 40.8s

Alternatives: 21

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: 94.1% 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: 96.9% accurate, 0.7× speedup

Math

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

FPCore

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

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 + 0.8333333333333334)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	}
	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 + 0.8333333333333334)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	}
	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 + 0.8333333333333334)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * t_1))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))))
	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 + 0.8333333333333334))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * t_1)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334))))))));
	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 + 0.8333333333333334)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	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 + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

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 5 6)) (/.f64 2 (*.f64 t 3))))) < +inf.0

   1. Initial program 99.6%

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

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

   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 c around inf 78.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv 78.8%

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

      2. +-commutative 78.8%

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

      3. metadata-eval 78.8%

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

      4. associate-*r/ 78.8%

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

      5. metadata-eval 78.8%

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

      6. associate-+r+ 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 98.8%

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

Alternative 2: 80.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{t + a}\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* (/ z t) (sqrt (+ t a)))))))))
        (t_2
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (*
               c
               (+ a (+ (/ -0.6666666666666666 t) 0.8333333333333334))))))))))
   (if (<= t -5e-198)
     (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
     (if (<= t 1.06e-197)
       t_2
       (if (<= t 2.45e-172)
         t_1
         (if (<= t 4.2e-111)
           (/
            x
            (+
             x
             (*
              y
              (exp
               (*
                2.0
                (*
                 b
                 (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))
           (if (<= t 2e-82)
             t_2
             (if (<= t 9000.0)
               t_1
               (/
                x
                (+
                 x
                 (*
                  y
                  (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * ((z / t) * sqrt((t + a)))))));
	double t_2 = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	double tmp;
	if (t <= -5e-198) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.06e-197) {
		tmp = t_2;
	} else if (t <= 2.45e-172) {
		tmp = t_1;
	} else if (t <= 4.2e-111) {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else if (t <= 2e-82) {
		tmp = t_2;
	} else if (t <= 9000.0) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	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 = x / (x + (y * exp((2.0d0 * ((z / t) * sqrt((t + a)))))))
    t_2 = x / (x + (y * exp((2.0d0 * (c * (a + (((-0.6666666666666666d0) / t) + 0.8333333333333334d0)))))))
    if (t <= (-5d-198)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1.06d-197) then
        tmp = t_2
    else if (t <= 2.45d-172) then
        tmp = t_1
    else if (t <= 4.2d-111) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    else if (t <= 2d-82) then
        tmp = t_2
    else if (t <= 9000.0d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    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 = x / (x + (y * Math.exp((2.0 * ((z / t) * Math.sqrt((t + a)))))));
	double t_2 = x / (x + (y * Math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	double tmp;
	if (t <= -5e-198) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.06e-197) {
		tmp = t_2;
	} else if (t <= 2.45e-172) {
		tmp = t_1;
	} else if (t <= 4.2e-111) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else if (t <= 2e-82) {
		tmp = t_2;
	} else if (t <= 9000.0) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * ((z / t) * math.sqrt((t + a)))))))
	t_2 = x / (x + (y * math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))))
	tmp = 0
	if t <= -5e-198:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1.06e-197:
		tmp = t_2
	elif t <= 2.45e-172:
		tmp = t_1
	elif t <= 4.2e-111:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	elif t <= 2e-82:
		tmp = t_2
	elif t <= 9000.0:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z / t) * sqrt(Float64(t + a))))))))
	t_2 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334))))))))
	tmp = 0.0
	if (t <= -5e-198)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1.06e-197)
		tmp = t_2;
	elseif (t <= 2.45e-172)
		tmp = t_1;
	elseif (t <= 4.2e-111)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))));
	elseif (t <= 2e-82)
		tmp = t_2;
	elseif (t <= 9000.0)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * ((z / t) * sqrt((t + a)))))));
	t_2 = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	tmp = 0.0;
	if (t <= -5e-198)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1.06e-197)
		tmp = t_2;
	elseif (t <= 2.45e-172)
		tmp = t_1;
	elseif (t <= 4.2e-111)
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	elseif (t <= 2e-82)
		tmp = t_2;
	elseif (t <= 9000.0)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z / t), $MachinePrecision] * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-198], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e-197], t$95$2, If[LessEqual[t, 2.45e-172], t$95$1, If[LessEqual[t, 4.2e-111], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-82], t$95$2, If[LessEqual[t, 9000.0], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.9999999999999999e-198

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 84.9%

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

   if -4.9999999999999999e-198 < t < 1.05999999999999997e-197 or 4.1999999999999997e-111 < t < 2e-82

   1. Initial program 91.3%

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

   3. Taylor expanded in c around inf 83.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv 83.2%

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

      2. +-commutative 83.2%

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

      3. metadata-eval 83.2%

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

      4. associate-*r/ 83.2%

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

      5. metadata-eval 83.2%

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

      6. associate-+r+ 83.2%

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

   5. Simplified 83.2%

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

   if 1.05999999999999997e-197 < t < 2.45e-172 or 2e-82 < t < 9e3

   1. Initial program 97.2%

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

      1. add-log-exp 97.2%

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

      2. associate-*l/ 97.2%

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

      3. *-commutative 97.2%

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

      4. fma-neg 97.2%

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

      5. associate-/r* 97.2%

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

      6. metadata-eval 97.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + \color{blue}{0.8333333333333334}\right) - \frac{\frac{2}{t}}{3}\right)\right)}\right)}} \]

      7. div-inv 97.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{2}{t} \cdot \frac{1}{3}}\right)\right)}\right)}} \]

      8. metadata-eval 97.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot \color{blue}{0.3333333333333333}\right)\right)}\right)}} \]

   4. Applied egg-rr 97.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot 0.3333333333333333\right)\right)}\right)}}} \]

   5. Taylor expanded in z around inf 75.9%

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

   if 2.45e-172 < t < 4.1999999999999997e-111

   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 83.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. associate-*r/ 83.9%

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

      2. metadata-eval 83.9%

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

      3. +-commutative 83.9%

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

   5. Simplified 83.9%

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

   if 9e3 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. +-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 92.7%

