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

Percentage Accurate: 93.8% → 97.3%

Time: 32.1s

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: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.7× speedup

Math

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

FPCore

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

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) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	}
	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) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b));
	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 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((z * math.sqrt((t + a))) / t) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b))
	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 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	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(Float64(a + 0.8333333333333334) - Float64(2.0 / Float64(t * 3.0))) * Float64(c - b)))
	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(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((z * sqrt((t + a))) / t) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	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[(N[(a + 0.8333333333333334), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(c - b), $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[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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 99.2%

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

   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. Taylor expanded in t around 0 77.6%

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

4. Final simplification 98.1%

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

Alternative 2: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\\ \mathbf{if}\;c \leq -1.48 \cdot 10^{+54} \lor \neg \left(c \leq 6.8 \cdot 10^{+161}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot t_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t} - b \cdot t_1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ a (+ 0.8333333333333334 (/ -0.6666666666666666 t)))))
   (if (or (<= c -1.48e+54) (not (<= c 6.8e+161)))
     (/ x (+ x (* y (exp (* 2.0 (* c t_1))))))
     (/
      x
      (+ x (* y (exp (* 2.0 (- (* (sqrt (+ t a)) (/ z t)) (* b t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a + (0.8333333333333334 + (-0.6666666666666666 / t));
	double tmp;
	if ((c <= -1.48e+54) || !(c <= 6.8e+161)) {
		tmp = x / (x + (y * exp((2.0 * (c * t_1)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((sqrt((t + a)) * (z / t)) - (b * t_1))))));
	}
	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) :: tmp
    t_1 = a + (0.8333333333333334d0 + ((-0.6666666666666666d0) / t))
    if ((c <= (-1.48d+54)) .or. (.not. (c <= 6.8d+161))) then
        tmp = x / (x + (y * exp((2.0d0 * (c * t_1)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((sqrt((t + a)) * (z / t)) - (b * t_1))))))
    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 = a + (0.8333333333333334 + (-0.6666666666666666 / t));
	double tmp;
	if ((c <= -1.48e+54) || !(c <= 6.8e+161)) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * t_1)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((Math.sqrt((t + a)) * (z / t)) - (b * t_1))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a + (0.8333333333333334 + (-0.6666666666666666 / t))
	tmp = 0
	if (c <= -1.48e+54) or not (c <= 6.8e+161):
		tmp = x / (x + (y * math.exp((2.0 * (c * t_1)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((math.sqrt((t + a)) * (z / t)) - (b * t_1))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a + Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t)))
	tmp = 0.0
	if ((c <= -1.48e+54) || !(c <= 6.8e+161))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * t_1))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(sqrt(Float64(t + a)) * Float64(z / t)) - Float64(b * t_1)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a + (0.8333333333333334 + (-0.6666666666666666 / t));
	tmp = 0.0;
	if ((c <= -1.48e+54) || ~((c <= 6.8e+161)))
		tmp = x / (x + (y * exp((2.0 * (c * t_1)))));
	else
		tmp = x / (x + (y * exp((2.0 * ((sqrt((t + a)) * (z / t)) - (b * t_1))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a + N[(0.8333333333333334 + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[c, -1.48e+54], N[Not[LessEqual[c, 6.8e+161]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.48e54 or 6.79999999999999986e161 < c

   1. Initial program 92.0%

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

   2. Taylor expanded in c around inf 93.2%

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

      1. cancel-sign-sub-inv 93.2%

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

      2. +-commutative 93.2%

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

      3. metadata-eval 93.2%

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

      4. associate-*r/ 93.2%

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

      5. metadata-eval 93.2%

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

      6. associate-+r+ 93.2%

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

   4. Simplified 93.2%

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

   if -1.48e54 < c < 6.79999999999999986e161

   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. Taylor expanded in c around 0 91.2%

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

      1. fma-neg 91.8%

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

      2. +-commutative 91.8%

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

      3. fma-neg 91.2%

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

      4. cancel-sign-sub-inv 91.2%

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

      5. +-commutative 91.2%

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

      6. metadata-eval 91.2%

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

      7. associate-*r/ 91.2%

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

      8. metadata-eval 91.2%

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

      9. associate-+r+ 91.2%

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

   4. Simplified 91.2%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.48 \cdot 10^{+54} \lor \neg \left(c \leq 6.8 \cdot 10^{+161}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t} - b \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \end{array} \]

Alternative 3: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{0.6944444444444444 - a \cdot a}{0.8333333333333334 - a} \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 1.85e-271)
   (/
    x
    (+
     x
     (*
      y
      (exp (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
   (if (<= t 1.02e-32)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (* c (+ a (+ 0.8333333333333334 (/ -0.6666666666666666 t)))))))))
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (*
           (/ (- 0.6944444444444444 (* a a)) (- 0.8333333333333334 a))
           (- c b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.85e-271) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 1.02e-32) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (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 <= 1.85d-271) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 1.02d-32) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (0.8333333333333334d0 + ((-0.6666666666666666d0) / t))))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (((0.6944444444444444d0 - (a * a)) / (0.8333333333333334d0 - a)) * (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 <= 1.85e-271) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 1.02e-32) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 1.85e-271:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 1.02e-32:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 1.85e-271)
		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 <= 1.02e-32)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t)))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(0.6944444444444444 - Float64(a * a)) / Float64(0.8333333333333334 - a)) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 1.85e-271)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 1.02e-32)
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	else
		tmp = x / (x + (y * exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 1.85e-271], 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, 1.02e-32], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(0.8333333333333334 + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(0.6944444444444444 - N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.85000000000000011e-271

   1. Initial program 91.8%

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

   2. Taylor expanded in t around 0 93.4%

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

   if 1.85000000000000011e-271 < t < 1.02000000000000002e-32

   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. Taylor expanded in c around inf 77.7%

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

      1. cancel-sign-sub-inv 77.7%

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

      2. +-commutative 77.7%

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

      3. metadata-eval 77.7%

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

      4. associate-*r/ 77.7%

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

      5. metadata-eval 77.7%

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

      6. associate-+r+ 77.7%

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

   4. Simplified 77.7%

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

   if 1.02000000000000002e-32 < t

   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. Taylor expanded in t around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-rgt-neg-in 89.8%

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

      3. +-commutative 89.8%

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

   4. Simplified 89.8%

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

      1. +-commutative 89.8%

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

      2. flip-+ 90.7%

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

      3. metadata-eval 90.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\color{blue}{0.6944444444444444} - a \cdot a}{0.8333333333333334 - a} \cdot \left(-\left(b - c\right)\right)\right)}} \]

   6. Applied egg-rr 90.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{0.6944444444444444 - a \cdot a}{0.8333333333333334 - a}} \cdot \left(-\left(b - c\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{0.6944444444444444 - a \cdot a}{0.8333333333333334 - a} \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 4: 80.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{0.6944444444444444 - a \cdot a}{0.8333333333333334 - a} \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.75e-247)
   (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))
   (if (<= t 1.02e-32)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (* c (+ a (+ 0.8333333333333334 (/ -0.6666666666666666 t)))))))))
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (*
           (/ (- 0.6944444444444444 (* a a)) (- 0.8333333333333334 a))
           (- c b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.75e-247) {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else if (t <= 1.02e-32) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (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 <= (-1.75d-247)) then
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    else if (t <= 1.02d-32) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (0.8333333333333334d0 + ((-0.6666666666666666d0) / t))))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (((0.6944444444444444d0 - (a * a)) / (0.8333333333333334d0 - a)) * (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 <= -1.75e-247) {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else if (t <= 1.02e-32) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.75e-247:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	elif t <= 1.02e-32:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.75e-247)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	elseif (t <= 1.02e-32)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t)))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(0.6944444444444444 - Float64(a * a)) / Float64(0.8333333333333334 - a)) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.75e-247)
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	elseif (t <= 1.02e-32)
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	else
		tmp = x / (x + (y * exp((2.0 * (((0.6944444444444444 - (a * a)) / (0.8333333333333334 - a)) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.75e-247], 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], If[LessEqual[t, 1.02e-32], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(0.8333333333333334 + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(0.6944444444444444 - N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e-247

   1. Initial program 93.6%

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

   2. Taylor expanded in t around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-rgt-neg-in 85.6%

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

      3. +-commutative 85.6%

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

   4. Simplified 85.6%

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

   if -1.75e-247 < t < 1.02000000000000002e-32

   1. Initial program 90.5%

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

   2. Taylor expanded in c around inf 76.6%

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

      1. cancel-sign-sub-inv 76.6%

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

      2. +-commutative 76.6%

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

      3. metadata-eval 76.6%

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

      4. associate-*r/ 76.6%

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

      5. metadata-eval 76.6%

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

      6. associate-+r+ 76.6%

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

   4. Simplified 76.6%

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

   if 1.02000000000000002e-32 < t

   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. Taylor expanded in t around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-rgt-neg-in 89.8%

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

      3. +-commutative 89.8%

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

   4. Simplified 89.8%

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

      1. +-commutative 89.8%

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

      2. flip-+ 90.7%

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

      3. metadata-eval 90.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\color{blue}{0.6944444444444444} - a \cdot a}{0.8333333333333334 - a} \cdot \left(-\left(b - c\right)\right)\right)}} \]

