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

Percentage Accurate: 94.1% → 97.5%

Time: 21.7s

Alternatives: 14

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% 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 99.6%

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

   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 82.4%

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

4. Final simplification 98.9%

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

Alternative 2: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.55 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} - \left(b - c\right) \cdot \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 1.55e-147)
   (/
    x
    (+
     x
     (*
      y
      (exp (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
   (if (<= t 2.8e+130)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (-
           (* z (sqrt (/ 1.0 t)))
           (* (- b c) (+ 0.8333333333333334 (/ -0.6666666666666666 t)))))))))
     (/ x (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.55e-147) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 2.8e+130) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) - ((b - c) * (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	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 <= 1.55d-147) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 2.8d+130) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) - ((b - c) * (0.8333333333333334d0 + ((-0.6666666666666666d0) / t))))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    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 <= 1.55e-147) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 2.8e+130) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) - ((b - c) * (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 1.55e-147:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 2.8e+130:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) - ((b - c) * (0.8333333333333334 + (-0.6666666666666666 / t))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 1.55e-147)
		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 <= 2.8e+130)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) - Float64(Float64(b - c) * Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t)))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 1.55e-147)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 2.8e+130)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) - ((b - c) * (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 1.55e-147], 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, 2.8e+130], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(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[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.5500000000000001e-147

   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 t around 0 90.7%

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

   if 1.5500000000000001e-147 < t < 2.7999999999999999e130

   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 0 96.5%

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

      1. *-commutative 96.5%

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

      2. *-commutative 96.5%

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

      3. cancel-sign-sub-inv 96.5%

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

      4. metadata-eval 96.5%

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

      5. associate-*r/ 96.5%

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

      6. metadata-eval 96.5%

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

   4. Simplified 96.5%

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

   if 2.7999999999999999e130 < t

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. *-commutative 95.6%

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

      3. distribute-rgt-neg-in 95.6%

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

      4. distribute-neg-in 95.6%

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

      5. metadata-eval 95.6%

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

   4. Simplified 95.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.55 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} - \left(b - c\right) \cdot \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 3: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 2.9e-146)
   (/
    x
    (+
     x
     (*
      y
      (exp (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
   (if (<= t 0.00013)
     (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
     (/ x (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 2.9e-146) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 0.00013) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= 2.9d-146) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 0.00013d0) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 2.9e-146) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 0.00013) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 2.9e-146:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 0.00013:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 2.9e-146)
		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 <= 0.00013)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 2.9e-146)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 0.00013)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 2.9e-146], 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, 0.00013], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.90000000000000011e-146

   1. Initial program 90.8%

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

   2. Taylor expanded in t around 0 90.8%

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

   if 2.90000000000000011e-146 < t < 1.29999999999999989e-4

   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 t around 0 58.7%

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

   3. Taylor expanded in a around 0 81.2%

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

   if 1.29999999999999989e-4 < t

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. distribute-neg-in 93.6%

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

      5. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.00013:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 4: 82.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{if}\;t \leq 7.5 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;t \leq 0.00017:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= t 7.5e-186)
     t_1
     (if (<= t 8.5e-147)
       (/ x (+ x (* y (exp (* 2.0 (* (sqrt a) (/ z t)))))))
       (if (<= t 0.00017)
         t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 7.5e-186) {
		tmp = t_1;
	} else if (t <= 8.5e-147) {
		tmp = x / (x + (y * exp((2.0 * (sqrt(a) * (z / t))))));
	} else if (t <= 0.00017) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	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((1.3333333333333333d0 * ((b - c) / t)))))
    if (t <= 7.5d-186) then
        tmp = t_1
    else if (t <= 8.5d-147) then
        tmp = x / (x + (y * exp((2.0d0 * (sqrt(a) * (z / t))))))
    else if (t <= 0.00017d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    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((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 7.5e-186) {
		tmp = t_1;
	} else if (t <= 8.5e-147) {
		tmp = x / (x + (y * Math.exp((2.0 * (Math.sqrt(a) * (z / t))))));
	} else if (t <= 0.00017) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if t <= 7.5e-186:
		tmp = t_1
	elif t <= 8.5e-147:
		tmp = x / (x + (y * math.exp((2.0 * (math.sqrt(a) * (z / t))))))
	elif t <= 0.00017:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))))
	tmp = 0.0
	if (t <= 7.5e-186)
		tmp = t_1;
	elseif (t <= 8.5e-147)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(sqrt(a) * Float64(z / t)))))));
	elseif (t <= 0.00017)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	tmp = 0.0;
	if (t <= 7.5e-186)
		tmp = t_1;
	elseif (t <= 8.5e-147)
		tmp = x / (x + (y * exp((2.0 * (sqrt(a) * (z / t))))));
	elseif (t <= 0.00017)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	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[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 7.5e-186], t$95$1, If[LessEqual[t, 8.5e-147], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[Sqrt[a], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00017], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 7.50000000000000076e-186 or 8.5000000000000002e-147 < t < 1.7e-4