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

      5. neg-sub0 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 92.7%

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

      8. +-commutative 92.7%

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

      9. sub-neg 92.7%

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

   5. Simplified 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{t + a}\right)}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{t + a}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{t + a}\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{if}\;t \leq -500:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{a \cdot 2}\right)}^{\left(c - b\right)}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* (/ z t) (sqrt (+ t a)))))))))
        (t_2
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))))
   (if (<= t -500.0)
     (/ x (+ x (* y (pow (exp (* a 2.0)) (- c b)))))
     (if (<= t 3.5e-194)
       t_2
       (if (<= t 5e-172)
         t_1
         (if (<= t 1.3e-109)
           t_2
           (if (<= t 9000.0)
             t_1
             (/
              x
              (+
               x
               (*
                y
                (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * ((z / t) * sqrt((t + a)))))));
	double t_2 = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	double tmp;
	if (t <= -500.0) {
		tmp = x / (x + (y * pow(exp((a * 2.0)), (c - b))));
	} else if (t <= 3.5e-194) {
		tmp = t_2;
	} else if (t <= 5e-172) {
		tmp = t_1;
	} else if (t <= 1.3e-109) {
		tmp = t_2;
	} else if (t <= 9000.0) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	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 = x / (x + (y * exp((2.0d0 * ((z / t) * sqrt((t + a)))))))
    t_2 = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    if (t <= (-500.0d0)) then
        tmp = x / (x + (y * (exp((a * 2.0d0)) ** (c - b))))
    else if (t <= 3.5d-194) then
        tmp = t_2
    else if (t <= 5d-172) then
        tmp = t_1
    else if (t <= 1.3d-109) then
        tmp = t_2
    else if (t <= 9000.0d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    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 = x / (x + (y * Math.exp((2.0 * ((z / t) * Math.sqrt((t + a)))))));
	double t_2 = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	double tmp;
	if (t <= -500.0) {
		tmp = x / (x + (y * Math.pow(Math.exp((a * 2.0)), (c - b))));
	} else if (t <= 3.5e-194) {
		tmp = t_2;
	} else if (t <= 5e-172) {
		tmp = t_1;
	} else if (t <= 1.3e-109) {
		tmp = t_2;
	} else if (t <= 9000.0) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * ((z / t) * math.sqrt((t + a)))))))
	t_2 = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	tmp = 0
	if t <= -500.0:
		tmp = x / (x + (y * math.pow(math.exp((a * 2.0)), (c - b))))
	elif t <= 3.5e-194:
		tmp = t_2
	elif t <= 5e-172:
		tmp = t_1
	elif t <= 1.3e-109:
		tmp = t_2
	elif t <= 9000.0:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z / t) * sqrt(Float64(t + a))))))))
	t_2 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))))
	tmp = 0.0
	if (t <= -500.0)
		tmp = Float64(x / Float64(x + Float64(y * (exp(Float64(a * 2.0)) ^ Float64(c - b)))));
	elseif (t <= 3.5e-194)
		tmp = t_2;
	elseif (t <= 5e-172)
		tmp = t_1;
	elseif (t <= 1.3e-109)
		tmp = t_2;
	elseif (t <= 9000.0)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * ((z / t) * sqrt((t + a)))))));
	t_2 = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	tmp = 0.0;
	if (t <= -500.0)
		tmp = x / (x + (y * (exp((a * 2.0)) ^ (c - b))));
	elseif (t <= 3.5e-194)
		tmp = t_2;
	elseif (t <= 5e-172)
		tmp = t_1;
	elseif (t <= 1.3e-109)
		tmp = t_2;
	elseif (t <= 9000.0)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z / t), $MachinePrecision] * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -500.0], N[(x / N[(x + N[(y * N[Power[N[Exp[N[(a * 2.0), $MachinePrecision]], $MachinePrecision], N[(c - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-194], t$95$2, If[LessEqual[t, 5e-172], t$95$1, If[LessEqual[t, 1.3e-109], t$95$2, If[LessEqual[t, 9000.0], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -500

   1. Initial program 87.5%

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

   3. Taylor expanded in a around inf 94.3%

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

      1. associate-*r* 94.3%

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

      2. exp-prod 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -500 < t < 3.5000000000000003e-194 or 4.9999999999999999e-172 < t < 1.2999999999999999e-109

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 91.2%

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

   if 3.5000000000000003e-194 < t < 4.9999999999999999e-172 or 1.2999999999999999e-109 < t < 9e3

   1. Initial program 95.5%

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

      1. add-log-exp 95.5%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

      4. fma-neg 95.5%

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

      5. associate-/r* 95.5%

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

      6. metadata-eval 95.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + \color{blue}{0.8333333333333334}\right) - \frac{\frac{2}{t}}{3}\right)\right)}\right)}} \]

      7. div-inv 95.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{2}{t} \cdot \frac{1}{3}}\right)\right)}\right)}} \]

      8. metadata-eval 95.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot \color{blue}{0.3333333333333333}\right)\right)}\right)}} \]

   4. Applied egg-rr 95.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot 0.3333333333333333\right)\right)}\right)}}} \]

   5. Taylor expanded in z around inf 73.7%

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

   if 9e3 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. +-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 92.7%

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

      5. neg-sub0 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 92.7%

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

      8. +-commutative 92.7%

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

      9. sub-neg 92.7%

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

   5. Simplified 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -500:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{a \cdot 2}\right)}^{\left(c - b\right)}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{t + a}\right)}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{t + a}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -340:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{a \cdot 2}\right)}^{\left(c - b\right)}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+170}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} - \left(b - c\right) \cdot \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -340.0)
   (/ x (+ x (* y (pow (exp (* a 2.0)) (- c b)))))
   (if (<= t 3.4e-301)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
     (if (<= t 4e+170)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (* z (sqrt (/ 1.0 t)))
             (* (- b c) (+ (/ -0.6666666666666666 t) 0.8333333333333334))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -340.0) {
		tmp = x / (x + (y * pow(exp((a * 2.0)), (c - b))));
	} else if (t <= 3.4e-301) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 4e+170) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) - ((b - c) * ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	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 (t <= (-340.0d0)) then
        tmp = x / (x + (y * (exp((a * 2.0d0)) ** (c - b))))
    else if (t <= 3.4d-301) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 4d+170) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) - ((b - c) * (((-0.6666666666666666d0) / t) + 0.8333333333333334d0)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    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 (t <= -340.0) {
		tmp = x / (x + (y * Math.pow(Math.exp((a * 2.0)), (c - b))));
	} else if (t <= 3.4e-301) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 4e+170) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) - ((b - c) * ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -340.0:
		tmp = x / (x + (y * math.pow(math.exp((a * 2.0)), (c - b))))
	elif t <= 3.4e-301:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 4e+170:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) - ((b - c) * ((-0.6666666666666666 / t) + 0.8333333333333334)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -340.0)
		tmp = Float64(x / Float64(x + Float64(y * (exp(Float64(a * 2.0)) ^ Float64(c - b)))));
	elseif (t <= 3.4e-301)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	elseif (t <= 4e+170)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) - Float64(Float64(b - c) * Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -340.0)
		tmp = x / (x + (y * (exp((a * 2.0)) ^ (c - b))));
	elseif (t <= 3.4e-301)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 4e+170)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) - ((b - c) * ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -340.0], N[(x / N[(x + N[(y * N[Power[N[Exp[N[(a * 2.0), $MachinePrecision]], $MachinePrecision], N[(c - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-301], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+170], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -340

   1. Initial program 87.5%

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

   3. Taylor expanded in a around inf 94.3%

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

      1. associate-*r* 94.3%

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

      2. exp-prod 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -340 < t < 3.4000000000000002e-301