   6. Applied egg-rr 90.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{0.6944444444444444 - a \cdot a}{0.8333333333333334 - a}} \cdot \left(-\left(b - c\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{0.6944444444444444 - a \cdot a}{0.8333333333333334 - a} \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 5: 52.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{if}\;a \leq 4.6 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-242}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+95} \lor \neg \left(a \leq 1.85 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(c \cdot 2\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \left(b - c\right) \cdot \left(a \cdot 2\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+ x (+ y (* (* a 2.0) (/ (* y (- (* c c) (* b b))) (+ b c))))))))
   (if (<= a 4.6e-294)
     t_1
     (if (<= a 3.25e-242)
       1.0
       (if (<= a 2.1e-151)
         t_1
         (if (<= a 5.3e-18)
           1.0
           (if (or (<= a 4.6e+95) (not (<= a 1.85e+142)))
             (/ x (+ x (* y (exp (* a (* c 2.0))))))
             (/ x (- x (* y (+ -1.0 (* (- b c) (* a 2.0)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	double tmp;
	if (a <= 4.6e-294) {
		tmp = t_1;
	} else if (a <= 3.25e-242) {
		tmp = 1.0;
	} else if (a <= 2.1e-151) {
		tmp = t_1;
	} else if (a <= 5.3e-18) {
		tmp = 1.0;
	} else if ((a <= 4.6e+95) || !(a <= 1.85e+142)) {
		tmp = x / (x + (y * exp((a * (c * 2.0)))));
	} else {
		tmp = x / (x - (y * (-1.0 + ((b - c) * (a * 2.0)))));
	}
	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) :: tmp
    t_1 = x / (x + (y + ((a * 2.0d0) * ((y * ((c * c) - (b * b))) / (b + c)))))
    if (a <= 4.6d-294) then
        tmp = t_1
    else if (a <= 3.25d-242) then
        tmp = 1.0d0
    else if (a <= 2.1d-151) then
        tmp = t_1
    else if (a <= 5.3d-18) then
        tmp = 1.0d0
    else if ((a <= 4.6d+95) .or. (.not. (a <= 1.85d+142))) then
        tmp = x / (x + (y * exp((a * (c * 2.0d0)))))
    else
        tmp = x / (x - (y * ((-1.0d0) + ((b - c) * (a * 2.0d0)))))
    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 = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	double tmp;
	if (a <= 4.6e-294) {
		tmp = t_1;
	} else if (a <= 3.25e-242) {
		tmp = 1.0;
	} else if (a <= 2.1e-151) {
		tmp = t_1;
	} else if (a <= 5.3e-18) {
		tmp = 1.0;
	} else if ((a <= 4.6e+95) || !(a <= 1.85e+142)) {
		tmp = x / (x + (y * Math.exp((a * (c * 2.0)))));
	} else {
		tmp = x / (x - (y * (-1.0 + ((b - c) * (a * 2.0)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))))
	tmp = 0
	if a <= 4.6e-294:
		tmp = t_1
	elif a <= 3.25e-242:
		tmp = 1.0
	elif a <= 2.1e-151:
		tmp = t_1
	elif a <= 5.3e-18:
		tmp = 1.0
	elif (a <= 4.6e+95) or not (a <= 1.85e+142):
		tmp = x / (x + (y * math.exp((a * (c * 2.0)))))
	else:
		tmp = x / (x - (y * (-1.0 + ((b - c) * (a * 2.0)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(Float64(y * Float64(Float64(c * c) - Float64(b * b))) / Float64(b + c))))))
	tmp = 0.0
	if (a <= 4.6e-294)
		tmp = t_1;
	elseif (a <= 3.25e-242)
		tmp = 1.0;
	elseif (a <= 2.1e-151)
		tmp = t_1;
	elseif (a <= 5.3e-18)
		tmp = 1.0;
	elseif ((a <= 4.6e+95) || !(a <= 1.85e+142))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(a * Float64(c * 2.0))))));
	else
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 + Float64(Float64(b - c) * Float64(a * 2.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	tmp = 0.0;
	if (a <= 4.6e-294)
		tmp = t_1;
	elseif (a <= 3.25e-242)
		tmp = 1.0;
	elseif (a <= 2.1e-151)
		tmp = t_1;
	elseif (a <= 5.3e-18)
		tmp = 1.0;
	elseif ((a <= 4.6e+95) || ~((a <= 1.85e+142)))
		tmp = x / (x + (y * exp((a * (c * 2.0)))));
	else
		tmp = x / (x - (y * (-1.0 + ((b - c) * (a * 2.0)))));
	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[(N[(a * 2.0), $MachinePrecision] * N[(N[(y * N[(N[(c * c), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 4.6e-294], t$95$1, If[LessEqual[a, 3.25e-242], 1.0, If[LessEqual[a, 2.1e-151], t$95$1, If[LessEqual[a, 5.3e-18], 1.0, If[Or[LessEqual[a, 4.6e+95], N[Not[LessEqual[a, 1.85e+142]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(a * N[(c * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x - N[(y * N[(-1.0 + N[(N[(b - c), $MachinePrecision] * N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 4.60000000000000032e-294 or 3.2499999999999999e-242 < a < 2.0999999999999999e-151

   1. Initial program 97.7%

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

   2. Taylor expanded in a around inf 47.9%

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

   3. Taylor expanded in a around 0 50.5%

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

      1. associate-*r* 50.5%

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

      2. *-commutative 50.5%

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

      3. *-commutative 50.5%

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

   5. Simplified 50.5%

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

      1. flip-- 60.1%

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

      2. associate-*l/ 62.4%

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

      3. *-commutative 62.4%

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

      4. +-commutative 62.4%

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

   7. Applied egg-rr 62.4%

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

   if 4.60000000000000032e-294 < a < 3.2499999999999999e-242 or 2.0999999999999999e-151 < a < 5.3000000000000003e-18

   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. Taylor expanded in c around inf 69.3%

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

      1. cancel-sign-sub-inv 69.3%

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

      2. +-commutative 69.3%

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

      3. metadata-eval 69.3%

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

      4. associate-*r/ 69.3%

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

      5. metadata-eval 69.3%

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

      6. associate-+r+ 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in c around 0 42.9%

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

      1. +-commutative 42.9%

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

   7. Simplified 42.9%

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

   8. Taylor expanded in x around inf 69.2%

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

   if 5.3000000000000003e-18 < a < 4.59999999999999994e95 or 1.8499999999999999e142 < a

   1. Initial program 90.3%

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

   2. Taylor expanded in a around inf 75.2%

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

   3. Taylor expanded in c around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*l* 67.2%

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

   5. Simplified 67.2%

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

   if 4.59999999999999994e95 < a < 1.8499999999999999e142

   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. Taylor expanded in a around inf 44.5%

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

   3. Taylor expanded in a around 0 79.1%

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

      1. associate-*r* 79.1%

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

      2. *-commutative 79.1%

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

   5. Simplified 79.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.6 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;a \leq 3.25 \cdot 10^{-242}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+95} \lor \neg \left(a \leq 1.85 \cdot 10^{+142}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(c \cdot 2\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \left(b - c\right) \cdot \left(a \cdot 2\right)\right)}\\ \end{array} \]

Alternative 6: 52.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(c \cdot 2\right)}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-156}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-84} \lor \neg \left(t \leq 1.12 \cdot 10^{+157}\right) \land t \leq 1.2 \cdot 10^{+231}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(a \cdot b\right) \cdot -2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -5e-310)
   (/ x (+ x (* y (exp (* a (* c 2.0))))))
   (if (<= t 9.5e-181)
     (/ x (+ x (+ y (* 2.0 (* y (* a c))))))
     (if (<= t 3.3e-156)
       1.0
       (if (or (<= t 1.75e-84) (and (not (<= t 1.12e+157)) (<= t 1.2e+231)))
         (/ x (+ x (+ y (* (* a 2.0) (/ (* y (- (* c c) (* b b))) (+ b c))))))
         (/ x (+ x (* y (exp (* (* a b) -2.0))))))))))

