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

Percentage Accurate: 94.0% → 97.2%

Time: 29.7s

Alternatives: 16

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: 94.0% 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: 97.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right), c - b, \sqrt{a + t} \cdot \frac{z}{t}\right)\right)}, x\right)} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (fma
   y
   (pow
    (exp 2.0)
    (fma
     (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t)))
     (- c b)
     (* (sqrt (+ a t)) (/ z t))))
   x)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / fma(y, pow(exp(2.0), fma((0.8333333333333334 + (a - (0.6666666666666666 / t))), (c - b), (sqrt((a + t)) * (z / t)))), x);
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / fma(y, (exp(2.0) ^ fma(Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t))), Float64(c - b), Float64(sqrt(Float64(a + t)) * Float64(z / t)))), x))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision] + N[(N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.8%

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

   1. +-commutative 96.8%

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

   2. fma-def 96.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 96.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((math.sqrt((a + t)) * z) / t) + ((c - b) * ((0.8333333333333334 + a) - (2.0 / (t * 3.0))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * t_1))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c / t) * -0.6666666666666666)))))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((sqrt((a + t)) * z) / t) + ((c - b) * ((0.8333333333333334 + a) - (2.0 / (t * 3.0))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c / t) * -0.6666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * N[(N[(0.8333333333333334 + a), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c / t), $MachinePrecision] * -0.6666666666666666), $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 57.6%

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

   3. Taylor expanded in c around inf 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 98.8%

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

Alternative 3: 90.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -10:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 10^{-284}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -10.0)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 1e-284)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* (- c b) -0.6666666666666666)) t))))))
     (if (<= t 2e+185)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (+
             (* z (sqrt (/ 1.0 t)))
             (* (- c b) (- 0.8333333333333334 (/ 0.6666666666666666 t)))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -10.0) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1e-284) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 2e+185) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 - (0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (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 <= (-10.0d0)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1d-284) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((c - b) * (-0.6666666666666666d0))) / t)))))
    else if (t <= 2d+185) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) + ((c - b) * (0.8333333333333334d0 - (0.6666666666666666d0 / t))))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (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 <= -10.0) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1e-284) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 2e+185) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 - (0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -10.0:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1e-284:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))))
	elif t <= 2e+185:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 - (0.6666666666666666 / t))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -10.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1e-284)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(Float64(c - b) * -0.6666666666666666)) / t))))));
	elseif (t <= 2e+185)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) + Float64(Float64(c - b) * Float64(0.8333333333333334 - Float64(0.6666666666666666 / t)))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * 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 <= -10.0)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1e-284)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	elseif (t <= 2e+185)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 - (0.6666666666666666 / t))))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -10.0], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-284], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+185], 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[(c - b), $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[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -10