   1. Initial program 93.0%

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

   3. Taylor expanded in t around 0 95.5%

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

   if 3.4000000000000002e-301 < t < 4.00000000000000014e170

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0 87.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\sqrt{\frac{1}{t}} \cdot z - \left(0.8333333333333334 - 0.6666666666666666 \cdot \frac{1}{t}\right) \cdot \left(b - c\right)\right)}}} \]
   4. Step-by-step derivation

      1. *-commutative 87.6%

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

      2. *-commutative 87.6%

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

      3. cancel-sign-sub-inv 87.6%

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

      4. metadata-eval 87.6%

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

      5. associate-*r/ 87.6%

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

      6. metadata-eval 87.6%

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

   5. Simplified 87.6%

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

   if 4.00000000000000014e170 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf 98.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. +-commutative 98.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 98.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 98.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 98.2%

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

      5. neg-sub0 98.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 98.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 98.2%

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

      8. +-commutative 98.2%

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

      9. sub-neg 98.2%

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

   5. Simplified 98.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -340:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{a \cdot 2}\right)}^{\left(c - b\right)}}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-301}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+170}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} - \left(b - c\right) \cdot \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ t_3 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -0.84:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-191}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* -0.6666666666666666 (/ c t))))))))
        (t_2 (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667))))))
        (t_3 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= a -0.84)
     t_3
     (if (<= a -2.7e-191)
       t_2
       (if (<= a -2.2e-268)
         t_1
         (if (<= a 8.6e-15) t_2 (if (<= a 5.3e+32) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (-0.6666666666666666 * (c / t))))));
	double t_2 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	double t_3 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	double tmp;
	if (a <= -0.84) {
		tmp = t_3;
	} else if (a <= -2.7e-191) {
		tmp = t_2;
	} else if (a <= -2.2e-268) {
		tmp = t_1;
	} else if (a <= 8.6e-15) {
		tmp = t_2;
	} else if (a <= 5.3e+32) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * ((-0.6666666666666666d0) * (c / t))))))
    t_2 = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    t_3 = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    if (a <= (-0.84d0)) then
        tmp = t_3
    else if (a <= (-2.7d-191)) then
        tmp = t_2
    else if (a <= (-2.2d-268)) then
        tmp = t_1
    else if (a <= 8.6d-15) then
        tmp = t_2
    else if (a <= 5.3d+32) then
        tmp = t_1
    else
        tmp = t_3
    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 = x / (x + (y * Math.exp((2.0 * (-0.6666666666666666 * (c / t))))));
	double t_2 = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	double t_3 = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	double tmp;
	if (a <= -0.84) {
		tmp = t_3;
	} else if (a <= -2.7e-191) {
		tmp = t_2;
	} else if (a <= -2.2e-268) {
		tmp = t_1;
	} else if (a <= 8.6e-15) {
		tmp = t_2;
	} else if (a <= 5.3e+32) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (-0.6666666666666666 * (c / t))))))
	t_2 = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	t_3 = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	tmp = 0
	if a <= -0.84:
		tmp = t_3
	elif a <= -2.7e-191:
		tmp = t_2
	elif a <= -2.2e-268:
		tmp = t_1
	elif a <= 8.6e-15:
		tmp = t_2
	elif a <= 5.3e+32:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(-0.6666666666666666 * Float64(c / t)))))))
	t_2 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))))
	t_3 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))))
	tmp = 0.0
	if (a <= -0.84)
		tmp = t_3;
	elseif (a <= -2.7e-191)
		tmp = t_2;
	elseif (a <= -2.2e-268)
		tmp = t_1;
	elseif (a <= 8.6e-15)
		tmp = t_2;
	elseif (a <= 5.3e+32)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (-0.6666666666666666 * (c / t))))));
	t_2 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	t_3 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	tmp = 0.0;
	if (a <= -0.84)
		tmp = t_3;
	elseif (a <= -2.7e-191)
		tmp = t_2;
	elseif (a <= -2.2e-268)
		tmp = t_1;
	elseif (a <= 8.6e-15)
		tmp = t_2;
	elseif (a <= 5.3e+32)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(-0.6666666666666666 * N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.84], t$95$3, If[LessEqual[a, -2.7e-191], t$95$2, If[LessEqual[a, -2.2e-268], t$95$1, If[LessEqual[a, 8.6e-15], t$95$2, If[LessEqual[a, 5.3e+32], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.839999999999999969 or 5.2999999999999999e32 < a

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 81.6%

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

   if -0.839999999999999969 < a < -2.69999999999999999e-191 or -2.20000000000000004e-268 < a < 8.5999999999999993e-15

   1. Initial program 98.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in t around inf 71.3%

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

   6. Taylor expanded in a around 0 71.3%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -2.69999999999999999e-191 < a < -2.20000000000000004e-268 or 8.5999999999999993e-15 < a < 5.2999999999999999e32

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0 55.0%

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

   4. Taylor expanded in c around inf 69.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.84:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 1.1 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(c - b\right) \cdot \left(a \cdot 2\right) + 1\right)}\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 520000000:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 1.1e-211)
   (/ x (+ x (* (* a -2.0) (* b y))))
   (if (<= c 4.6e-150)
     (/ x (+ x (* (* a 2.0) (* c y))))
     (if (<= c 3e-47)
       (/ x (+ x (* y (+ (* (- c b) (* a 2.0)) 1.0))))
       (if (<= c 1.65e-16)
         (/ x (+ x y))
         (if (<= c 520000000.0)
           (/
            x
            (+
             x
             (*
              y
              (+
               (*
                2.0
                (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))
               1.0))))
           (/ x (* y (exp (* (- c b) 1.6666666666666667))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.1e-211) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else if (c <= 4.6e-150) {
		tmp = x / (x + ((a * 2.0) * (c * y)));
	} else if (c <= 3e-47) {
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	} else if (c <= 1.65e-16) {
		tmp = x / (x + y);
	} else if (c <= 520000000.0) {
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 1.0)));
	} else {
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	}
	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 (c <= 1.1d-211) then
        tmp = x / (x + ((a * (-2.0d0)) * (b * y)))
    else if (c <= 4.6d-150) then
        tmp = x / (x + ((a * 2.0d0) * (c * y)))
    else if (c <= 3d-47) then
        tmp = x / (x + (y * (((c - b) * (a * 2.0d0)) + 1.0d0)))
    else if (c <= 1.65d-16) then
        tmp = x / (x + y)
    else if (c <= 520000000.0d0) then
        tmp = x / (x + (y * ((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))) + 1.0d0)))
    else
        tmp = x / (y * exp(((c - b) * 1.6666666666666667d0)))
    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 (c <= 1.1e-211) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else if (c <= 4.6e-150) {
		tmp = x / (x + ((a * 2.0) * (c * y)));
	} else if (c <= 3e-47) {
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	} else if (c <= 1.65e-16) {
		tmp = x / (x + y);
	} else if (c <= 520000000.0) {
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 1.0)));
	} else {
		tmp = x / (y * Math.exp(((c - b) * 1.6666666666666667)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 1.1e-211:
		tmp = x / (x + ((a * -2.0) * (b * y)))
	elif c <= 4.6e-150:
		tmp = x / (x + ((a * 2.0) * (c * y)))
	elif c <= 3e-47:
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)))
	elif c <= 1.65e-16:
		tmp = x / (x + y)
	elif c <= 520000000.0:
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 1.0)))
	else:
		tmp = x / (y * math.exp(((c - b) * 1.6666666666666667)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 1.1e-211)
		tmp = Float64(x / Float64(x + Float64(Float64(a * -2.0) * Float64(b * y))));
	elseif (c <= 4.6e-150)
		tmp = Float64(x / Float64(x + Float64(Float64(a * 2.0) * Float64(c * y))));
	elseif (c <= 3e-47)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(Float64(c - b) * Float64(a * 2.0)) + 1.0))));
	elseif (c <= 1.65e-16)
		tmp = Float64(x / Float64(x + y));
	elseif (c <= 520000000.0)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334)))) + 1.0))));
	else
		tmp = Float64(x / Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 1.1e-211)
		tmp = x / (x + ((a * -2.0) * (b * y)));
	elseif (c <= 4.6e-150)
		tmp = x / (x + ((a * 2.0) * (c * y)));
	elseif (c <= 3e-47)
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	elseif (c <= 1.65e-16)
		tmp = x / (x + y);
	elseif (c <= 520000000.0)
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 1.0)));
	else
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 1.1e-211], N[(x / N[(x + N[(N[(a * -2.0), $MachinePrecision] * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e-150], N[(x / N[(x + N[(N[(a * 2.0), $MachinePrecision] * N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e-47], N[(x / N[(x + N[(y * N[(N[(N[(c - b), $MachinePrecision] * N[(a * 2.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e-16], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 520000000.0], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < 1.09999999999999999e-211