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((a * (c * 2.0)))));
	} else if (t <= 9.5e-181) {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	} else if (t <= 3.3e-156) {
		tmp = 1.0;
	} else if ((t <= 1.75e-84) || (!(t <= 1.12e+157) && (t <= 1.2e+231))) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else {
		tmp = x / (x + (y * exp(((a * b) * -2.0))));
	}
	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 (t <= (-5d-310)) then
        tmp = x / (x + (y * exp((a * (c * 2.0d0)))))
    else if (t <= 9.5d-181) then
        tmp = x / (x + (y + (2.0d0 * (y * (a * c)))))
    else if (t <= 3.3d-156) then
        tmp = 1.0d0
    else if ((t <= 1.75d-84) .or. (.not. (t <= 1.12d+157)) .and. (t <= 1.2d+231)) then
        tmp = x / (x + (y + ((a * 2.0d0) * ((y * ((c * c) - (b * b))) / (b + c)))))
    else
        tmp = x / (x + (y * exp(((a * b) * (-2.0d0)))))
    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 (t <= -5e-310) {
		tmp = x / (x + (y * Math.exp((a * (c * 2.0)))));
	} else if (t <= 9.5e-181) {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	} else if (t <= 3.3e-156) {
		tmp = 1.0;
	} else if ((t <= 1.75e-84) || (!(t <= 1.12e+157) && (t <= 1.2e+231))) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else {
		tmp = x / (x + (y * Math.exp(((a * b) * -2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -5e-310:
		tmp = x / (x + (y * math.exp((a * (c * 2.0)))))
	elif t <= 9.5e-181:
		tmp = x / (x + (y + (2.0 * (y * (a * c)))))
	elif t <= 3.3e-156:
		tmp = 1.0
	elif (t <= 1.75e-84) or (not (t <= 1.12e+157) and (t <= 1.2e+231)):
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))))
	else:
		tmp = x / (x + (y * math.exp(((a * b) * -2.0))))
	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(a * Float64(c * 2.0))))));
	elseif (t <= 9.5e-181)
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(y * Float64(a * c))))));
	elseif (t <= 3.3e-156)
		tmp = 1.0;
	elseif ((t <= 1.75e-84) || (!(t <= 1.12e+157) && (t <= 1.2e+231)))
		tmp = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(Float64(y * Float64(Float64(c * c) - Float64(b * b))) / Float64(b + c))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(a * b) * -2.0)))));
	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((a * (c * 2.0)))));
	elseif (t <= 9.5e-181)
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	elseif (t <= 3.3e-156)
		tmp = 1.0;
	elseif ((t <= 1.75e-84) || (~((t <= 1.12e+157)) && (t <= 1.2e+231)))
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	else
		tmp = x / (x + (y * exp(((a * b) * -2.0))));
	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[(a * N[(c * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-181], N[(x / N[(x + N[(y + N[(2.0 * N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-156], 1.0, If[Or[LessEqual[t, 1.75e-84], And[N[Not[LessEqual[t, 1.12e+157]], $MachinePrecision], LessEqual[t, 1.2e+231]]], N[(x / N[(x + N[(y + N[(N[(a * 2.0), $MachinePrecision] * N[(N[(y * N[(N[(c * c), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(N[(a * b), $MachinePrecision] * -2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.999999999999985e-310

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf 83.4%

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

   3. Taylor expanded in c around inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. *-commutative 68.3%

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

      3. associate-*l* 68.3%

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

   5. Simplified 68.3%

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

   if -4.999999999999985e-310 < t < 9.49999999999999998e-181

   1. Initial program 86.1%

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

   2. Taylor expanded in a around inf 35.6%

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

   3. Taylor expanded in c around inf 43.7%

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

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

      3. associate-*l* 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in a around 0 57.4%

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

      1. associate-*r* 62.6%

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

   8. Simplified 62.6%

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

   if 9.49999999999999998e-181 < t < 3.2999999999999999e-156

   1. Initial program 71.4%

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

   2. Taylor expanded in c around inf 44.4%

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

      1. cancel-sign-sub-inv 44.4%

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

      2. +-commutative 44.4%

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

      3. metadata-eval 44.4%

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

      4. associate-*r/ 44.4%

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

      5. metadata-eval 44.4%

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

      6. associate-+r+ 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in c around 0 16.8%

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

      1. +-commutative 16.8%

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

   7. Simplified 16.8%

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

   8. Taylor expanded in x around inf 86.2%

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

   if 3.2999999999999999e-156 < t < 1.7500000000000001e-84 or 1.11999999999999995e157 < t < 1.20000000000000003e231

   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. Taylor expanded in a around inf 51.9%

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

   3. Taylor expanded in a around 0 50.2%

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

      1. associate-*r* 50.2%

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

      2. *-commutative 50.2%

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

      3. *-commutative 50.2%

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

   5. Simplified 50.2%

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

      1. flip-- 64.9%

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

      2. associate-*l/ 68.6%

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

      3. *-commutative 68.6%

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

      4. +-commutative 68.6%

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

   7. Applied egg-rr 68.6%

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

   if 1.7500000000000001e-84 < t < 1.11999999999999995e157 or 1.20000000000000003e231 < 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. Taylor expanded in a around inf 66.1%

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

   3. Taylor expanded in c around 0 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(c \cdot 2\right)}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-156}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-84} \lor \neg \left(t \leq 1.12 \cdot 10^{+157}\right) \land t \leq 1.2 \cdot 10^{+231}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(a \cdot b\right) \cdot -2}}\\ \end{array} \]

Alternative 7: 67.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq 5.9 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-158}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;t \leq 760000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= t 5.9e-305)
     t_1
     (if (<= t 2.6e-174)
       (/ x (+ x (+ y (* 2.0 (* y (* a c))))))
       (if (<= t 5.5e-158)
         1.0
         (if (<= t 1.25e-77)
           (/
            x
            (+ x (+ y (* (* a 2.0) (/ (* y (- (* c c) (* b b))) (+ b c))))))
           (if (<= t 760000000000.0)
             t_1
             (/ 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 t_1 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= 5.9e-305) {
		tmp = t_1;
	} else if (t <= 2.6e-174) {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	} else if (t <= 5.5e-158) {
		tmp = 1.0;
	} else if (t <= 1.25e-77) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else if (t <= 760000000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    if (t <= 5.9d-305) then
        tmp = t_1
    else if (t <= 2.6d-174) then
        tmp = x / (x + (y + (2.0d0 * (y * (a * c)))))
    else if (t <= 5.5d-158) then
        tmp = 1.0d0
    else if (t <= 1.25d-77) then
        tmp = x / (x + (y + ((a * 2.0d0) * ((y * ((c * c) - (b * b))) / (b + c)))))
    else if (t <= 760000000000.0d0) then
        tmp = t_1
    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 t_1 = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= 5.9e-305) {
		tmp = t_1;
	} else if (t <= 2.6e-174) {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	} else if (t <= 5.5e-158) {
		tmp = 1.0;
	} else if (t <= 1.25e-77) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else if (t <= 760000000000.0) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	tmp = 0
	if t <= 5.9e-305:
		tmp = t_1
	elif t <= 2.6e-174:
		tmp = x / (x + (y + (2.0 * (y * (a * c)))))
	elif t <= 5.5e-158:
		tmp = 1.0
	elif t <= 1.25e-77:
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))))
	elif t <= 760000000000.0:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	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(a * Float64(c - b)))))))
	tmp = 0.0
	if (t <= 5.9e-305)
		tmp = t_1;
	elseif (t <= 2.6e-174)
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(y * Float64(a * c))))));
	elseif (t <= 5.5e-158)
		tmp = 1.0;
	elseif (t <= 1.25e-77)
		tmp = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(Float64(y * Float64(Float64(c * c) - Float64(b * b))) / Float64(b + c))))));
	elseif (t <= 760000000000.0)
		tmp = t_1;
	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)
	t_1 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	tmp = 0.0;
	if (t <= 5.9e-305)
		tmp = t_1;
	elseif (t <= 2.6e-174)
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	elseif (t <= 5.5e-158)
		tmp = 1.0;
	elseif (t <= 1.25e-77)
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	elseif (t <= 760000000000.0)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	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[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 5.9e-305], t$95$1, If[LessEqual[t, 2.6e-174], N[(x / N[(x + N[(y + N[(2.0 * N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-158], 1.0, If[LessEqual[t, 1.25e-77], N[(x / N[(x + N[(y + N[(N[(a * 2.0), $MachinePrecision] * N[(N[(y * N[(N[(c * c), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 760000000000.0], t$95$1, 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 5 regimes

2. if t < 5.9000000000000005e-305 or 1.24999999999999991e-77 < t < 7.6e11

   1. Initial program 94.3%

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

   2. 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 5.9000000000000005e-305 < t < 2.6000000000000002e-174

   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. Taylor expanded in a around inf 36.5%

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

   3. Taylor expanded in c around inf 44.9%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*l* 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in a around 0 59.0%

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

      1. associate-*r* 64.3%

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

   8. Simplified 64.3%

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

   if 2.6000000000000002e-174 < t < 5.50000000000000025e-158

   1. Initial program 71.4%

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

   2. Taylor expanded in c around inf 44.4%

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

      1. cancel-sign-sub-inv 44.4%

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

      2. +-commutative 44.4%

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

      3. metadata-eval 44.4%

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

      4. associate-*r/ 44.4%

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

      5. metadata-eval 44.4%

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

      6. associate-+r+ 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in c around 0 16.8%

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

      1. +-commutative 16.8%

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

   7. Simplified 16.8%

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

   8. Taylor expanded in x around inf 86.2%

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

   if 5.50000000000000025e-158 < t < 1.24999999999999991e-77

   1. Initial program 96.7%

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

   2. Taylor expanded in a around inf 42.3%

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

   3. Taylor expanded in a around 0 55.4%

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

      1. associate-*r* 55.4%

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

      2. *-commutative 55.4%

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

      3. *-commutative 55.4%

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

   5. Simplified 55.4%

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

      1. flip-- 64.9%

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

      2. associate-*l/ 68.2%

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

      3. *-commutative 68.2%

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

      4. +-commutative 68.2%

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

   7. Applied egg-rr 68.2%

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

   if 7.6e11 < 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. Taylor expanded in t around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. distribute-rgt-neg-in 93.0%

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

      3. +-commutative 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in a around 0 87.6%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
   6. Step-by-step derivation

      1. +-commutative 87.6%

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

      2. *-commutative 87.6%

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

   7. Simplified 87.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667} + x}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.9 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-158}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;t \leq 760000000000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 8: 77.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;t \leq 900000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))))
   (if (<= t -4.1e-299)
     t_1
     (if (<= t 1.8e-126)
       (/ x (+ x (* y (exp (* 2.0 (* b (/ 0.6666666666666666 t)))))))
       (if (<= t 1.35e-32)
         (/ x (+ x (+ y (* (* a 2.0) (/ (* y (- (* c c) (* b b))) (+ b c))))))
         (if (<= t 900000.0)
           (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
           t_1))))))