   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 100.0%

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

   if -10 < t < 1.00000000000000004e-284

   1. Initial program 96.0%

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

   2. Taylor expanded in t around 0 96.1%

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

   if 1.00000000000000004e-284 < t < 2e185

   1. Initial program 96.2%

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

   2. Taylor expanded in a around 0 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*r/ 93.3%

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

      3. metadata-eval 93.3%

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

   4. Simplified 93.3%

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

   if 2e185 < t

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 92.8%

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

      1. associate-*r* 92.8%

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

      2. neg-mul-1 92.8%

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

      3. neg-sub0 92.8%

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

      4. associate--r- 92.8%

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

      5. neg-sub0 92.8%

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

      6. +-commutative 92.8%

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

      7. sub-neg 92.8%

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

      8. *-commutative 92.8%

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

      9. +-commutative 92.8%

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

   4. Simplified 92.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -10:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 10^{-284}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 4: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0001:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -0.0001)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 1.9e-149)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* (- c b) -0.6666666666666666)) t))))))
     (if (<= t 1.5e-18)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (* c (+ a (- 0.8333333333333334 (/ 0.6666666666666666 t)))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -0.0001) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.9e-149) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 1.5e-18) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (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 <= (-0.0001d0)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1.9d-149) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((c - b) * (-0.6666666666666666d0))) / t)))))
    else if (t <= 1.5d-18) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (0.8333333333333334d0 - (0.6666666666666666d0 / t))))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (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 <= -0.0001) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.9e-149) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 1.5e-18) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -0.0001:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1.9e-149:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))))
	elif t <= 1.5e-18:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -0.0001)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1.9e-149)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(Float64(c - b) * -0.6666666666666666)) / t))))));
	elseif (t <= 1.5e-18)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(0.8333333333333334 - Float64(0.6666666666666666 / t)))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * 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 <= -0.0001)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1.9e-149)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	elseif (t <= 1.5e-18)
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -0.0001], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-149], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-18], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(0.8333333333333334 - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.00000000000000005e-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 a around inf 100.0%

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

   if -1.00000000000000005e-4 < t < 1.90000000000000003e-149

   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 0 92.3%

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

   if 1.90000000000000003e-149 < t < 1.49999999999999991e-18

   1. Initial program 97.1%

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

   2. Taylor expanded in c around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-*r/ 75.9%

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

      3. metadata-eval 75.9%

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

      4. associate--l+ 75.9%

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

   4. Simplified 75.9%

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

   if 1.49999999999999991e-18 < t

   1. Initial program 97.2%

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