   1. Initial program 92.5%

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

   2. Taylor expanded in t around 0 82.1%

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

   3. Taylor expanded in a around 0 77.5%

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

   if 7.50000000000000076e-186 < t < 8.5000000000000002e-147

   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 t around 0 81.6%

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

   3. Taylor expanded in z around inf 81.6%

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

   if 1.7e-4 < t

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. distribute-neg-in 93.6%

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

      5. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;t \leq 0.00017:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 5: 82.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{if}\;t \leq 3.5 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right) + 1\right)}\\ \mathbf{elif}\;t \leq 0.000195:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= t 3.5e-164)
     t_1
     (if (<= t 6.2e-147)
       (/ x (+ x (* y (+ (* 2.0 (* -0.6666666666666666 (/ c t))) 1.0))))
       (if (<= t 0.000195)
         t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 3.5e-164) {
		tmp = t_1;
	} else if (t <= 6.2e-147) {
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)));
	} else if (t <= 0.000195) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	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((1.3333333333333333d0 * ((b - c) / t)))))
    if (t <= 3.5d-164) then
        tmp = t_1
    else if (t <= 6.2d-147) then
        tmp = x / (x + (y * ((2.0d0 * ((-0.6666666666666666d0) * (c / t))) + 1.0d0)))
    else if (t <= 0.000195d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    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((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 3.5e-164) {
		tmp = t_1;
	} else if (t <= 6.2e-147) {
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)));
	} else if (t <= 0.000195) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if t <= 3.5e-164:
		tmp = t_1
	elif t <= 6.2e-147:
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)))
	elif t <= 0.000195:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))))
	tmp = 0.0
	if (t <= 3.5e-164)
		tmp = t_1;
	elseif (t <= 6.2e-147)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(-0.6666666666666666 * Float64(c / t))) + 1.0))));
	elseif (t <= 0.000195)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	tmp = 0.0;
	if (t <= 3.5e-164)
		tmp = t_1;
	elseif (t <= 6.2e-147)
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)));
	elseif (t <= 0.000195)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	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[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 3.5e-164], t$95$1, If[LessEqual[t, 6.2e-147], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(-0.6666666666666666 * N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.000195], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 3.5e-164 or 6.2000000000000005e-147 < t < 1.94999999999999996e-4

   1. Initial program 93.0%

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

   2. Taylor expanded in t around 0 81.7%

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

   3. Taylor expanded in a around 0 76.0%

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

   if 3.5e-164 < t < 6.2000000000000005e-147

   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 64.0%

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

      1. cancel-sign-sub-inv 64.0%

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

      2. +-commutative 64.0%

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

      3. metadata-eval 64.0%

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

      4. associate-*r/ 64.0%

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

      5. metadata-eval 64.0%

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

      6. associate-+r+ 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in c around 0 88.2%