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 * ((a + 0.8333333333333334) * (c - b))))));
	double tmp;
	if (t <= -4.1e-299) {
		tmp = t_1;
	} else if (t <= 1.8e-126) {
		tmp = x / (x + (y * exp((2.0 * (b * (0.6666666666666666 / t))))));
	} else if (t <= 1.35e-32) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else if (t <= 900000.0) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    if (t <= (-4.1d-299)) then
        tmp = t_1
    else if (t <= 1.8d-126) then
        tmp = x / (x + (y * exp((2.0d0 * (b * (0.6666666666666666d0 / t))))))
    else if (t <= 1.35d-32) then
        tmp = x / (x + (y + ((a * 2.0d0) * ((y * ((c * c) - (b * b))) / (b + c)))))
    else if (t <= 900000.0d0) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else
        tmp = t_1
    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 * ((a + 0.8333333333333334) * (c - b))))));
	double tmp;
	if (t <= -4.1e-299) {
		tmp = t_1;
	} else if (t <= 1.8e-126) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * (0.6666666666666666 / t))))));
	} else if (t <= 1.35e-32) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else if (t <= 900000.0) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	tmp = 0
	if t <= -4.1e-299:
		tmp = t_1
	elif t <= 1.8e-126:
		tmp = x / (x + (y * math.exp((2.0 * (b * (0.6666666666666666 / t))))))
	elif t <= 1.35e-32:
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))))
	elif t <= 900000.0:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	else:
		tmp = t_1
	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(a + 0.8333333333333334) * Float64(c - b)))))))
	tmp = 0.0
	if (t <= -4.1e-299)
		tmp = t_1;
	elseif (t <= 1.8e-126)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(0.6666666666666666 / t)))))));
	elseif (t <= 1.35e-32)
		tmp = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(Float64(y * Float64(Float64(c * c) - Float64(b * b))) / Float64(b + c))))));
	elseif (t <= 900000.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	tmp = 0.0;
	if (t <= -4.1e-299)
		tmp = t_1;
	elseif (t <= 1.8e-126)
		tmp = x / (x + (y * exp((2.0 * (b * (0.6666666666666666 / t))))));
	elseif (t <= 1.35e-32)
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	elseif (t <= 900000.0)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	else
		tmp = t_1;
	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[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e-299], t$95$1, If[LessEqual[t, 1.8e-126], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-32], N[(x / N[(x + N[(y + N[(N[(a * 2.0), $MachinePrecision] * N[(N[(y * N[(N[(c * c), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 900000.0], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.1000000000000001e-299 or 9e5 < t

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-rgt-neg-in 89.7%

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

      3. +-commutative 89.7%

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

   4. Simplified 89.7%

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

   if -4.1000000000000001e-299 < t < 1.8e-126

   1. Initial program 87.0%

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

   2. Taylor expanded in b around inf 69.5%

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

      1. associate-*r/ 69.5%

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

      2. metadata-eval 69.5%

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

      3. +-commutative 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in t around 0 76.7%

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

      1. associate-*r/ 76.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 76.7%

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

      3. *-commutative 76.7%

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

   7. Simplified 76.7%

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

   if 1.8e-126 < t < 1.3499999999999999e-32

   1. Initial program 96.3%

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

   2. Taylor expanded in a around inf 46.7%

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

   3. Taylor expanded in a around 0 57.9%

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

      1. associate-*r* 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

   5. Simplified 57.9%

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

      1. flip-- 68.2%

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

      2. associate-*l/ 68.2%

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

      3. *-commutative 68.2%

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

      4. +-commutative 68.2%

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

   7. Applied egg-rr 68.2%

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

   if 1.3499999999999999e-32 < t < 9e5

   1. Initial program 93.3%

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

   2. Taylor expanded in a around inf 74.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;t \leq 900000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 9: 66.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;t \leq 7.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-155}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.58 \cdot 10^{-145}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(y - x\right)}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))))
   (if (<= t 7.4e-305)
     t_1
     (if (<= t 1.7e-181)
       (/ x (+ x (+ y (* 2.0 (* y (* a c))))))
       (if (<= t 1.25e-155)
         1.0
         (if (<= t 1.58e-145)
           (* (- y x) (/ x (* (+ x y) (- y x))))
           (if (<= t 3.1e-40)
             (/
              x
              (+ x (+ y (* (* a 2.0) (/ (* y (- (* c c) (* b b))) (+ b c))))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	double tmp;
	if (t <= 7.4e-305) {
		tmp = t_1;
	} else if (t <= 1.7e-181) {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	} else if (t <= 1.25e-155) {
		tmp = 1.0;
	} else if (t <= 1.58e-145) {
		tmp = (y - x) * (x / ((x + y) * (y - x)));
	} else if (t <= 3.1e-40) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    if (t <= 7.4d-305) then
        tmp = t_1
    else if (t <= 1.7d-181) then
        tmp = x / (x + (y + (2.0d0 * (y * (a * c)))))
    else if (t <= 1.25d-155) then
        tmp = 1.0d0
    else if (t <= 1.58d-145) then
        tmp = (y - x) * (x / ((x + y) * (y - x)))
    else if (t <= 3.1d-40) then
        tmp = x / (x + (y + ((a * 2.0d0) * ((y * ((c * c) - (b * b))) / (b + c)))))
    else
        tmp = t_1
    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(((c - b) * 1.6666666666666667))));
	double tmp;
	if (t <= 7.4e-305) {
		tmp = t_1;
	} else if (t <= 1.7e-181) {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	} else if (t <= 1.25e-155) {
		tmp = 1.0;
	} else if (t <= 1.58e-145) {
		tmp = (y - x) * (x / ((x + y) * (y - x)));
	} else if (t <= 3.1e-40) {
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	tmp = 0
	if t <= 7.4e-305:
		tmp = t_1
	elif t <= 1.7e-181:
		tmp = x / (x + (y + (2.0 * (y * (a * c)))))
	elif t <= 1.25e-155:
		tmp = 1.0
	elif t <= 1.58e-145:
		tmp = (y - x) * (x / ((x + y) * (y - x)))
	elif t <= 3.1e-40:
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))))
	tmp = 0.0
	if (t <= 7.4e-305)
		tmp = t_1;
	elseif (t <= 1.7e-181)
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(y * Float64(a * c))))));
	elseif (t <= 1.25e-155)
		tmp = 1.0;
	elseif (t <= 1.58e-145)
		tmp = Float64(Float64(y - x) * Float64(x / Float64(Float64(x + y) * Float64(y - x))));
	elseif (t <= 3.1e-40)
		tmp = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(Float64(y * Float64(Float64(c * c) - Float64(b * b))) / Float64(b + c))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	tmp = 0.0;
	if (t <= 7.4e-305)
		tmp = t_1;
	elseif (t <= 1.7e-181)
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	elseif (t <= 1.25e-155)
		tmp = 1.0;
	elseif (t <= 1.58e-145)
		tmp = (y - x) * (x / ((x + y) * (y - x)));
	elseif (t <= 3.1e-40)
		tmp = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	else
		tmp = t_1;
	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[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 7.4e-305], t$95$1, If[LessEqual[t, 1.7e-181], N[(x / N[(x + N[(y + N[(2.0 * N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-155], 1.0, If[LessEqual[t, 1.58e-145], N[(N[(y - x), $MachinePrecision] * N[(x / N[(N[(x + y), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-40], N[(x / N[(x + N[(y + N[(N[(a * 2.0), $MachinePrecision] * N[(N[(y * N[(N[(c * c), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < 7.39999999999999954e-305 or 3.10000000000000011e-40 < t

   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. Taylor expanded in t around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-rgt-neg-in 87.0%

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

      3. +-commutative 87.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in a around 0 81.4%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
   6. Step-by-step derivation

      1. +-commutative 81.4%

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

      2. *-commutative 81.4%

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

   7. Simplified 81.4%

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

   if 7.39999999999999954e-305 < t < 1.7e-181

   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. Taylor expanded in a around inf 36.5%

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

   3. Taylor expanded in c around inf 44.9%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

      3. associate-*l* 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in a around 0 59.0%

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

      1. associate-*r* 64.3%

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

   8. Simplified 64.3%

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

   if 1.7e-181 < t < 1.25e-155

   1. Initial program 71.4%

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

   2. Taylor expanded in c around inf 44.4%

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

      1. cancel-sign-sub-inv 44.4%

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

      2. +-commutative 44.4%

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

      3. metadata-eval 44.4%

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

      4. associate-*r/ 44.4%

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

      5. metadata-eval 44.4%

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

      6. associate-+r+ 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in c around 0 16.8%

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

      1. +-commutative 16.8%

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

   7. Simplified 16.8%

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

   8. Taylor expanded in x around inf 86.2%

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

   if 1.25e-155 < t < 1.58000000000000003e-145

   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. Taylor expanded in c around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in c around 0 67.7%

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

      1. +-commutative 67.7%

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

   7. Simplified 67.7%

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

      1. flip-+ 100.0%

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

      2. associate-/r/ 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. difference-of-squares 100.0%