   2. Taylor expanded in t around inf 88.6%

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

      1. associate-*r* 88.6%

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

      2. neg-mul-1 88.6%

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

      3. neg-sub0 88.6%

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

      4. associate--r- 88.6%

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

      5. neg-sub0 88.6%

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

      6. +-commutative 88.6%

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

      7. sub-neg 88.6%

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

      8. *-commutative 88.6%

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

      9. +-commutative 88.6%

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

   4. Simplified 88.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0001:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 5: 71.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{c}{t} \cdot -0.6666666666666666\right)}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{0.6666666666666666 \cdot b}{t}}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667))))))
        (t_2 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= t -3.5e-240)
     t_2
     (if (<= t 3e-174)
       (/ x (+ x (* y (exp (* 2.0 (* (/ c t) -0.6666666666666666))))))
       (if (<= t 1.05e-38)
         (/ x (+ x (* y (exp (* 2.0 (/ (* 0.6666666666666666 b) t))))))
         (if (<= t 1.2e-20)
           t_1
           (if (<= t 9.6e+32)
             (/ x (+ x (* y (exp (* -2.0 (* a b))))))
             (if (<= t 2.1e+187) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	double t_2 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= -3.5e-240) {
		tmp = t_2;
	} else if (t <= 3e-174) {
		tmp = x / (x + (y * exp((2.0 * ((c / t) * -0.6666666666666666)))));
	} else if (t <= 1.05e-38) {
		tmp = x / (x + (y * exp((2.0 * ((0.6666666666666666 * b) / t)))));
	} else if (t <= 1.2e-20) {
		tmp = t_1;
	} else if (t <= 9.6e+32) {
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	} else if (t <= 2.1e+187) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    t_2 = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    if (t <= (-3.5d-240)) then
        tmp = t_2
    else if (t <= 3d-174) then
        tmp = x / (x + (y * exp((2.0d0 * ((c / t) * (-0.6666666666666666d0))))))
    else if (t <= 1.05d-38) then
        tmp = x / (x + (y * exp((2.0d0 * ((0.6666666666666666d0 * b) / t)))))
    else if (t <= 1.2d-20) then
        tmp = t_1
    else if (t <= 9.6d+32) then
        tmp = x / (x + (y * exp(((-2.0d0) * (a * b)))))
    else if (t <= 2.1d+187) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	double t_2 = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= -3.5e-240) {
		tmp = t_2;
	} else if (t <= 3e-174) {
		tmp = x / (x + (y * Math.exp((2.0 * ((c / t) * -0.6666666666666666)))));
	} else if (t <= 1.05e-38) {
		tmp = x / (x + (y * Math.exp((2.0 * ((0.6666666666666666 * b) / t)))));
	} else if (t <= 1.2e-20) {
		tmp = t_1;
	} else if (t <= 9.6e+32) {
		tmp = x / (x + (y * Math.exp((-2.0 * (a * b)))));
	} else if (t <= 2.1e+187) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	t_2 = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	tmp = 0
	if t <= -3.5e-240:
		tmp = t_2
	elif t <= 3e-174:
		tmp = x / (x + (y * math.exp((2.0 * ((c / t) * -0.6666666666666666)))))
	elif t <= 1.05e-38:
		tmp = x / (x + (y * math.exp((2.0 * ((0.6666666666666666 * b) / t)))))
	elif t <= 1.2e-20:
		tmp = t_1
	elif t <= 9.6e+32:
		tmp = x / (x + (y * math.exp((-2.0 * (a * b)))))
	elif t <= 2.1e+187:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))))
	t_2 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))))
	tmp = 0.0
	if (t <= -3.5e-240)
		tmp = t_2;
	elseif (t <= 3e-174)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c / t) * -0.6666666666666666))))));
	elseif (t <= 1.05e-38)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(0.6666666666666666 * b) / t))))));
	elseif (t <= 1.2e-20)
		tmp = t_1;
	elseif (t <= 9.6e+32)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(a * b))))));
	elseif (t <= 2.1e+187)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	t_2 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	tmp = 0.0;
	if (t <= -3.5e-240)
		tmp = t_2;
	elseif (t <= 3e-174)
		tmp = x / (x + (y * exp((2.0 * ((c / t) * -0.6666666666666666)))));
	elseif (t <= 1.05e-38)
		tmp = x / (x + (y * exp((2.0 * ((0.6666666666666666 * b) / t)))));
	elseif (t <= 1.2e-20)
		tmp = t_1;
	elseif (t <= 9.6e+32)
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	elseif (t <= 2.1e+187)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-240], t$95$2, If[LessEqual[t, 3e-174], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c / t), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-38], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(0.6666666666666666 * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-20], t$95$1, If[LessEqual[t, 9.6e+32], N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+187], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.50000000000000016e-240 or 2.1e187 < t