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

      1. remove-double-neg 88.2%

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

      2. sub-neg 88.2%

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

      3. associate--r+ 88.2%

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

      4. neg-mul-1 88.2%

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

      5. neg-mul-1 88.2%

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

      6. associate--r+ 88.2%

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

      7. sub-neg 88.2%

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

      8. remove-double-neg 88.2%

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

      9. associate--l+ 88.2%

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

      10. associate-*r/ 88.2%

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

      11. metadata-eval 88.2%

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

   7. Simplified 88.2%

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

   8. Taylor expanded in t around 0 88.2%

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

   if 1.94999999999999996e-4 < t

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. distribute-neg-in 93.6%

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

      5. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right) + 1\right)}\\ \mathbf{elif}\;t \leq 0.000195:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 6: 82.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{if}\;t \leq 2 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 0.00023:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= t 2e-223)
     t_1
     (if (<= t 4e-147)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (* c (+ a (+ 0.8333333333333334 (/ -0.6666666666666666 t)))))))))
       (if (<= t 0.00023)
         t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 2e-223) {
		tmp = t_1;
	} else if (t <= 4e-147) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else if (t <= 0.00023) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	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((1.3333333333333333d0 * ((b - c) / t)))))
    if (t <= 2d-223) then
        tmp = t_1
    else if (t <= 4d-147) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (0.8333333333333334d0 + ((-0.6666666666666666d0) / t))))))))
    else if (t <= 0.00023d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    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((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 2e-223) {
		tmp = t_1;
	} else if (t <= 4e-147) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	} else if (t <= 0.00023) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if t <= 2e-223:
		tmp = t_1
	elif t <= 4e-147:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))))
	elif t <= 0.00023:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))))
	tmp = 0.0
	if (t <= 2e-223)
		tmp = t_1;
	elseif (t <= 4e-147)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(0.8333333333333334 + Float64(-0.6666666666666666 / t)))))))));
	elseif (t <= 0.00023)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	tmp = 0.0;
	if (t <= 2e-223)
		tmp = t_1;
	elseif (t <= 4e-147)
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 + (-0.6666666666666666 / t))))))));
	elseif (t <= 0.00023)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	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[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2e-223], t$95$1, If[LessEqual[t, 4e-147], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(0.8333333333333334 + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00023], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.9999999999999999e-223 or 3.9999999999999999e-147 < t < 2.3000000000000001e-4

   1. Initial program 91.7%

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

   2. Taylor expanded in t around 0 82.6%

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

   3. Taylor expanded in a around 0 76.7%

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

   if 1.9999999999999999e-223 < t < 3.9999999999999999e-147

   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 80.0%

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

      1. cancel-sign-sub-inv 80.0%

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

      2. +-commutative 80.0%

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

      3. metadata-eval 80.0%

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

      4. associate-*r/ 80.0%

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

      5. metadata-eval 80.0%

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

      6. associate-+r+ 80.0%

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

   4. Simplified 80.0%

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

   if 2.3000000000000001e-4 < t

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. distribute-neg-in 93.6%

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

      5. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{-223}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 0.00023:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 7: 76.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{if}\;t \leq 2.9 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right) + 1\right)}\\ \mathbf{elif}\;t \leq 0.00019:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= t 2.9e-164)
     t_1
     (if (<= t 6.2e-147)
       (/ x (+ x (* y (+ (* 2.0 (* -0.6666666666666666 (/ c t))) 1.0))))
       (if (<= t 0.00019)
         t_1
         (/ x (+ x (* y (exp (* (- b c) -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((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 2.9e-164) {
		tmp = t_1;
	} else if (t <= 6.2e-147) {
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)));
	} else if (t <= 0.00019) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    if (t <= 2.9d-164) then
        tmp = t_1
    else if (t <= 6.2d-147) then
        tmp = x / (x + (y * ((2.0d0 * ((-0.6666666666666666d0) * (c / t))) + 1.0d0)))
    else if (t <= 0.00019d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= 2.9e-164) {
		tmp = t_1;
	} else if (t <= 6.2e-147) {
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)));
	} else if (t <= 0.00019) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if t <= 2.9e-164:
		tmp = t_1
	elif t <= 6.2e-147:
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)))
	elif t <= 0.00019:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))))
	tmp = 0.0
	if (t <= 2.9e-164)
		tmp = t_1;
	elseif (t <= 6.2e-147)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(-0.6666666666666666 * Float64(c / t))) + 1.0))));
	elseif (t <= 0.00019)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	tmp = 0.0;
	if (t <= 2.9e-164)
		tmp = t_1;
	elseif (t <= 6.2e-147)
		tmp = x / (x + (y * ((2.0 * (-0.6666666666666666 * (c / t))) + 1.0)));
	elseif (t <= 0.00019)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp(((b - c) * -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[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2.9e-164], t$95$1, If[LessEqual[t, 6.2e-147], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(-0.6666666666666666 * N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.00019], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 2.9e-164 or 6.2000000000000005e-147 < t < 1.9000000000000001e-4

   1. Initial program 93.0%

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

   2. Taylor expanded in t around 0 81.7%

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

   3. Taylor expanded in a around 0 76.0%

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

   if 2.9e-164 < t < 6.2000000000000005e-147

   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 64.0%

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

      1. cancel-sign-sub-inv 64.0%

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

      2. +-commutative 64.0%

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

      3. metadata-eval 64.0%

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

      4. associate-*r/ 64.0%

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

      5. metadata-eval 64.0%

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

      6. associate-+r+ 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in c around 0 88.2%