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

       2. +-commutative 100.0%

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

   11. Simplified 100.0%

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

   if 1.58000000000000003e-145 < t < 3.10000000000000011e-40

   1. Initial program 96.9%

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

   2. Taylor expanded in a around inf 45.9%

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

   3. Taylor expanded in a around 0 52.4%

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

      1. associate-*r* 52.4%

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

      2. *-commutative 52.4%

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

      3. *-commutative 52.4%

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

   5. Simplified 52.4%

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

      1. flip-- 61.1%

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

      2. associate-*l/ 64.1%

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

      3. *-commutative 64.1%

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

      4. +-commutative 64.1%

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

   7. Applied egg-rr 64.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.4 \cdot 10^{-305}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-155}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.58 \cdot 10^{-145}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(y - x\right)}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 10: 80.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-247} \lor \neg \left(t \leq 2.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.75e-247) (not (<= t 2.3e-11)))
   (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (*
        2.0
        (* c (+ a (+ 0.8333333333333334 (/ -0.6666666666666666 t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.75e-247) || !(t <= 2.3e-11)) {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / 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 <= (-1.75d-247)) .or. (.not. (t <= 2.3d-11))) then
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (0.8333333333333334d0 + ((-0.6666666666666666d0) / 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 <= -1.75e-247) || !(t <= 2.3e-11)) {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.75e-247) or not (t <= 2.3e-11):
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.75e-247) || !(t <= 2.3e-11))
		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(c * Float64(a + Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.75e-247) || ~((t <= 2.3e-11)))
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	else
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.75e-247], N[Not[LessEqual[t, 2.3e-11]], $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[(c * N[(a + N[(0.8333333333333334 + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e-247 or 2.30000000000000014e-11 < t

   1. Initial program 96.7%

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

   2. Taylor expanded in t around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-rgt-neg-in 89.7%

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

      3. +-commutative 89.7%

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

   4. Simplified 89.7%

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

   if -1.75e-247 < t < 2.30000000000000014e-11

   1. Initial program 90.5%

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

   2. Taylor expanded in c around inf 76.1%

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

      1. cancel-sign-sub-inv 76.1%

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

      2. +-commutative 76.1%

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

      3. metadata-eval 76.1%

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

      4. associate-*r/ 76.1%

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

      5. metadata-eval 76.1%

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

      6. associate-+r+ 76.1%

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

   4. Simplified 76.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-247} \lor \neg \left(t \leq 2.3 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \end{array} \]

Alternative 11: 72.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 10^{-33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1e-297)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 1e-33)
     (/ x (+ x (* y (exp (* 2.0 (* b (/ 0.6666666666666666 t)))))))
     (/ 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 <= -1e-297) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1e-33) {
		tmp = x / (x + (y * exp((2.0 * (b * (0.6666666666666666 / t))))));
	} 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 <= (-1d-297)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1d-33) then
        tmp = x / (x + (y * exp((2.0d0 * (b * (0.6666666666666666d0 / t))))))
    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 <= -1e-297) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1e-33) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * (0.6666666666666666 / t))))));
	} 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 <= -1e-297:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1e-33:
		tmp = x / (x + (y * math.exp((2.0 * (b * (0.6666666666666666 / t))))))
	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 <= -1e-297)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1e-33)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(0.6666666666666666 / t)))))));
	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 <= -1e-297)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1e-33)
		tmp = x / (x + (y * exp((2.0 * (b * (0.6666666666666666 / t))))));
	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, -1e-297], 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, 1e-33], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(0.6666666666666666 / t), $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 < -1.00000000000000004e-297

   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. Taylor expanded in a around inf 84.4%

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

   if -1.00000000000000004e-297 < t < 1.0000000000000001e-33

   1. Initial program 90.0%

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

   2. Taylor expanded in b around inf 67.8%

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

      1. associate-*r/ 67.8%

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

      2. metadata-eval 67.8%

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

      3. +-commutative 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in t around 0 69.0%

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

      1. associate-*r/ 69.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 69.0%

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

      3. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if 1.0000000000000001e-33 < t

   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. Taylor expanded in t around inf 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-rgt-neg-in 89.8%

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

      3. +-commutative 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in a around 0 84.4%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
   6. Step-by-step derivation

      1. +-commutative 84.4%

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

      2. *-commutative 84.4%

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

   7. Simplified 84.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 10^{-33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 12: 51.9% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{if}\;c \leq -2.32 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-104}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-208}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+ x (+ y (* (* a 2.0) (/ (* y (- (* c c) (* b b))) (+ b c))))))))
   (if (<= c -2.32e+42)
     1.0
     (if (<= c -5.2e-86)
       t_1
       (if (<= c -7.2e-104)
         1.0
         (if (<= c -3.6e-209)
           (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))
           (if (<= c 2e-208)
             1.0
             (if (<= c 4.2e+197)
               t_1
               (/ x (+ x (+ y (* (* a 2.0) (* y (- 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 + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	double tmp;
	if (c <= -2.32e+42) {
		tmp = 1.0;
	} else if (c <= -5.2e-86) {
		tmp = t_1;
	} else if (c <= -7.2e-104) {
		tmp = 1.0;
	} else if (c <= -3.6e-209) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 2e-208) {
		tmp = 1.0;
	} else if (c <= 4.2e+197) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y + ((a * 2.0) * (y * (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) :: tmp
    t_1 = x / (x + (y + ((a * 2.0d0) * ((y * ((c * c) - (b * b))) / (b + c)))))
    if (c <= (-2.32d+42)) then
        tmp = 1.0d0
    else if (c <= (-5.2d-86)) then
        tmp = t_1
    else if (c <= (-7.2d-104)) then
        tmp = 1.0d0
    else if (c <= (-3.6d-209)) then
        tmp = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    else if (c <= 2d-208) then
        tmp = 1.0d0
    else if (c <= 4.2d+197) then
        tmp = t_1
    else
        tmp = x / (x + (y + ((a * 2.0d0) * (y * (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 + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	double tmp;
	if (c <= -2.32e+42) {
		tmp = 1.0;
	} else if (c <= -5.2e-86) {
		tmp = t_1;
	} else if (c <= -7.2e-104) {
		tmp = 1.0;
	} else if (c <= -3.6e-209) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 2e-208) {
		tmp = 1.0;
	} else if (c <= 4.2e+197) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y + ((a * 2.0) * (y * (c - b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))))
	tmp = 0
	if c <= -2.32e+42:
		tmp = 1.0
	elif c <= -5.2e-86:
		tmp = t_1
	elif c <= -7.2e-104:
		tmp = 1.0
	elif c <= -3.6e-209:
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	elif c <= 2e-208:
		tmp = 1.0
	elif c <= 4.2e+197:
		tmp = t_1
	else:
		tmp = x / (x + (y + ((a * 2.0) * (y * (c - b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(Float64(y * Float64(Float64(c * c) - Float64(b * b))) / Float64(b + c))))))
	tmp = 0.0
	if (c <= -2.32e+42)
		tmp = 1.0;
	elseif (c <= -5.2e-86)
		tmp = t_1;
	elseif (c <= -7.2e-104)
		tmp = 1.0;
	elseif (c <= -3.6e-209)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))));
	elseif (c <= 2e-208)
		tmp = 1.0;
	elseif (c <= 4.2e+197)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(y * Float64(c - b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y + ((a * 2.0) * ((y * ((c * c) - (b * b))) / (b + c)))));
	tmp = 0.0;
	if (c <= -2.32e+42)
		tmp = 1.0;
	elseif (c <= -5.2e-86)
		tmp = t_1;
	elseif (c <= -7.2e-104)
		tmp = 1.0;
	elseif (c <= -3.6e-209)
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	elseif (c <= 2e-208)
		tmp = 1.0;
	elseif (c <= 4.2e+197)
		tmp = t_1;
	else
		tmp = x / (x + (y + ((a * 2.0) * (y * (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[(N[(a * 2.0), $MachinePrecision] * N[(N[(y * N[(N[(c * c), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.32e+42], 1.0, If[LessEqual[c, -5.2e-86], t$95$1, If[LessEqual[c, -7.2e-104], 1.0, If[LessEqual[c, -3.6e-209], N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e-208], 1.0, If[LessEqual[c, 4.2e+197], t$95$1, N[(x / N[(x + N[(y + N[(N[(a * 2.0), $MachinePrecision] * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.31999999999999991e42 or -5.2000000000000002e-86 < c < -7.1999999999999996e-104 or -3.60000000000000016e-209 < c < 2.0000000000000002e-208

   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. Taylor expanded in c around inf 73.9%

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

      1. cancel-sign-sub-inv 73.9%

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

      2. +-commutative 73.9%

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

      3. metadata-eval 73.9%

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

      4. associate-*r/ 73.9%

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

      5. metadata-eval 73.9%

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

      6. associate-+r+ 73.9%

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

   4. Simplified 73.9%

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

   5. Taylor expanded in c around 0 37.5%

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

      1. +-commutative 37.5%

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

   7. Simplified 37.5%

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

   8. Taylor expanded in x around inf 64.7%

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

   if -2.31999999999999991e42 < c < -5.2000000000000002e-86 or 2.0000000000000002e-208 < c < 4.20000000000000013e197

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 60.0%

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

   3. Taylor expanded in a around 0 50.3%

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

      1. associate-*r* 50.3%

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

      2. *-commutative 50.3%

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

      3. *-commutative 50.3%

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

   5. Simplified 50.3%

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

      1. flip-- 61.8%

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

      2. associate-*l/ 63.0%

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

      3. *-commutative 63.0%

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

      4. +-commutative 63.0%

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

   7. Applied egg-rr 63.0%

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

   if -7.1999999999999996e-104 < c < -3.60000000000000016e-209

   1. Initial program 95.7%

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

   2. Taylor expanded in b around inf 83.3%

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

      1. associate-*r/ 83.3%

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

      2. metadata-eval 83.3%

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

      3. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   5. Taylor expanded in t around 0 74.9%