   1. Initial program 97.3%

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

   3. Taylor expanded in a around inf 65.2%

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

   4. Taylor expanded in a around 0 42.7%

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

      1. associate-*r* 42.7%

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

      2. *-commutative 42.7%

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

      3. *-commutative 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in b around inf 49.1%

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

      1. associate-*r* 49.1%

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

   9. Simplified 49.1%

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

   if 1.09999999999999999e-211 < c < 4.60000000000000006e-150

   1. Initial program 88.9%

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

   3. Taylor expanded in a around inf 51.6%

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

   4. Taylor expanded in a around 0 30.9%

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

      1. associate-*r* 30.9%

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

      2. *-commutative 30.9%

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

      3. *-commutative 30.9%

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

   6. Simplified 30.9%

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

   7. Taylor expanded in c around inf 52.0%

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

      1. associate-*r* 52.0%

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

      2. *-commutative 52.0%

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

   9. Simplified 52.0%

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

   if 4.60000000000000006e-150 < c < 3.00000000000000017e-47

   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 a around inf 77.7%

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

   4. Taylor expanded in a around 0 63.2%

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

      1. associate-*r* 63.2%

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

      2. *-commutative 63.2%

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

      3. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if 3.00000000000000017e-47 < c < 1.64999999999999994e-16

   1. Initial program 83.3%

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

   3. Taylor expanded in a around inf 83.9%

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

   4. Taylor expanded in a around 0 83.8%

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

   if 1.64999999999999994e-16 < c < 5.2e8

   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 63.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. associate-*r/ 63.7%

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

      2. metadata-eval 63.7%

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

      3. +-commutative 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in b around 0 51.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 51.6%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)\right)} \]

      2. metadata-eval 51.6%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)\right)} \]

      3. +-commutative 51.6%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)\right)} \]

   8. Simplified 51.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)\right)}} \]

   if 5.2e8 < c

   1. Initial program 94.9%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around inf 78.3%

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

   6. Taylor expanded in a around 0 74.9%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   7. Taylor expanded in x around 0 68.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.1 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(c - b\right) \cdot \left(a \cdot 2\right) + 1\right)}\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 520000000:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -2.5e-275)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 4.9e-111)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))
     (if (<= t 9000.0)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (* c (+ a (+ (/ -0.6666666666666666 t) 0.8333333333333334))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2.5e-275) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 4.9e-111) {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else if (t <= 9000.0) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	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 (t <= (-2.5d-275)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 4.9d-111) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    else if (t <= 9000.0d0) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (((-0.6666666666666666d0) / t) + 0.8333333333333334d0)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    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 (t <= -2.5e-275) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 4.9e-111) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else if (t <= 9000.0) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -2.5e-275:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 4.9e-111:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	elif t <= 9000.0:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -2.5e-275)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 4.9e-111)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))));
	elseif (t <= 9000.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -2.5e-275)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 4.9e-111)
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	elseif (t <= 9000.0)
		tmp = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -2.5e-275], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-111], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9000.0], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.49999999999999992e-275

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 81.5%

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

   if -2.49999999999999992e-275 < t < 4.90000000000000019e-111

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 78.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. associate-*r/ 78.3%

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

      2. metadata-eval 78.3%

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

      3. +-commutative 78.3%

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

   5. Simplified 78.3%

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

   if 4.90000000000000019e-111 < t < 9e3

   1. Initial program 97.3%

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

   3. Taylor expanded in c around inf 67.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv 67.6%

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

      2. +-commutative 67.6%

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

      3. metadata-eval 67.6%

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

      4. associate-*r/ 67.6%

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

      5. metadata-eval 67.6%

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

      6. associate-+r+ 67.6%

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

   5. Simplified 67.6%

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

   if 9e3 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. +-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 92.7%

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

      5. neg-sub0 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 92.7%

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

      8. +-commutative 92.7%

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

      9. sub-neg 92.7%

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

   5. Simplified 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 9000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-277}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 35000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.8e-277)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 35000.0)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))
     (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.8e-277) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 35000.0) {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	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 (t <= (-3.8d-277)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 35000.0d0) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    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 (t <= -3.8e-277) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 35000.0) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.8e-277:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 35000.0:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.8e-277)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 35000.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.8e-277)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 35000.0)
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.8e-277], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 35000.0], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999986e-277

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 81.5%

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

   if -3.79999999999999986e-277 < t < 35000

   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 b around inf 67.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. associate-*r/ 67.0%

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

      2. metadata-eval 67.0%

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

      3. +-commutative 67.0%

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

   5. Simplified 67.0%

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

   if 35000 < t

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. +-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 92.7%

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

      5. neg-sub0 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 92.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 92.7%

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

      8. +-commutative 92.7%

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

      9. sub-neg 92.7%

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

   5. Simplified 92.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-277}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 35000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-310} \lor \neg \left(t \leq 125\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -5e-310) (not (<= t 125.0)))
   (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))
   (/ x (+ x (* y (exp (* 2.0 (* (- b c) (+ a 0.8333333333333334)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -5e-310) || !(t <= 125.0)) {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (a + 0.8333333333333334))))));
	}
	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 ((t <= (-5d-310)) .or. (.not. (t <= 125.0d0))) then
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * (a + 0.8333333333333334d0))))))
    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 ((t <= -5e-310) || !(t <= 125.0)) {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (a + 0.8333333333333334))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -5e-310) or not (t <= 125.0):
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (a + 0.8333333333333334))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -5e-310) || !(t <= 125.0))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(a + 0.8333333333333334)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -5e-310) || ~((t <= 125.0)))
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (a + 0.8333333333333334))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -5e-310], N[Not[LessEqual[t, 125.0]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.999999999999985e-310 or 125 < t