   1. Initial program 99.0%

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

   2. Taylor expanded in a around inf 80.8%

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

   if -3.50000000000000016e-240 < t < 3.00000000000000021e-174

   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 0 90.5%

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

   3. Taylor expanded in c around inf 74.6%

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

      1. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   if 3.00000000000000021e-174 < t < 1.05000000000000006e-38

   1. Initial program 94.9%

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

   2. Taylor expanded in b around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. associate-*r/ 73.0%

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

      3. metadata-eval 73.0%

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

      4. +-commutative 73.0%

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

   4. Simplified 73.0%

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

   5. Taylor expanded in t around 0 75.5%

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

      1. associate-*r/ 75.5%

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

   7. Simplified 75.5%

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

   if 1.05000000000000006e-38 < t < 1.19999999999999996e-20 or 9.59999999999999965e32 < t < 2.1e187

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 93.8%

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

      1. associate-*r* 93.8%

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

      2. neg-mul-1 93.8%

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

      3. neg-sub0 93.8%

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

      4. associate--r- 93.8%

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

      5. neg-sub0 93.8%

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

      6. +-commutative 93.8%

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

      7. sub-neg 93.8%

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

      8. *-commutative 93.8%

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

      9. +-commutative 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in a around 0 95.9%

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

   if 1.19999999999999996e-20 < t < 9.59999999999999965e32

   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 69.6%

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

   3. Taylor expanded in c around 0 75.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{c}{t} \cdot -0.6666666666666666\right)}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{0.6666666666666666 \cdot b}{t}}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 6: 78.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{c}{t} \cdot -0.6666666666666666\right)}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{0.6666666666666666 \cdot b}{t}}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))
   (if (<= t -5e-293)
     t_1
     (if (<= t 6e-173)
       (/ x (+ x (* y (exp (* 2.0 (* (/ c t) -0.6666666666666666))))))
       (if (<= t 1.2e-19)
         (/ x (+ x (* y (exp (* 2.0 (/ (* 0.6666666666666666 b) t))))))
         (if (<= t 9.6e+32) (/ x (+ x (* y (exp (* -2.0 (* a b)))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	double tmp;
	if (t <= -5e-293) {
		tmp = t_1;
	} else if (t <= 6e-173) {
		tmp = x / (x + (y * exp((2.0 * ((c / t) * -0.6666666666666666)))));
	} else if (t <= 1.2e-19) {
		tmp = x / (x + (y * exp((2.0 * ((0.6666666666666666 * b) / t)))));
	} else if (t <= 9.6e+32) {
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + a))))))
    if (t <= (-5d-293)) then
        tmp = t_1
    else if (t <= 6d-173) then
        tmp = x / (x + (y * exp((2.0d0 * ((c / t) * (-0.6666666666666666d0))))))
    else if (t <= 1.2d-19) then
        tmp = x / (x + (y * exp((2.0d0 * ((0.6666666666666666d0 * b) / t)))))
    else if (t <= 9.6d+32) then
        tmp = x / (x + (y * exp(((-2.0d0) * (a * b)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	double tmp;
	if (t <= -5e-293) {
		tmp = t_1;
	} else if (t <= 6e-173) {
		tmp = x / (x + (y * Math.exp((2.0 * ((c / t) * -0.6666666666666666)))));
	} else if (t <= 1.2e-19) {
		tmp = x / (x + (y * Math.exp((2.0 * ((0.6666666666666666 * b) / t)))));
	} else if (t <= 9.6e+32) {
		tmp = x / (x + (y * Math.exp((-2.0 * (a * b)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	tmp = 0
	if t <= -5e-293:
		tmp = t_1
	elif t <= 6e-173:
		tmp = x / (x + (y * math.exp((2.0 * ((c / t) * -0.6666666666666666)))))
	elif t <= 1.2e-19:
		tmp = x / (x + (y * math.exp((2.0 * ((0.6666666666666666 * b) / t)))))
	elif t <= 9.6e+32:
		tmp = x / (x + (y * math.exp((-2.0 * (a * b)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))))
	tmp = 0.0
	if (t <= -5e-293)
		tmp = t_1;
	elseif (t <= 6e-173)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c / t) * -0.6666666666666666))))));
	elseif (t <= 1.2e-19)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(0.6666666666666666 * b) / t))))));
	elseif (t <= 9.6e+32)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(a * b))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	tmp = 0.0;
	if (t <= -5e-293)
		tmp = t_1;
	elseif (t <= 6e-173)
		tmp = x / (x + (y * exp((2.0 * ((c / t) * -0.6666666666666666)))));
	elseif (t <= 1.2e-19)
		tmp = x / (x + (y * exp((2.0 * ((0.6666666666666666 * b) / t)))));
	elseif (t <= 9.6e+32)
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e-293], t$95$1, If[LessEqual[t, 6e-173], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c / t), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-19], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(0.6666666666666666 * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+32], N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.0000000000000003e-293 or 9.59999999999999965e32 < t

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 89.5%

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

      1. associate-*r* 89.5%

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

      2. neg-mul-1 89.5%

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

      3. neg-sub0 89.5%

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

      4. associate--r- 89.5%

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

      5. neg-sub0 89.5%

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

      6. +-commutative 89.5%

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

      7. sub-neg 89.5%

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

      8. *-commutative 89.5%

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

      9. +-commutative 89.5%

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

   4. Simplified 89.5%

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

   if -5.0000000000000003e-293 < t < 6.0000000000000002e-173

   1. Initial program 92.1%

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

   2. Taylor expanded in t around 0 89.5%

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

   3. Taylor expanded in c around inf 74.5%

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

      1. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   if 6.0000000000000002e-173 < t < 1.20000000000000011e-19

   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 b around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-*r/ 68.1%

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

      3. metadata-eval 68.1%

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

      4. +-commutative 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in t around 0 70.3%