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

      1. remove-double-neg 88.2%

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

      2. sub-neg 88.2%

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

      3. associate--r+ 88.2%

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

      4. neg-mul-1 88.2%

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

      5. neg-mul-1 88.2%

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

      6. associate--r+ 88.2%

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

      7. sub-neg 88.2%

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

      8. remove-double-neg 88.2%

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

      9. associate--l+ 88.2%

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

      10. associate-*r/ 88.2%

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

      11. metadata-eval 88.2%

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

   7. Simplified 88.2%

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

   8. Taylor expanded in t around 0 88.2%

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

   if 1.9000000000000001e-4 < t

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. *-commutative 93.6%

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

      3. distribute-rgt-neg-in 93.6%

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

      4. distribute-neg-in 93.6%

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

      5. metadata-eval 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in a around 0 79.9%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right) + 1\right)}\\ \mathbf{elif}\;t \leq 0.00019:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 8: 59.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{+294}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+122}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) -2e+294)
   1.0
   (if (<= (- b c) -2e-49)
     (/ x (* y (exp (* (- b c) -1.6666666666666667))))
     (if (<= (- b c) 2e+122)
       1.0
       (if (<= (- b c) 2e+155)
         (/ x (+ x (+ y (* 2.0 (* a (* y (- c b)))))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -2e+294) {
		tmp = 1.0;
	} else if ((b - c) <= -2e-49) {
		tmp = x / (y * exp(((b - c) * -1.6666666666666667)));
	} else if ((b - c) <= 2e+122) {
		tmp = 1.0;
	} else if ((b - c) <= 2e+155) {
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	} 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 - c) <= (-2d+294)) then
        tmp = 1.0d0
    else if ((b - c) <= (-2d-49)) then
        tmp = x / (y * exp(((b - c) * (-1.6666666666666667d0))))
    else if ((b - c) <= 2d+122) then
        tmp = 1.0d0
    else if ((b - c) <= 2d+155) then
        tmp = x / (x + (y + (2.0d0 * (a * (y * (c - b))))))
    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 - c) <= -2e+294) {
		tmp = 1.0;
	} else if ((b - c) <= -2e-49) {
		tmp = x / (y * Math.exp(((b - c) * -1.6666666666666667)));
	} else if ((b - c) <= 2e+122) {
		tmp = 1.0;
	} else if ((b - c) <= 2e+155) {
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= -2e+294:
		tmp = 1.0
	elif (b - c) <= -2e-49:
		tmp = x / (y * math.exp(((b - c) * -1.6666666666666667)))
	elif (b - c) <= 2e+122:
		tmp = 1.0
	elif (b - c) <= 2e+155:
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= -2e+294)
		tmp = 1.0;
	elseif (Float64(b - c) <= -2e-49)
		tmp = Float64(x / Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667))));
	elseif (Float64(b - c) <= 2e+122)
		tmp = 1.0;
	elseif (Float64(b - c) <= 2e+155)
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	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 - c) <= -2e+294)
		tmp = 1.0;
	elseif ((b - c) <= -2e-49)
		tmp = x / (y * exp(((b - c) * -1.6666666666666667)));
	elseif ((b - c) <= 2e+122)
		tmp = 1.0;
	elseif ((b - c) <= 2e+155)
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], -2e+294], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], -2e-49], N[(x / N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 2e+122], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 2e+155], N[(x / N[(x + N[(y + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b c) < -2.00000000000000013e294 or -1.99999999999999987e-49 < (-.f64 b c) < 2.00000000000000003e122 or 2.00000000000000001e155 < (-.f64 b c)

   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 68.2%

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

      1. mul-1-neg 68.2%

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

      2. *-commutative 68.2%

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

      3. distribute-rgt-neg-in 68.2%

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

      4. distribute-neg-in 68.2%

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

      5. metadata-eval 68.2%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in x around inf 69.5%

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

   if -2.00000000000000013e294 < (-.f64 b c) < -1.99999999999999987e-49

   1. Initial program 95.6%

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

   2. Taylor expanded in t around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. *-commutative 72.3%

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

      3. distribute-rgt-neg-in 72.3%

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

      4. distribute-neg-in 72.3%

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

      5. metadata-eval 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in a around 0 67.9%