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf 88.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. +-commutative 88.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 88.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 88.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 88.5%

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

      5. neg-sub0 88.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 88.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 88.5%

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

      8. +-commutative 88.5%

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

      9. sub-neg 88.5%

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

   5. Simplified 88.5%

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

   if -4.999999999999985e-310 < t < 125

   1. Initial program 96.2%

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

      1. add-log-exp 96.2%

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

      2. associate-*l/ 94.9%

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

      3. *-commutative 94.9%

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

      4. fma-neg 94.9%

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

      5. associate-/r* 94.9%

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

      6. metadata-eval 94.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + \color{blue}{0.8333333333333334}\right) - \frac{\frac{2}{t}}{3}\right)\right)}\right)}} \]

      7. div-inv 94.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{2}{t} \cdot \frac{1}{3}}\right)\right)}\right)}} \]

      8. metadata-eval 94.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot \color{blue}{0.3333333333333333}\right)\right)}\right)}} \]

   4. Applied egg-rr 94.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot 0.3333333333333333\right)\right)}\right)}}} \]

   5. Taylor expanded in t around inf 31.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(e^{-\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)}\right)}}} \]
   6. Step-by-step derivation

      1. distribute-lft-neg-in 31.8%

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

      2. +-commutative 31.8%

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

   7. Simplified 31.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}}} \]
   8. Step-by-step derivation

      1. rem-log-exp 31.8%

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

      2. *-un-lft-identity 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(1 \cdot e^{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)}}} \]

      3. log-prod 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\log 1 + \log \left(e^{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)\right)}}} \]

      4. metadata-eval 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{0} + \log \left(e^{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)\right)}} \]

      5. add-log-exp 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)}} \]

      6. rem-log-exp 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}} \]

      7. add-sqr-sqrt 0.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(\sqrt{-\left(a + 0.8333333333333334\right)} \cdot \sqrt{-\left(a + 0.8333333333333334\right)}\right)} \cdot \left(b - c\right)\right)}} \]

      8. sqrt-unprod 65.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\sqrt{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(-\left(a + 0.8333333333333334\right)\right)}} \cdot \left(b - c\right)\right)}} \]

      9. sqr-neg 65.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \sqrt{\color{blue}{\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)}} \cdot \left(b - c\right)\right)}} \]

      10. sqrt-unprod 65.3%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(\sqrt{a + 0.8333333333333334} \cdot \sqrt{a + 0.8333333333333334}\right)} \cdot \left(b - c\right)\right)}} \]

      11. add-sqr-sqrt 65.3%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)}} \]

   9. Applied egg-rr 65.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(0 + \left(a + 0.8333333333333334\right) \cdot \left(b - c\right)\right)}}} \]
   10. Step-by-step derivation

       1. +-lft-identity 65.3%

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

       2. *-commutative 65.3%

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

   11. Simplified 65.3%

       \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-310} \lor \neg \left(t \leq 125\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 125:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -5e-310)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 125.0)
     (/ x (+ x (* y (exp (* 2.0 (* (- b c) (+ a 0.8333333333333334)))))))
     (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -5e-310) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 125.0) {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (a + 0.8333333333333334))))));
	} else {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	}
	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 (t <= (-5d-310)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 125.0d0) then
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * (a + 0.8333333333333334d0))))))
    else
        tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    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 (t <= -5e-310) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 125.0) {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (a + 0.8333333333333334))))));
	} else {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -5e-310:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 125.0:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (a + 0.8333333333333334))))))
	else:
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -5e-310)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 125.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(a + 0.8333333333333334)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -5e-310)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 125.0)
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (a + 0.8333333333333334))))));
	else
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -5e-310], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 125.0], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.999999999999985e-310

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 78.8%

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

   if -4.999999999999985e-310 < t < 125

   1. Initial program 96.2%

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

      1. add-log-exp 96.2%

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

      2. associate-*l/ 94.9%

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

      3. *-commutative 94.9%

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

      4. fma-neg 94.9%

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

      5. associate-/r* 94.9%

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

      6. metadata-eval 94.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + \color{blue}{0.8333333333333334}\right) - \frac{\frac{2}{t}}{3}\right)\right)}\right)}} \]

      7. div-inv 94.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{2}{t} \cdot \frac{1}{3}}\right)\right)}\right)}} \]

      8. metadata-eval 94.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot \color{blue}{0.3333333333333333}\right)\right)}\right)}} \]

   4. Applied egg-rr 94.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\log \left(e^{\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, -\left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t} \cdot 0.3333333333333333\right)\right)}\right)}}} \]

   5. Taylor expanded in t around inf 31.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(e^{-\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)}\right)}}} \]
   6. Step-by-step derivation

      1. distribute-lft-neg-in 31.8%

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

      2. +-commutative 31.8%

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

   7. Simplified 31.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}}} \]
   8. Step-by-step derivation

      1. rem-log-exp 31.8%

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

      2. *-un-lft-identity 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \log \color{blue}{\left(1 \cdot e^{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)}}} \]

      3. log-prod 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\log 1 + \log \left(e^{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)\right)}}} \]

      4. metadata-eval 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{0} + \log \left(e^{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)\right)}} \]

      5. add-log-exp 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\log \left(e^{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}\right)}} \]

      6. rem-log-exp 31.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(b - c\right)}\right)}} \]

      7. add-sqr-sqrt 0.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(\sqrt{-\left(a + 0.8333333333333334\right)} \cdot \sqrt{-\left(a + 0.8333333333333334\right)}\right)} \cdot \left(b - c\right)\right)}} \]

      8. sqrt-unprod 65.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\sqrt{\left(-\left(a + 0.8333333333333334\right)\right) \cdot \left(-\left(a + 0.8333333333333334\right)\right)}} \cdot \left(b - c\right)\right)}} \]

      9. sqr-neg 65.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \sqrt{\color{blue}{\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)}} \cdot \left(b - c\right)\right)}} \]

      10. sqrt-unprod 65.3%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(\sqrt{a + 0.8333333333333334} \cdot \sqrt{a + 0.8333333333333334}\right)} \cdot \left(b - c\right)\right)}} \]

      11. add-sqr-sqrt 65.3%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(0 + \color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)}} \]

   9. Applied egg-rr 65.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(0 + \left(a + 0.8333333333333334\right) \cdot \left(b - c\right)\right)}}} \]
   10. Step-by-step derivation