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

      1. associate-*r/ 74.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 74.9%

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

      3. *-commutative 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in b around 0 66.8%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 1.3333333333333333 \cdot \frac{b}{t}\right)}} \]

   if 4.20000000000000013e197 < c

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 57.0%

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

   3. Taylor expanded in a around 0 67.8%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. *-commutative 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.32 \cdot 10^{+42}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-104}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-208}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \frac{y \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \]

Alternative 13: 50.1% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right) + \left(a \cdot a\right) \cdot \left(y \cdot \left(c \cdot c\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))))
   (if (<= c -1.3e-21)
     1.0
     (if (<= c -7.8e-210)
       t_1
       (if (<= c 8.2e-304)
         1.0
         (if (<= c 4.7e+21)
           t_1
           (if (<= c 6e+193)
             (/
              x
              (+ x (+ y (* 2.0 (+ (* y (* a c)) (* (* a a) (* y (* c c))))))))
             (/ x (+ x (+ y (* (* a 2.0) (* y (- 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 * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -1.3e-21) {
		tmp = 1.0;
	} else if (c <= -7.8e-210) {
		tmp = t_1;
	} else if (c <= 8.2e-304) {
		tmp = 1.0;
	} else if (c <= 4.7e+21) {
		tmp = t_1;
	} else if (c <= 6e+193) {
		tmp = x / (x + (y + (2.0 * ((y * (a * c)) + ((a * a) * (y * (c * c)))))));
	} else {
		tmp = x / (x + (y + ((a * 2.0) * (y * (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) :: tmp
    t_1 = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    if (c <= (-1.3d-21)) then
        tmp = 1.0d0
    else if (c <= (-7.8d-210)) then
        tmp = t_1
    else if (c <= 8.2d-304) then
        tmp = 1.0d0
    else if (c <= 4.7d+21) then
        tmp = t_1
    else if (c <= 6d+193) then
        tmp = x / (x + (y + (2.0d0 * ((y * (a * c)) + ((a * a) * (y * (c * c)))))))
    else
        tmp = x / (x + (y + ((a * 2.0d0) * (y * (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 * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -1.3e-21) {
		tmp = 1.0;
	} else if (c <= -7.8e-210) {
		tmp = t_1;
	} else if (c <= 8.2e-304) {
		tmp = 1.0;
	} else if (c <= 4.7e+21) {
		tmp = t_1;
	} else if (c <= 6e+193) {
		tmp = x / (x + (y + (2.0 * ((y * (a * c)) + ((a * a) * (y * (c * c)))))));
	} else {
		tmp = x / (x + (y + ((a * 2.0) * (y * (c - b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	tmp = 0
	if c <= -1.3e-21:
		tmp = 1.0
	elif c <= -7.8e-210:
		tmp = t_1
	elif c <= 8.2e-304:
		tmp = 1.0
	elif c <= 4.7e+21:
		tmp = t_1
	elif c <= 6e+193:
		tmp = x / (x + (y + (2.0 * ((y * (a * c)) + ((a * a) * (y * (c * c)))))))
	else:
		tmp = x / (x + (y + ((a * 2.0) * (y * (c - b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))))
	tmp = 0.0
	if (c <= -1.3e-21)
		tmp = 1.0;
	elseif (c <= -7.8e-210)
		tmp = t_1;
	elseif (c <= 8.2e-304)
		tmp = 1.0;
	elseif (c <= 4.7e+21)
		tmp = t_1;
	elseif (c <= 6e+193)
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(Float64(y * Float64(a * c)) + Float64(Float64(a * a) * Float64(y * Float64(c * c))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(y * Float64(c - b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	tmp = 0.0;
	if (c <= -1.3e-21)
		tmp = 1.0;
	elseif (c <= -7.8e-210)
		tmp = t_1;
	elseif (c <= 8.2e-304)
		tmp = 1.0;
	elseif (c <= 4.7e+21)
		tmp = t_1;
	elseif (c <= 6e+193)
		tmp = x / (x + (y + (2.0 * ((y * (a * c)) + ((a * a) * (y * (c * c)))))));
	else
		tmp = x / (x + (y + ((a * 2.0) * (y * (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[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.3e-21], 1.0, If[LessEqual[c, -7.8e-210], t$95$1, If[LessEqual[c, 8.2e-304], 1.0, If[LessEqual[c, 4.7e+21], t$95$1, If[LessEqual[c, 6e+193], N[(x / N[(x + N[(y + N[(2.0 * N[(N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision] + N[(N[(a * a), $MachinePrecision] * N[(y * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y + N[(N[(a * 2.0), $MachinePrecision] * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.30000000000000009e-21 or -7.7999999999999995e-210 < c < 8.20000000000000005e-304

   1. Initial program 93.8%

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

   2. Taylor expanded in c around inf 78.9%

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

      1. cancel-sign-sub-inv 78.9%

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

      2. +-commutative 78.9%

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

      3. metadata-eval 78.9%

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

      4. associate-*r/ 78.9%

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

      5. metadata-eval 78.9%

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

      6. associate-+r+ 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in c around 0 36.4%

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

      1. +-commutative 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in x around inf 64.7%

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

   if -1.30000000000000009e-21 < c < -7.7999999999999995e-210 or 8.20000000000000005e-304 < c < 4.7e21

   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. Taylor expanded in b around inf 82.2%

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

      1. associate-*r/ 82.2%

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

      2. metadata-eval 82.2%

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

      3. +-commutative 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in t around 0 64.6%

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

      1. associate-*r/ 64.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 64.6%

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

      3. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in b around 0 57.7%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 1.3333333333333333 \cdot \frac{b}{t}\right)}} \]

   if 4.7e21 < c < 6e193

   1. Initial program 90.7%

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

   2. Taylor expanded in a around inf 63.8%

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

   3. Taylor expanded in c around inf 51.7%

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

      1. associate-*r* 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-*l* 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in a around 0 54.0%

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

      1. distribute-lft-out 54.0%

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

      2. associate-*r* 57.2%

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

      3. unpow2 57.2%

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

      4. *-commutative 57.2%

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

      5. unpow2 57.2%

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

   8. Simplified 57.2%

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

   if 6e193 < c

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 57.0%

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

   3. Taylor expanded in a around 0 67.8%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. *-commutative 67.8%

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

   5. Simplified 67.8%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{-304}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right) + \left(a \cdot a\right) \cdot \left(y \cdot \left(c \cdot c\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \]

Alternative 14: 49.5% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;c \leq -8.8 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(c \cdot y\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))))
   (if (<= c -8.8e-21)
     1.0
     (if (<= c -5e-210)
       t_1
       (if (<= c 6.5e-303)
         1.0
         (if (<= c 5.4e+28) t_1 (/ x (+ x (+ y (* 2.0 (* a (* c y))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -8.8e-21) {
		tmp = 1.0;
	} else if (c <= -5e-210) {
		tmp = t_1;
	} else if (c <= 6.5e-303) {
		tmp = 1.0;
	} else if (c <= 5.4e+28) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (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) :: t_1
    real(8) :: tmp
    t_1 = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    if (c <= (-8.8d-21)) then
        tmp = 1.0d0
    else if (c <= (-5d-210)) then
        tmp = t_1
    else if (c <= 6.5d-303) then
        tmp = 1.0d0
    else if (c <= 5.4d+28) then
        tmp = t_1
    else
        tmp = x / (x + (y + (2.0d0 * (a * (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 t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -8.8e-21) {
		tmp = 1.0;
	} else if (c <= -5e-210) {
		tmp = t_1;
	} else if (c <= 6.5e-303) {
		tmp = 1.0;
	} else if (c <= 5.4e+28) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (c * y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	tmp = 0
	if c <= -8.8e-21:
		tmp = 1.0
	elif c <= -5e-210:
		tmp = t_1
	elif c <= 6.5e-303:
		tmp = 1.0
	elif c <= 5.4e+28:
		tmp = t_1
	else:
		tmp = x / (x + (y + (2.0 * (a * (c * y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))))
	tmp = 0.0
	if (c <= -8.8e-21)
		tmp = 1.0;
	elseif (c <= -5e-210)
		tmp = t_1;
	elseif (c <= 6.5e-303)
		tmp = 1.0;
	elseif (c <= 5.4e+28)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(a * Float64(c * y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	tmp = 0.0;
	if (c <= -8.8e-21)
		tmp = 1.0;
	elseif (c <= -5e-210)
		tmp = t_1;
	elseif (c <= 6.5e-303)
		tmp = 1.0;
	elseif (c <= 5.4e+28)
		tmp = t_1;
	else
		tmp = x / (x + (y + (2.0 * (a * (c * y)))));
	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[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.8e-21], 1.0, If[LessEqual[c, -5e-210], t$95$1, If[LessEqual[c, 6.5e-303], 1.0, If[LessEqual[c, 5.4e+28], t$95$1, N[(x / N[(x + N[(y + N[(2.0 * N[(a * N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.8000000000000002e-21 or -5.0000000000000002e-210 < c < 6.50000000000000028e-303