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

   6. Taylor expanded in x around 0 66.8%

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

   if 2.00000000000000003e122 < (-.f64 b c) < 2.00000000000000001e155

   1. Initial program 76.9%

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

   2. Taylor expanded in a around inf 47.8%

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

   3. Taylor expanded in a around 0 63.2%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{+294}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+122}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 68.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-250} \lor \neg \left(t \leq 3.9 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -5.5e-250) (not (<= t 3.9e-30)))
   (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -5.5e-250) || !(t <= 3.9e-30)) {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	} 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 ((t <= (-5.5d-250)) .or. (.not. (t <= 3.9d-30))) then
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    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 ((t <= -5.5e-250) || !(t <= 3.9e-30)) {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -5.5e-250) or not (t <= 3.9e-30):
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -5.5e-250) || !(t <= 3.9e-30))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -5.5e-250) || ~((t <= 3.9e-30)))
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -5.5e-250], N[Not[LessEqual[t, 3.9e-30]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -5.5e-250 or 3.9000000000000003e-30 < t

   1. Initial program 96.5%

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

   2. Taylor expanded in t around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. *-commutative 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. distribute-neg-in 86.5%

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

      5. metadata-eval 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in a around 0 75.6%

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

   if -5.5e-250 < t < 3.9000000000000003e-30

   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 t around inf 32.8%

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

      1. mul-1-neg 32.8%

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

      2. *-commutative 32.8%

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

      3. distribute-rgt-neg-in 32.8%

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

      4. distribute-neg-in 32.8%

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

      5. metadata-eval 32.8%

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

   4. Simplified 32.8%

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

   5. Taylor expanded in x around inf 54.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-250} \lor \neg \left(t \leq 3.9 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 50.9% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+164} \lor \neg \left(y \leq 4.2 \cdot 10^{+203}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 4.8e+74)
   1.0
   (if (or (<= y 8e+164) (not (<= y 4.2e+203)))
     (/ x (* y (+ (* 2.0 (* a (- c b))) 1.0)))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 4.8e+74) {
		tmp = 1.0;
	} else if ((y <= 8e+164) || !(y <= 4.2e+203)) {
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0));
	} 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 (y <= 4.8d+74) then
        tmp = 1.0d0
    else if ((y <= 8d+164) .or. (.not. (y <= 4.2d+203))) then
        tmp = x / (y * ((2.0d0 * (a * (c - b))) + 1.0d0))
    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 (y <= 4.8e+74) {
		tmp = 1.0;
	} else if ((y <= 8e+164) || !(y <= 4.2e+203)) {
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 4.8e+74:
		tmp = 1.0
	elif (y <= 8e+164) or not (y <= 4.2e+203):
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 4.8e+74)
		tmp = 1.0;
	elseif ((y <= 8e+164) || !(y <= 4.2e+203))
		tmp = Float64(x / Float64(y * Float64(Float64(2.0 * Float64(a * Float64(c - b))) + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 4.8e+74)
		tmp = 1.0;
	elseif ((y <= 8e+164) || ~((y <= 4.2e+203)))
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 4.8e+74], 1.0, If[Or[LessEqual[y, 8e+164], N[Not[LessEqual[y, 4.2e+203]], $MachinePrecision]], N[(x / N[(y * N[(N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < 4.80000000000000017e74 or 8e164 < y < 4.19999999999999967e203

   1. Initial program 94.5%

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

   2. Taylor expanded in t around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. distribute-neg-in 67.7%

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

      5. metadata-eval 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in x around inf 58.3%