       1. +-lft-identity 65.3%

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

       2. *-commutative 65.3%

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

   11. Simplified 65.3%

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

   if 125 < t

   1. Initial program 98.3%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 92.5%

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

   6. Taylor expanded in a around 0 78.3%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 125:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-172} \lor \neg \left(t \leq 9000\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.02e-172) (not (<= t 9000.0)))
   (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))
   (/ x (+ x (* y (exp (* 2.0 (* -0.6666666666666666 (/ c t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.02e-172) || !(t <= 9000.0)) {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (-0.6666666666666666 * (c / t))))));
	}
	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 ((t <= (-1.02d-172)) .or. (.not. (t <= 9000.0d0))) then
        tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((-0.6666666666666666d0) * (c / t))))))
    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 ((t <= -1.02e-172) || !(t <= 9000.0)) {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (-0.6666666666666666 * (c / t))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.02e-172) or not (t <= 9000.0):
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (-0.6666666666666666 * (c / t))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.02e-172) || !(t <= 9000.0))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(-0.6666666666666666 * Float64(c / t)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.02e-172) || ~((t <= 9000.0)))
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	else
		tmp = x / (x + (y * exp((2.0 * (-0.6666666666666666 * (c / t))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.02e-172], N[Not[LessEqual[t, 9000.0]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(-0.6666666666666666 * N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e-172 or 9e3 < t

   1. Initial program 96.7%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around inf 90.7%

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

   6. Taylor expanded in a around 0 78.5%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -1.02e-172 < t < 9e3

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 72.9%

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

   4. Taylor expanded in c around inf 60.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-172} \lor \neg \left(t \leq 9000\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -530000000000 \lor \neg \left(c \leq 2.35 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -530000000000.0) (not (<= c 2.35e+25)))
   (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))
   (/ x (+ x (* y (exp (* -2.0 (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -530000000000.0) || !(c <= 2.35e+25)) {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	}
	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 ((c <= (-530000000000.0d0)) .or. (.not. (c <= 2.35d+25))) then
        tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    else
        tmp = x / (x + (y * exp(((-2.0d0) * (a * b)))))
    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 ((c <= -530000000000.0) || !(c <= 2.35e+25)) {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * Math.exp((-2.0 * (a * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (c <= -530000000000.0) or not (c <= 2.35e+25):
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	else:
		tmp = x / (x + (y * math.exp((-2.0 * (a * b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -530000000000.0) || !(c <= 2.35e+25))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(a * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((c <= -530000000000.0) || ~((c <= 2.35e+25)))
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	else
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -530000000000.0], N[Not[LessEqual[c, 2.35e+25]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.3e11 or 2.3499999999999999e25 < c

   1. Initial program 96.2%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in t around inf 79.0%

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

   6. Taylor expanded in a around 0 74.4%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -5.3e11 < c < 2.3499999999999999e25

   1. Initial program 96.0%

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

   3. Taylor expanded in a around inf 65.1%

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

   4. Taylor expanded in c around 0 62.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -530000000000 \lor \neg \left(c \leq 2.35 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 720:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 720.0)
   (/ x (+ x (* y (exp (* -2.0 (* a b))))))
   (/ x (+ x (* y (exp (* c 1.6666666666666667)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 720.0) {
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	} else {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	}
	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 (c <= 720.0d0) then
        tmp = x / (x + (y * exp(((-2.0d0) * (a * b)))))
    else
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    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 (c <= 720.0) {
		tmp = x / (x + (y * Math.exp((-2.0 * (a * b)))));
	} else {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 720.0:
		tmp = x / (x + (y * math.exp((-2.0 * (a * b)))))
	else:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 720.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(a * b))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 720.0)
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	else
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 720.0], N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 720

   1. Initial program 96.4%

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

   3. Taylor expanded in a around inf 65.6%

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

   4. Taylor expanded in c around 0 62.3%

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

   if 720 < c

   1. Initial program 95.2%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 76.6%

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

   6. Taylor expanded in a around 0 71.9%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   7. Taylor expanded in c around inf 68.8%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{1.6666666666666667 \cdot c}}} \]
   8. Step-by-step derivation

      1. *-commutative 68.8%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{c \cdot 1.6666666666666667}}} \]

   9. Simplified 68.8%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{c \cdot 1.6666666666666667}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 720:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 11500000000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 11500000000.0)
   (/ x (+ x (* y (exp (* b -1.6666666666666667)))))
   (/ x (* y (exp (* (- c b) 1.6666666666666667))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 11500000000.0) {
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	} else {
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	}
	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 (c <= 11500000000.0d0) then
        tmp = x / (x + (y * exp((b * (-1.6666666666666667d0)))))
    else
        tmp = x / (y * exp(((c - b) * 1.6666666666666667d0)))
    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 (c <= 11500000000.0) {
		tmp = x / (x + (y * Math.exp((b * -1.6666666666666667))));
	} else {
		tmp = x / (y * Math.exp(((c - b) * 1.6666666666666667)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 11500000000.0:
		tmp = x / (x + (y * math.exp((b * -1.6666666666666667))))
	else:
		tmp = x / (y * math.exp(((c - b) * 1.6666666666666667)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 11500000000.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(b * -1.6666666666666667)))));
	else
		tmp = Float64(x / Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 11500000000.0)
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	else
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 11500000000.0], N[(x / N[(x + N[(y * N[Exp[N[(b * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.15e10

   1. Initial program 96.4%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t around inf 69.1%

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

   6. Taylor expanded in a around 0 59.7%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   7. Taylor expanded in c around 0 57.8%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{-1.6666666666666667 \cdot b}}} \]
   8. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{b \cdot -1.6666666666666667}}} \]

   9. Simplified 57.8%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{b \cdot -1.6666666666666667}}} \]

   if 1.15e10 < c

   1. Initial program 94.9%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around inf 78.3%

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

   6. Taylor expanded in a around 0 74.9%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   7. Taylor expanded in x around 0 68.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 11500000000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 57.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 460:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 460.0)
   (/ x (+ x (* y (exp (* b -1.6666666666666667)))))
   (/ x (+ x (* y (exp (* c 1.6666666666666667)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 460.0) {
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	} else {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	}
	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 (c <= 460.0d0) then
        tmp = x / (x + (y * exp((b * (-1.6666666666666667d0)))))
    else
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    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 (c <= 460.0) {
		tmp = x / (x + (y * Math.exp((b * -1.6666666666666667))));
	} else {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 460.0:
		tmp = x / (x + (y * math.exp((b * -1.6666666666666667))))
	else:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 460.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(b * -1.6666666666666667)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 460.0)
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	else
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 460.0], N[(x / N[(x + N[(y * N[Exp[N[(b * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 460

   1. Initial program 96.4%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t around inf 69.5%

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

   6. Taylor expanded in a around 0 60.3%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   7. Taylor expanded in c around 0 58.4%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{-1.6666666666666667 \cdot b}}} \]
   8. Step-by-step derivation

      1. *-commutative 58.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{b \cdot -1.6666666666666667}}} \]