   1. Initial program 93.8%

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

   2. Taylor expanded in c around inf 78.9%

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

      1. cancel-sign-sub-inv 78.9%

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

      2. +-commutative 78.9%

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

      3. metadata-eval 78.9%

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

      4. associate-*r/ 78.9%

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

      5. metadata-eval 78.9%

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

      6. associate-+r+ 78.9%

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

   4. Simplified 78.9%

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

   5. Taylor expanded in c around 0 36.4%

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

      1. +-commutative 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in x around inf 64.7%

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

   if -8.8000000000000002e-21 < c < -5.0000000000000002e-210 or 6.50000000000000028e-303 < c < 5.4000000000000003e28

   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. Taylor expanded in b around inf 82.2%

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

      1. associate-*r/ 82.2%

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

      2. metadata-eval 82.2%

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

      3. +-commutative 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in t around 0 64.6%

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

      1. associate-*r/ 64.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 64.6%

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

      3. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in b around 0 57.7%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 1.3333333333333333 \cdot \frac{b}{t}\right)}} \]

   if 5.4000000000000003e28 < c

   1. Initial program 91.6%

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

   2. Taylor expanded in a around inf 60.7%

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

   3. Taylor expanded in c around inf 52.5%

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

      1. associate-*r* 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*l* 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in a around 0 52.6%

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

      1. *-commutative 52.6%

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

   8. Simplified 52.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.8 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(c \cdot y\right)\right)\right)}\\ \end{array} \]

Alternative 15: 50.9% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-208}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -8.5e-21)
   1.0
   (if (<= c -5.2e-209)
     (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))
     (if (<= c 3.3e-208) 1.0 (/ x (+ x (+ y (* (* a 2.0) (* y (- c b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -8.5e-21) {
		tmp = 1.0;
	} else if (c <= -5.2e-209) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 3.3e-208) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + ((a * 2.0) * (y * (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 (c <= (-8.5d-21)) then
        tmp = 1.0d0
    else if (c <= (-5.2d-209)) then
        tmp = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    else if (c <= 3.3d-208) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + ((a * 2.0d0) * (y * (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 (c <= -8.5e-21) {
		tmp = 1.0;
	} else if (c <= -5.2e-209) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 3.3e-208) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + ((a * 2.0) * (y * (c - b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -8.5e-21:
		tmp = 1.0
	elif c <= -5.2e-209:
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	elif c <= 3.3e-208:
		tmp = 1.0
	else:
		tmp = x / (x + (y + ((a * 2.0) * (y * (c - b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -8.5e-21)
		tmp = 1.0;
	elseif (c <= -5.2e-209)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))));
	elseif (c <= 3.3e-208)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(Float64(a * 2.0) * Float64(y * Float64(c - b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -8.5e-21)
		tmp = 1.0;
	elseif (c <= -5.2e-209)
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	elseif (c <= 3.3e-208)
		tmp = 1.0;
	else
		tmp = x / (x + (y + ((a * 2.0) * (y * (c - b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -8.5e-21], 1.0, If[LessEqual[c, -5.2e-209], N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e-208], 1.0, N[(x / N[(x + N[(y + N[(N[(a * 2.0), $MachinePrecision] * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.4999999999999993e-21 or -5.19999999999999969e-209 < c < 3.30000000000000006e-208

   1. Initial program 94.8%

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

   2. Taylor expanded in c around inf 73.1%

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

      1. cancel-sign-sub-inv 73.1%

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

      2. +-commutative 73.1%

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

      3. metadata-eval 73.1%

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

      4. associate-*r/ 73.1%

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

      5. metadata-eval 73.1%

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

      6. associate-+r+ 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in c around 0 38.5%

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

      1. +-commutative 38.5%

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

   7. Simplified 38.5%

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

   8. Taylor expanded in x around inf 62.9%

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

   if -8.4999999999999993e-21 < c < -5.19999999999999969e-209

   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. Taylor expanded in b around inf 83.5%

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

      1. associate-*r/ 83.5%

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

      2. metadata-eval 83.5%

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

      3. +-commutative 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in t around 0 64.1%

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

      1. associate-*r/ 64.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 64.1%

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

      3. *-commutative 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in b around 0 56.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 1.3333333333333333 \cdot \frac{b}{t}\right)}} \]

   if 3.30000000000000006e-208 < c

   1. Initial program 93.4%

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

   2. Taylor expanded in a around inf 60.8%

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

   3. Taylor expanded in a around 0 54.5%

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

      1. associate-*r* 54.5%

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

      2. *-commutative 54.5%

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

      3. *-commutative 54.5%

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

   5. Simplified 54.5%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-208}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(a \cdot 2\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \end{array} \]

Alternative 16: 46.8% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{-79} \lor \neg \left(a \leq 1.9 \cdot 10^{+14}\right) \land a \leq 6.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a 4.4e-79) (and (not (<= a 1.9e+14)) (<= a 6.2e+57)))
   (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= 4.4e-79) || (!(a <= 1.9e+14) && (a <= 6.2e+57))) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= 4.4d-79) .or. (.not. (a <= 1.9d+14)) .and. (a <= 6.2d+57)) then
        tmp = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= 4.4e-79) || (!(a <= 1.9e+14) && (a <= 6.2e+57))) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= 4.4e-79) or (not (a <= 1.9e+14) and (a <= 6.2e+57)):
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= 4.4e-79) || (!(a <= 1.9e+14) && (a <= 6.2e+57)))
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= 4.4e-79) || (~((a <= 1.9e+14)) && (a <= 6.2e+57)))
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, 4.4e-79], And[N[Not[LessEqual[a, 1.9e+14]], $MachinePrecision], LessEqual[a, 6.2e+57]]], N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if a < 4.3999999999999998e-79 or 1.9e14 < a < 6.20000000000000026e57

   1. Initial program 96.3%

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

   2. Taylor expanded in b around inf 71.7%

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

      1. associate-*r/ 71.7%

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

      2. metadata-eval 71.7%

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

      3. +-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in t around 0 57.3%

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

      1. associate-*r/ 57.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 57.3%

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

      3. *-commutative 57.3%

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

   7. Simplified 57.3%

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

   8. Taylor expanded in b around 0 54.7%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 1.3333333333333333 \cdot \frac{b}{t}\right)}} \]

   if 4.3999999999999998e-79 < a < 1.9e14 or 6.20000000000000026e57 < a

   1. Initial program 91.8%

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

   2. Taylor expanded in c around inf 67.0%

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

      1. cancel-sign-sub-inv 67.0%

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

      2. +-commutative 67.0%

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

      3. metadata-eval 67.0%

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

      4. associate-*r/ 67.0%

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

      5. metadata-eval 67.0%

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

      6. associate-+r+ 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in c around 0 30.0%

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

      1. +-commutative 30.0%

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

   7. Simplified 30.0%

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

   8. Taylor expanded in x around inf 58.4%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{-79} \lor \neg \left(a \leq 1.9 \cdot 10^{+14}\right) \land a \leq 6.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17: 52.2% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-163}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-79}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(y - x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.45e+197)
   (/ x (* y (- 1.0 (* 2.0 (* a (- b c))))))
   (if (<= b 2.25e-163)
     1.0
     (if (<= b 8e-79) (* (- y x) (/ x (* (+ x y) (- y x)))) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.45e+197) {
		tmp = x / (y * (1.0 - (2.0 * (a * (b - c)))));
	} else if (b <= 2.25e-163) {
		tmp = 1.0;
	} else if (b <= 8e-79) {
		tmp = (y - x) * (x / ((x + y) * (y - x)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.45d+197)) then
        tmp = x / (y * (1.0d0 - (2.0d0 * (a * (b - c)))))
    else if (b <= 2.25d-163) then
        tmp = 1.0d0
    else if (b <= 8d-79) then
        tmp = (y - x) * (x / ((x + y) * (y - x)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.45e+197) {
		tmp = x / (y * (1.0 - (2.0 * (a * (b - c)))));
	} else if (b <= 2.25e-163) {
		tmp = 1.0;
	} else if (b <= 8e-79) {
		tmp = (y - x) * (x / ((x + y) * (y - x)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.45e+197:
		tmp = x / (y * (1.0 - (2.0 * (a * (b - c)))))
	elif b <= 2.25e-163:
		tmp = 1.0
	elif b <= 8e-79:
		tmp = (y - x) * (x / ((x + y) * (y - x)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.45e+197)
		tmp = Float64(x / Float64(y * Float64(1.0 - Float64(2.0 * Float64(a * Float64(b - c))))));
	elseif (b <= 2.25e-163)
		tmp = 1.0;
	elseif (b <= 8e-79)
		tmp = Float64(Float64(y - x) * Float64(x / Float64(Float64(x + y) * Float64(y - x))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.45e+197)
		tmp = x / (y * (1.0 - (2.0 * (a * (b - c)))));
	elseif (b <= 2.25e-163)
		tmp = 1.0;
	elseif (b <= 8e-79)
		tmp = (y - x) * (x / ((x + y) * (y - x)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.45e+197], N[(x / N[(y * N[(1.0 - N[(2.0 * N[(a * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e-163], 1.0, If[LessEqual[b, 8e-79], N[(N[(y - x), $MachinePrecision] * N[(x / N[(N[(x + y), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.45000000000000013e197