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

   if 4.80000000000000017e74 < y < 8e164 or 4.19999999999999967e203 < y

   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 80.6%

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

   3. Taylor expanded in a around 0 68.6%

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

      1. associate-*r* 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in y around inf 63.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+164} \lor \neg \left(y \leq 4.2 \cdot 10^{+203}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 50.8% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+165}:\\ \;\;\;\;\frac{x}{y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+204}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 2.2e+74)
   1.0
   (if (<= y 2.9e+165)
     (/ x (* y (+ (* 2.0 (* a (- c b))) 1.0)))
     (if (<= y 1.08e+204) 1.0 (/ x (+ x (+ y (* 2.0 (* y (* a c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 2.2e+74) {
		tmp = 1.0;
	} else if (y <= 2.9e+165) {
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0));
	} else if (y <= 1.08e+204) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	}
	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 (y <= 2.2d+74) then
        tmp = 1.0d0
    else if (y <= 2.9d+165) then
        tmp = x / (y * ((2.0d0 * (a * (c - b))) + 1.0d0))
    else if (y <= 1.08d+204) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + (2.0d0 * (y * (a * c)))))
    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 (y <= 2.2e+74) {
		tmp = 1.0;
	} else if (y <= 2.9e+165) {
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0));
	} else if (y <= 1.08e+204) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 2.2e+74:
		tmp = 1.0
	elif y <= 2.9e+165:
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0))
	elif y <= 1.08e+204:
		tmp = 1.0
	else:
		tmp = x / (x + (y + (2.0 * (y * (a * c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 2.2e+74)
		tmp = 1.0;
	elseif (y <= 2.9e+165)
		tmp = Float64(x / Float64(y * Float64(Float64(2.0 * Float64(a * Float64(c - b))) + 1.0)));
	elseif (y <= 1.08e+204)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(y * Float64(a * c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 2.2e+74)
		tmp = 1.0;
	elseif (y <= 2.9e+165)
		tmp = x / (y * ((2.0 * (a * (c - b))) + 1.0));
	elseif (y <= 1.08e+204)
		tmp = 1.0;
	else
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 2.2e+74], 1.0, If[LessEqual[y, 2.9e+165], N[(x / N[(y * N[(N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+204], 1.0, N[(x / N[(x + N[(y + N[(2.0 * N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.2000000000000001e74 or 2.90000000000000006e165 < y < 1.08e204

   1. Initial program 94.5%

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

   2. Taylor expanded in t around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. distribute-neg-in 67.7%

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

      5. metadata-eval 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in x around inf 58.3%

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

   if 2.2000000000000001e74 < y < 2.90000000000000006e165

   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 78.0%

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

   3. Taylor expanded in a around 0 69.3%

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

      1. associate-*r* 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in y around inf 64.7%

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

   if 1.08e204 < y

   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 83.9%

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

   3. Taylor expanded in a around 0 67.7%

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

      1. associate-*r* 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in c around inf 67.7%

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

      1. associate-*r* 67.7%

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

      2. *-commutative 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+165}:\\ \;\;\;\;\frac{x}{y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+204}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \end{array} \]

Alternative 12: 50.7% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{y + 2 \cdot \left(\left(a \cdot y\right) \cdot \left(c - b\right)\right)}\\ \mathbf{elif}\;y \leq 2.06 \cdot 10^{+192}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 3.6e+74)
   1.0
   (if (<= y 8.5e+164)
     (/ x (+ y (* 2.0 (* (* a y) (- c b)))))
     (if (<= y 2.06e+192) 1.0 (/ x (+ x (+ y (* 2.0 (* y (* a c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 3.6e+74) {
		tmp = 1.0;
	} else if (y <= 8.5e+164) {
		tmp = x / (y + (2.0 * ((a * y) * (c - b))));
	} else if (y <= 2.06e+192) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	}
	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 (y <= 3.6d+74) then
        tmp = 1.0d0
    else if (y <= 8.5d+164) then
        tmp = x / (y + (2.0d0 * ((a * y) * (c - b))))
    else if (y <= 2.06d+192) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + (2.0d0 * (y * (a * c)))))
    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 (y <= 3.6e+74) {
		tmp = 1.0;
	} else if (y <= 8.5e+164) {
		tmp = x / (y + (2.0 * ((a * y) * (c - b))));
	} else if (y <= 2.06e+192) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 3.6e+74:
		tmp = 1.0
	elif y <= 8.5e+164:
		tmp = x / (y + (2.0 * ((a * y) * (c - b))))
	elif y <= 2.06e+192:
		tmp = 1.0
	else:
		tmp = x / (x + (y + (2.0 * (y * (a * c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 3.6e+74)
		tmp = 1.0;
	elseif (y <= 8.5e+164)
		tmp = Float64(x / Float64(y + Float64(2.0 * Float64(Float64(a * y) * Float64(c - b)))));
	elseif (y <= 2.06e+192)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(y * Float64(a * c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 3.6e+74)
		tmp = 1.0;
	elseif (y <= 8.5e+164)
		tmp = x / (y + (2.0 * ((a * y) * (c - b))));
	elseif (y <= 2.06e+192)
		tmp = 1.0;
	else
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 3.6e+74], 1.0, If[LessEqual[y, 8.5e+164], N[(x / N[(y + N[(2.0 * N[(N[(a * y), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.06e+192], 1.0, N[(x / N[(x + N[(y + N[(2.0 * N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.59999999999999988e74 or 8.50000000000000027e164 < y < 2.0600000000000001e192