   9. Simplified 58.4%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{b \cdot -1.6666666666666667}}} \]

   if 460 < c

   1. Initial program 95.2%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 76.6%

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

   6. Taylor expanded in a around 0 71.9%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   7. Taylor expanded in c around inf 68.8%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{1.6666666666666667 \cdot c}}} \]
   8. Step-by-step derivation

      1. *-commutative 68.8%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{c \cdot 1.6666666666666667}}} \]

   9. Simplified 68.8%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{c \cdot 1.6666666666666667}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 460:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.3% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(c - b\right) \cdot \left(a \cdot 2\right) + 1\right)}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+270}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b 6.1e-195)
   (/ x (+ x (* y (+ (* (- c b) (* a 2.0)) 1.0))))
   (if (<= b 2.5e+102)
     (/ x (+ x (* (* a -2.0) (* b y))))
     (if (<= b 1.9e+270)
       (/ x (+ x y))
       (/
        x
        (+
         x
         (*
          y
          (+
           (* 2.0 (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))
           1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= 6.1e-195) {
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	} else if (b <= 2.5e+102) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else if (b <= 1.9e+270) {
		tmp = x / (x + y);
	} else {
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 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 (b <= 6.1d-195) then
        tmp = x / (x + (y * (((c - b) * (a * 2.0d0)) + 1.0d0)))
    else if (b <= 2.5d+102) then
        tmp = x / (x + ((a * (-2.0d0)) * (b * y)))
    else if (b <= 1.9d+270) then
        tmp = x / (x + y)
    else
        tmp = x / (x + (y * ((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))) + 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 (b <= 6.1e-195) {
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	} else if (b <= 2.5e+102) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else if (b <= 1.9e+270) {
		tmp = x / (x + y);
	} else {
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= 6.1e-195:
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)))
	elif b <= 2.5e+102:
		tmp = x / (x + ((a * -2.0) * (b * y)))
	elif b <= 1.9e+270:
		tmp = x / (x + y)
	else:
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= 6.1e-195)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(Float64(c - b) * Float64(a * 2.0)) + 1.0))));
	elseif (b <= 2.5e+102)
		tmp = Float64(x / Float64(x + Float64(Float64(a * -2.0) * Float64(b * y))));
	elseif (b <= 1.9e+270)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334)))) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= 6.1e-195)
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	elseif (b <= 2.5e+102)
		tmp = x / (x + ((a * -2.0) * (b * y)));
	elseif (b <= 1.9e+270)
		tmp = x / (x + y);
	else
		tmp = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, 6.1e-195], N[(x / N[(x + N[(y * N[(N[(N[(c - b), $MachinePrecision] * N[(a * 2.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+102], N[(x / N[(x + N[(N[(a * -2.0), $MachinePrecision] * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e+270], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < 6.1000000000000003e-195

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf 64.8%

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

   4. Taylor expanded in a around 0 50.5%

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

      1. associate-*r* 50.5%

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

      2. *-commutative 50.5%

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

      3. *-commutative 50.5%

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

   6. Simplified 50.5%

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

   if 6.1000000000000003e-195 < b < 2.5e102

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf 59.0%

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

   4. Taylor expanded in a around 0 37.2%

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

      1. associate-*r* 37.2%

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

      2. *-commutative 37.2%

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

      3. *-commutative 37.2%

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

   6. Simplified 37.2%

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

   7. Taylor expanded in b around inf 46.6%

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

      1. associate-*r* 46.6%

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

   9. Simplified 46.6%

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

   if 2.5e102 < b < 1.90000000000000009e270

   1. Initial program 94.9%

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

   3. Taylor expanded in a around inf 72.6%

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

   4. Taylor expanded in a around 0 45.2%

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

   if 1.90000000000000009e270 < b

   1. Initial program 85.7%

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

   3. Taylor expanded in b around inf 86.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   4. Step-by-step derivation

      1. associate-*r/ 86.2%

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

      2. metadata-eval 86.2%

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

      3. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in b around 0 72.3%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 72.3%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)\right)} \]

      2. metadata-eval 72.3%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)\right)} \]

      3. +-commutative 72.3%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)\right)} \]

   8. Simplified 72.3%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(c - b\right) \cdot \left(a \cdot 2\right) + 1\right)}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+270}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.0% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.051 \lor \neg \left(b \leq 5.5 \cdot 10^{-193}\right) \land b \leq 5.3 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -0.051) (and (not (<= b 5.5e-193)) (<= b 5.3e+101)))
   (/ x (+ x (* (* a -2.0) (* b y))))
   (/ x (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -0.051) || (!(b <= 5.5e-193) && (b <= 5.3e+101))) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else {
		tmp = x / (x + y);
	}
	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 ((b <= (-0.051d0)) .or. (.not. (b <= 5.5d-193)) .and. (b <= 5.3d+101)) then
        tmp = x / (x + ((a * (-2.0d0)) * (b * y)))
    else
        tmp = x / (x + y)
    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 ((b <= -0.051) || (!(b <= 5.5e-193) && (b <= 5.3e+101))) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -0.051) or (not (b <= 5.5e-193) and (b <= 5.3e+101)):
		tmp = x / (x + ((a * -2.0) * (b * y)))
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -0.051) || (!(b <= 5.5e-193) && (b <= 5.3e+101)))
		tmp = Float64(x / Float64(x + Float64(Float64(a * -2.0) * Float64(b * y))));
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -0.051) || (~((b <= 5.5e-193)) && (b <= 5.3e+101)))
		tmp = x / (x + ((a * -2.0) * (b * y)));
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -0.051], And[N[Not[LessEqual[b, 5.5e-193]], $MachinePrecision], LessEqual[b, 5.3e+101]]], N[(x / N[(x + N[(N[(a * -2.0), $MachinePrecision] * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.0509999999999999967 or 5.50000000000000014e-193 < b < 5.30000000000000006e101

   1. Initial program 95.9%

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

   3. Taylor expanded in a around inf 63.7%

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

   4. Taylor expanded in a around 0 48.6%

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

      1. associate-*r* 48.6%

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

      2. *-commutative 48.6%

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

      3. *-commutative 48.6%

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

   6. Simplified 48.6%

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

   7. Taylor expanded in b around inf 53.7%

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

      1. associate-*r* 53.7%

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

   9. Simplified 53.7%

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

   if -0.0509999999999999967 < b < 5.50000000000000014e-193 or 5.30000000000000006e101 < b