   1. Initial program 82.0%

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

   2. Taylor expanded in a around inf 73.6%

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

   3. Taylor expanded in a around 0 60.8%

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

      1. associate-*r* 60.8%

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

      2. *-commutative 60.8%

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

      3. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in y around inf 60.4%

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

   if -2.45000000000000013e197 < b < 2.2499999999999999e-163 or 8e-79 < b

   1. Initial program 96.3%

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

   2. Taylor expanded in c around inf 70.7%

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

      1. cancel-sign-sub-inv 70.7%

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

      2. +-commutative 70.7%

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

      3. metadata-eval 70.7%

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

      4. associate-*r/ 70.7%

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

      5. metadata-eval 70.7%

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

      6. associate-+r+ 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in c around 0 40.6%

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

      1. +-commutative 40.6%

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

   7. Simplified 40.6%

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

   8. Taylor expanded in x around inf 54.5%

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

   if 2.2499999999999999e-163 < b < 8e-79

   1. Initial program 84.4%

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

   2. Taylor expanded in c around inf 74.5%

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

      1. cancel-sign-sub-inv 74.5%

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

      2. +-commutative 74.5%

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

      3. metadata-eval 74.5%

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

      4. associate-*r/ 74.5%

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

      5. metadata-eval 74.5%

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

      6. associate-+r+ 74.5%

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

   4. Simplified 74.5%

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

   5. Taylor expanded in c around 0 34.0%

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

      1. +-commutative 34.0%

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

   7. Simplified 34.0%

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

      1. flip-+ 59.4%

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

      2. associate-/r/ 64.4%

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

   9. Applied egg-rr 64.4%

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

       1. difference-of-squares 64.4%

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

       2. +-commutative 64.4%

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

   11. Simplified 64.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-163}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-79}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(x + y\right) \cdot \left(y - x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 18: 48.2% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \left(y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 7.5e-294)
   (/ x (+ x y))
   (if (<= a 4e+14)
     1.0
     (if (<= a 1.8e+62)
       (/ x (+ x (* 1.3333333333333333 (* y (/ b t)))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 7.5e-294) {
		tmp = x / (x + y);
	} else if (a <= 4e+14) {
		tmp = 1.0;
	} else if (a <= 1.8e+62) {
		tmp = x / (x + (1.3333333333333333 * (y * (b / t))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 7.5d-294) then
        tmp = x / (x + y)
    else if (a <= 4d+14) then
        tmp = 1.0d0
    else if (a <= 1.8d+62) then
        tmp = x / (x + (1.3333333333333333d0 * (y * (b / t))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 7.5e-294) {
		tmp = x / (x + y);
	} else if (a <= 4e+14) {
		tmp = 1.0;
	} else if (a <= 1.8e+62) {
		tmp = x / (x + (1.3333333333333333 * (y * (b / t))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 7.5e-294:
		tmp = x / (x + y)
	elif a <= 4e+14:
		tmp = 1.0
	elif a <= 1.8e+62:
		tmp = x / (x + (1.3333333333333333 * (y * (b / t))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 7.5e-294)
		tmp = Float64(x / Float64(x + y));
	elseif (a <= 4e+14)
		tmp = 1.0;
	elseif (a <= 1.8e+62)
		tmp = Float64(x / Float64(x + Float64(1.3333333333333333 * Float64(y * Float64(b / t)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 7.5e-294)
		tmp = x / (x + y);
	elseif (a <= 4e+14)
		tmp = 1.0;
	elseif (a <= 1.8e+62)
		tmp = x / (x + (1.3333333333333333 * (y * (b / t))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 7.5e-294], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+14], 1.0, If[LessEqual[a, 1.8e+62], N[(x / N[(x + N[(1.3333333333333333 * N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if a < 7.5000000000000004e-294

   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. Taylor expanded in c around inf 70.3%

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

      1. cancel-sign-sub-inv 70.3%

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

      2. +-commutative 70.3%

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

      3. metadata-eval 70.3%

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

      4. associate-*r/ 70.3%

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

      5. metadata-eval 70.3%

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

      6. associate-+r+ 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in c around 0 48.6%

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

      1. +-commutative 48.6%

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

   7. Simplified 48.6%

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

   if 7.5000000000000004e-294 < a < 4e14 or 1.8e62 < a

   1. Initial program 93.3%

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

   2. Taylor expanded in c around inf 70.6%

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

      1. cancel-sign-sub-inv 70.6%

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

      2. +-commutative 70.6%

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

      3. metadata-eval 70.6%

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

      4. associate-*r/ 70.6%

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

      5. metadata-eval 70.6%

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

      6. associate-+r+ 70.6%

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

   4. Simplified 70.6%

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

   5. Taylor expanded in c around 0 36.0%

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

      1. +-commutative 36.0%

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

   7. Simplified 36.0%

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

   8. Taylor expanded in x around inf 57.8%

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

   if 4e14 < a < 1.8e62

   1. Initial program 89.5%

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

   2. Taylor expanded in b around inf 69.8%

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

      1. associate-*r/ 69.8%

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

      2. metadata-eval 69.8%

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

      3. +-commutative 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in t around 0 59.6%

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

      1. associate-*r/ 59.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{0.6666666666666666 \cdot b}{t}}}} \]

      2. associate-*l/ 59.6%

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

      3. *-commutative 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in b around 0 59.9%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 1.3333333333333333 \cdot \frac{b}{t}\right)}} \]

   9. Taylor expanded in b around inf 54.7%

      \[\leadsto \frac{x}{x + \color{blue}{1.3333333333333333 \cdot \frac{b \cdot y}{t}}} \]
   10. Step-by-step derivation

       1. *-commutative 54.7%

          \[\leadsto \frac{x}{x + 1.3333333333333333 \cdot \frac{\color{blue}{y \cdot b}}{t}} \]

       2. associate-*r/ 54.8%

          \[\leadsto \frac{x}{x + 1.3333333333333333 \cdot \color{blue}{\left(y \cdot \frac{b}{t}\right)}} \]

   11. Simplified 54.8%

       \[\leadsto \frac{x}{x + \color{blue}{1.3333333333333333 \cdot \left(y \cdot \frac{b}{t}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \left(y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19: 52.5% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+134}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.32e+134) (* -0.5 (/ x (* a (* b y)))) 1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.32e+134) {
		tmp = -0.5 * (x / (a * (b * y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.32d+134)) then
        tmp = (-0.5d0) * (x / (a * (b * y)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.32e+134) {
		tmp = -0.5 * (x / (a * (b * y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.32e+134:
		tmp = -0.5 * (x / (a * (b * y)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.32e+134)
		tmp = Float64(-0.5 * Float64(x / Float64(a * Float64(b * y))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.32e+134)
		tmp = -0.5 * (x / (a * (b * y)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.32e+134], N[(-0.5 * N[(x / N[(a * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if b < -1.32e134

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 55.8%

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

   3. Taylor expanded in a around 0 50.4%

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

      1. associate-*r* 50.4%

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

      2. *-commutative 50.4%

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

      3. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in b around inf 45.1%

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

   if -1.32e134 < b

   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. Taylor expanded in c around inf 71.9%

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

      1. cancel-sign-sub-inv 71.9%

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

      2. +-commutative 71.9%

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

      3. metadata-eval 71.9%

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

      4. associate-*r/ 71.9%

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

      5. metadata-eval 71.9%

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

      6. associate-+r+ 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in c around 0 41.7%

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

      1. +-commutative 41.7%

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

   7. Simplified 41.7%

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

   8. Taylor expanded in x around inf 54.0%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.32 \cdot 10^{+134}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(b \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 20: 49.1% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 4.2e-297) (/ x (+ x y)) 1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 4.2e-297) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 4.2d-297) then
        tmp = x / (x + y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 4.2e-297) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 4.2e-297:
		tmp = x / (x + y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 4.2e-297)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 4.2e-297)
		tmp = x / (x + y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 4.2e-297], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if a < 4.20000000000000027e-297

   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. Taylor expanded in c around inf 70.3%

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

      1. cancel-sign-sub-inv 70.3%

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

      2. +-commutative 70.3%

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

      3. metadata-eval 70.3%

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

      4. associate-*r/ 70.3%

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

      5. metadata-eval 70.3%

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

      6. associate-+r+ 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in c around 0 48.6%

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

      1. +-commutative 48.6%

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

   7. Simplified 48.6%

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

   if 4.20000000000000027e-297 < a

   1. Initial program 92.9%

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

   2. Taylor expanded in c around inf 70.0%

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

      1. cancel-sign-sub-inv 70.0%

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

      2. +-commutative 70.0%

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

      3. metadata-eval 70.0%

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

      4. associate-*r/ 70.0%

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

      5. metadata-eval 70.0%

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

      6. associate-+r+ 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in c around 0 36.4%

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

      1. +-commutative 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in x around inf 55.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{-297}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 21: 51.9% accurate, 231.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

2. Taylor expanded in c around inf 70.1%

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

   1. cancel-sign-sub-inv 70.1%

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

   2. +-commutative 70.1%

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

   3. metadata-eval 70.1%

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

   4. associate-*r/ 70.1%

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

   5. metadata-eval 70.1%

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

   6. associate-+r+ 70.1%

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

4. Simplified 70.1%

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

5. Taylor expanded in c around 0 39.2%

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

   1. +-commutative 39.2%

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

7. Simplified 39.2%

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

8. Taylor expanded in x around inf 50.1%

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

9. Final simplification 50.1%

   \[\leadsto 1 \]

Developer target: 95.3% 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 2023297 
(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)))))))))))