   1. Initial program 94.5%

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

   2. Taylor expanded in t around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. distribute-neg-in 67.7%

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

      5. metadata-eval 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in x around inf 58.3%

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

   if 3.59999999999999988e74 < y < 8.50000000000000027e164

   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 78.0%

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

   3. Taylor expanded in x around 0 59.8%

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

   4. Taylor expanded in a around 0 64.7%

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

      1. associate-*r* 64.9%

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

   6. Simplified 64.8%

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

   if 2.0600000000000001e192 < y

   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 83.9%

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

   3. Taylor expanded in a around 0 67.7%

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

      1. associate-*r* 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in c around inf 67.7%

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

      1. associate-*r* 67.7%

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

      2. *-commutative 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{y + 2 \cdot \left(\left(a \cdot y\right) \cdot \left(c - b\right)\right)}\\ \mathbf{elif}\;y \leq 2.06 \cdot 10^{+192}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \end{array} \]

Alternative 13: 51.6% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+195}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 6e+61)
   1.0
   (if (<= y 1.6e+169)
     (/ x (+ x (+ y (* 2.0 (* a (* y (- c b)))))))
     (if (<= y 1.65e+195) 1.0 (/ x (+ x (+ y (* 2.0 (* y (* a c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 6e+61) {
		tmp = 1.0;
	} else if (y <= 1.6e+169) {
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	} else if (y <= 1.65e+195) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	}
	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 (y <= 6d+61) then
        tmp = 1.0d0
    else if (y <= 1.6d+169) then
        tmp = x / (x + (y + (2.0d0 * (a * (y * (c - b))))))
    else if (y <= 1.65d+195) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + (2.0d0 * (y * (a * c)))))
    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 (y <= 6e+61) {
		tmp = 1.0;
	} else if (y <= 1.6e+169) {
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	} else if (y <= 1.65e+195) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 6e+61:
		tmp = 1.0
	elif y <= 1.6e+169:
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))))
	elif y <= 1.65e+195:
		tmp = 1.0
	else:
		tmp = x / (x + (y + (2.0 * (y * (a * c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 6e+61)
		tmp = 1.0;
	elseif (y <= 1.6e+169)
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	elseif (y <= 1.65e+195)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(y * Float64(a * c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 6e+61)
		tmp = 1.0;
	elseif (y <= 1.6e+169)
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	elseif (y <= 1.65e+195)
		tmp = 1.0;
	else
		tmp = x / (x + (y + (2.0 * (y * (a * c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 6e+61], 1.0, If[LessEqual[y, 1.6e+169], N[(x / N[(x + N[(y + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+195], 1.0, N[(x / N[(x + N[(y + N[(2.0 * N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6e61 or 1.5999999999999999e169 < y < 1.65e195

   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 t around inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. *-commutative 67.0%

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

      3. distribute-rgt-neg-in 67.0%

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

      4. distribute-neg-in 67.0%

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

      5. metadata-eval 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in x around inf 58.3%

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

   if 6e61 < y < 1.5999999999999999e169

   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 78.5%

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

   3. Taylor expanded in a around 0 67.9%

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

   if 1.65e195 < y

   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 83.9%

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

   3. Taylor expanded in a around 0 67.7%

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

      1. associate-*r* 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in c around inf 67.7%

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

      1. associate-*r* 67.7%

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

      2. *-commutative 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+195}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)\right)}\\ \end{array} \]

Alternative 14: 52.3% 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 95.3%

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

2. Taylor expanded in t around inf 68.6%

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

   1. mul-1-neg 68.6%

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

   2. *-commutative 68.6%

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

   3. distribute-rgt-neg-in 68.6%

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

   4. distribute-neg-in 68.6%

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

   5. metadata-eval 68.6%

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

4. Simplified 68.6%

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

5. Taylor expanded in x around inf 53.9%

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

6. Final simplification 53.9%

   \[\leadsto 1 \]

Developer target: 95.4% 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 2023308 
(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)))))))))))