   1. Initial program 96.2%

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

   3. Taylor expanded in a around inf 66.1%

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

   4. Taylor expanded in a around 0 40.0%

      \[\leadsto \color{blue}{\frac{x}{x + y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.051 \lor \neg \left(b \leq 5.5 \cdot 10^{-193}\right) \land b \leq 5.3 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.9% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+37} \lor \neg \left(z \leq 6.6 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4.6e+37) (not (<= z 6.6e-111)))
   (/ x (+ x (* (* a -2.0) (* b y))))
   (/ x (+ x (* (* a 2.0) (* c y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.6e+37) || !(z <= 6.6e-111)) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else {
		tmp = x / (x + ((a * 2.0) * (c * y)));
	}
	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 ((z <= (-4.6d+37)) .or. (.not. (z <= 6.6d-111))) then
        tmp = x / (x + ((a * (-2.0d0)) * (b * y)))
    else
        tmp = x / (x + ((a * 2.0d0) * (c * y)))
    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 ((z <= -4.6e+37) || !(z <= 6.6e-111)) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else {
		tmp = x / (x + ((a * 2.0) * (c * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4.6e+37) or not (z <= 6.6e-111):
		tmp = x / (x + ((a * -2.0) * (b * y)))
	else:
		tmp = x / (x + ((a * 2.0) * (c * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4.6e+37) || !(z <= 6.6e-111))
		tmp = Float64(x / Float64(x + Float64(Float64(a * -2.0) * Float64(b * y))));
	else
		tmp = Float64(x / Float64(x + Float64(Float64(a * 2.0) * Float64(c * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4.6e+37) || ~((z <= 6.6e-111)))
		tmp = x / (x + ((a * -2.0) * (b * y)));
	else
		tmp = x / (x + ((a * 2.0) * (c * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4.6e+37], N[Not[LessEqual[z, 6.6e-111]], $MachinePrecision]], N[(x / N[(x + N[(N[(a * -2.0), $MachinePrecision] * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(N[(a * 2.0), $MachinePrecision] * N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000005e37 or 6.6e-111 < z

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 67.1%

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

   4. Taylor expanded in a around 0 42.3%

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

      1. associate-*r* 42.3%

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

      2. *-commutative 42.3%

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

      3. *-commutative 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in b around inf 44.8%

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

      1. associate-*r* 44.8%

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

   9. Simplified 44.8%

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

   if -4.60000000000000005e37 < z < 6.6e-111

   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 a around inf 62.1%

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

   4. Taylor expanded in a around 0 44.0%

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

      1. associate-*r* 44.0%

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

      2. *-commutative 44.0%

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

      3. *-commutative 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in c around inf 46.0%

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

      1. associate-*r* 46.0%

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

      2. *-commutative 46.0%

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

   9. Simplified 46.0%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+37} \lor \neg \left(z \leq 6.6 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.6% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(c - b\right) \cdot \left(a \cdot 2\right) + 1\right)}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b 1.1e-194)
   (/ x (+ x (* y (+ (* (- c b) (* a 2.0)) 1.0))))
   (if (<= b 3.1e+102) (/ x (+ x (* (* a -2.0) (* b y)))) (/ x (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= 1.1e-194) {
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	} else if (b <= 3.1e+102) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else {
		tmp = x / (x + y);
	}
	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 (b <= 1.1d-194) then
        tmp = x / (x + (y * (((c - b) * (a * 2.0d0)) + 1.0d0)))
    else if (b <= 3.1d+102) then
        tmp = x / (x + ((a * (-2.0d0)) * (b * y)))
    else
        tmp = x / (x + y)
    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 (b <= 1.1e-194) {
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	} else if (b <= 3.1e+102) {
		tmp = x / (x + ((a * -2.0) * (b * y)));
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= 1.1e-194:
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)))
	elif b <= 3.1e+102:
		tmp = x / (x + ((a * -2.0) * (b * y)))
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= 1.1e-194)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(Float64(c - b) * Float64(a * 2.0)) + 1.0))));
	elseif (b <= 3.1e+102)
		tmp = Float64(x / Float64(x + Float64(Float64(a * -2.0) * Float64(b * y))));
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= 1.1e-194)
		tmp = x / (x + (y * (((c - b) * (a * 2.0)) + 1.0)));
	elseif (b <= 3.1e+102)
		tmp = x / (x + ((a * -2.0) * (b * y)));
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, 1.1e-194], N[(x / N[(x + N[(y * N[(N[(N[(c - b), $MachinePrecision] * N[(a * 2.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e+102], N[(x / N[(x + N[(N[(a * -2.0), $MachinePrecision] * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 1.1000000000000001e-194

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf 64.8%

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

   4. Taylor expanded in a around 0 50.5%

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

      1. associate-*r* 50.5%

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

      2. *-commutative 50.5%

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

      3. *-commutative 50.5%

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

   6. Simplified 50.5%

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

   if 1.1000000000000001e-194 < b < 3.09999999999999987e102

   1. Initial program 94.4%

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

   3. Taylor expanded in a around inf 59.0%

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

   4. Taylor expanded in a around 0 37.2%

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

      1. associate-*r* 37.2%

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

      2. *-commutative 37.2%

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

      3. *-commutative 37.2%

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

   6. Simplified 37.2%

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

   7. Taylor expanded in b around inf 46.6%

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

      1. associate-*r* 46.6%

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

   9. Simplified 46.6%

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

   if 3.09999999999999987e102 < b

   1. Initial program 93.5%

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

   3. Taylor expanded in a around inf 72.6%

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

   4. Taylor expanded in a around 0 39.0%

      \[\leadsto \color{blue}{\frac{x}{x + y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(c - b\right) \cdot \left(a \cdot 2\right) + 1\right)}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{x + \left(a \cdot -2\right) \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.2% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+216}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5.1e+216) (* -0.5 (/ x (* a (* b y)))) (/ x (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.1e+216) {
		tmp = -0.5 * (x / (a * (b * y)));
	} else {
		tmp = x / (x + y);
	}
	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 (b <= (-5.1d+216)) then
        tmp = (-0.5d0) * (x / (a * (b * y)))
    else
        tmp = x / (x + y)
    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 (b <= -5.1e+216) {
		tmp = -0.5 * (x / (a * (b * y)));
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5.1e+216:
		tmp = -0.5 * (x / (a * (b * y)))
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5.1e+216)
		tmp = Float64(-0.5 * Float64(x / Float64(a * Float64(b * y))));
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -5.1e+216)
		tmp = -0.5 * (x / (a * (b * y)));
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5.1e+216], N[(-0.5 * N[(x / N[(a * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.1000000000000001e216

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf 75.8%

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

   4. Taylor expanded in a around 0 71.9%

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

      1. associate-*r* 71.9%

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

      2. *-commutative 71.9%

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

      3. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in b around inf 64.9%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{x}{a \cdot \left(b \cdot y\right)}} \]

   if -5.1000000000000001e216 < b

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 63.8%

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

   4. Taylor expanded in a around 0 38.2%

      \[\leadsto \color{blue}{\frac{x}{x + y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.1 \cdot 10^{+216}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.0% accurate, 46.2× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} \end{array} \]

FPCore

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

C

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

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)
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);
}

Python

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

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + y))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in a around inf 65.0%

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

4. Taylor expanded in a around 0 36.1%

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

5. Final simplification 36.1%

   \[\leadsto \frac{x}{x + y} \]
6. Add Preprocessing

Developer target: 95.6% accurate, 0.9× 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 2024027 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

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

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