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

      1. associate-*r/ 70.3%

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

   7. Simplified 70.3%

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

   if 1.20000000000000011e-19 < t < 9.59999999999999965e32

   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 74.1%

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

   3. Taylor expanded in c around 0 80.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-293}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{c}{t} \cdot -0.6666666666666666\right)}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{0.6666666666666666 \cdot b}{t}}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 7: 67.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-310}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= t -2e-310)
     t_1
     (if (<= t 2.55e-198)
       (/ x (- x (* y (- -1.0 (/ (* c -1.3333333333333333) t)))))
       (if (<= t 3.2e-96)
         1.0
         (if (<= t 5.2e+187)
           (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= -2e-310) {
		tmp = t_1;
	} else if (t <= 2.55e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 3.2e-96) {
		tmp = 1.0;
	} else if (t <= 5.2e+187) {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    if (t <= (-2d-310)) then
        tmp = t_1
    else if (t <= 2.55d-198) then
        tmp = x / (x - (y * ((-1.0d0) - ((c * (-1.3333333333333333d0)) / t))))
    else if (t <= 3.2d-96) then
        tmp = 1.0d0
    else if (t <= 5.2d+187) then
        tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= -2e-310) {
		tmp = t_1;
	} else if (t <= 2.55e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 3.2e-96) {
		tmp = 1.0;
	} else if (t <= 5.2e+187) {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	tmp = 0
	if t <= -2e-310:
		tmp = t_1
	elif t <= 2.55e-198:
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))))
	elif t <= 3.2e-96:
		tmp = 1.0
	elif t <= 5.2e+187:
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))))
	tmp = 0.0
	if (t <= -2e-310)
		tmp = t_1;
	elseif (t <= 2.55e-198)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(Float64(c * -1.3333333333333333) / t)))));
	elseif (t <= 3.2e-96)
		tmp = 1.0;
	elseif (t <= 5.2e+187)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	tmp = 0.0;
	if (t <= -2e-310)
		tmp = t_1;
	elseif (t <= 2.55e-198)
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	elseif (t <= 3.2e-96)
		tmp = 1.0;
	elseif (t <= 5.2e+187)
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-310], t$95$1, If[LessEqual[t, 2.55e-198], N[(x / N[(x - N[(y * N[(-1.0 - N[(N[(c * -1.3333333333333333), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-96], 1.0, If[LessEqual[t, 5.2e+187], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.999999999999994e-310 or 5.1999999999999997e187 < t

   1. Initial program 99.0%

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

   2. Taylor expanded in a around inf 81.0%

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

   if -1.999999999999994e-310 < t < 2.5499999999999998e-198

   1. Initial program 90.0%

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

   2. Taylor expanded in t around 0 86.7%

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

   3. Taylor expanded in c around inf 70.9%

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

      1. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in c around 0 77.4%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + -1.3333333333333333 \cdot \frac{c}{t}\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 77.4%

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

   8. Simplified 77.4%

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

   if 2.5499999999999998e-198 < t < 3.20000000000000012e-96

   1. Initial program 94.1%

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

   2. Taylor expanded in a around inf 34.7%

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

   3. Taylor expanded in a around 0 37.5%

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

   4. Taylor expanded in x around inf 57.3%

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

   if 3.20000000000000012e-96 < t < 5.1999999999999997e187

   1. Initial program 97.3%

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

   2. Taylor expanded in t around inf 80.8%

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

      1. associate-*r* 80.8%

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

      2. neg-mul-1 80.8%

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

      3. neg-sub0 80.8%

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

      4. associate--r- 80.8%

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

      5. neg-sub0 80.8%

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

      6. +-commutative 80.8%

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

      7. sub-neg 80.8%

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

      8. *-commutative 80.8%

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

      9. +-commutative 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in a around 0 82.1%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 8: 79.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-9} \lor \neg \left(c \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -1.8e-9) (not (<= c 8e-37)))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (* 2.0 (* c (+ a (- 0.8333333333333334 (/ 0.6666666666666666 t)))))))))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (*
        2.0
        (* b (- (/ 0.6666666666666666 t) (+ 0.8333333333333334 a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -1.8e-9) || !(c <= 8e-37)) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (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 ((c <= (-1.8d-9)) .or. (.not. (c <= 8d-37))) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (0.8333333333333334d0 - (0.6666666666666666d0 / t))))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (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 ((c <= -1.8e-9) || !(c <= 8e-37)) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (0.8333333333333334 + a)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (c <= -1.8e-9) or not (c <= 8e-37):
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (0.8333333333333334 + a)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -1.8e-9) || !(c <= 8e-37))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(0.8333333333333334 - Float64(0.6666666666666666 / t)))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(0.8333333333333334 + a))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((c <= -1.8e-9) || ~((c <= 8e-37)))
		tmp = x / (x + (y * exp((2.0 * (c * (a + (0.8333333333333334 - (0.6666666666666666 / t))))))));
	else
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (0.8333333333333334 + a)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -1.8e-9], N[Not[LessEqual[c, 8e-37]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(0.8333333333333334 - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.8e-9 or 8.00000000000000053e-37 < c

   1. Initial program 95.4%

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

   2. Taylor expanded in c around inf 86.9%

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

      1. +-commutative 86.9%

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

      2. associate-*r/ 86.9%

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

      3. metadata-eval 86.9%

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

      4. associate--l+ 86.9%

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

   4. Simplified 86.9%

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

   if -1.8e-9 < c < 8.00000000000000053e-37

   1. Initial program 98.4%

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

   2. Taylor expanded in b around inf 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*r/ 82.5%

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

      3. metadata-eval 82.5%

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

      4. +-commutative 82.5%

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

   4. Simplified 82.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-9} \lor \neg \left(c \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}\\ \end{array} \]

Alternative 9: 63.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-96}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))))
   (if (<= t -5.5e-299)
     t_1
     (if (<= t 2.9e-198)
       (/ x (- x (* y (- -1.0 (/ (* c -1.3333333333333333) t)))))
       (if (<= t 4.6e-96)
         1.0
         (if (<= t 5.7e+187) t_1 (/ x (+ x (* y (exp (* -2.0 (* a b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	double tmp;
	if (t <= -5.5e-299) {
		tmp = t_1;
	} else if (t <= 2.9e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 4.6e-96) {
		tmp = 1.0;
	} else if (t <= 5.7e+187) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    if (t <= (-5.5d-299)) then
        tmp = t_1
    else if (t <= 2.9d-198) then
        tmp = x / (x - (y * ((-1.0d0) - ((c * (-1.3333333333333333d0)) / t))))
    else if (t <= 4.6d-96) then
        tmp = 1.0d0
    else if (t <= 5.7d+187) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp(((-2.0d0) * (a * b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	double tmp;
	if (t <= -5.5e-299) {
		tmp = t_1;
	} else if (t <= 2.9e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 4.6e-96) {
		tmp = 1.0;
	} else if (t <= 5.7e+187) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((-2.0 * (a * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	tmp = 0
	if t <= -5.5e-299:
		tmp = t_1
	elif t <= 2.9e-198:
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))))
	elif t <= 4.6e-96:
		tmp = 1.0
	elif t <= 5.7e+187:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((-2.0 * (a * b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))))
	tmp = 0.0
	if (t <= -5.5e-299)
		tmp = t_1;
	elseif (t <= 2.9e-198)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(Float64(c * -1.3333333333333333) / t)))));
	elseif (t <= 4.6e-96)
		tmp = 1.0;
	elseif (t <= 5.7e+187)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(a * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	tmp = 0.0;
	if (t <= -5.5e-299)
		tmp = t_1;
	elseif (t <= 2.9e-198)
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	elseif (t <= 4.6e-96)
		tmp = 1.0;
	elseif (t <= 5.7e+187)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-299], t$95$1, If[LessEqual[t, 2.9e-198], N[(x / N[(x - N[(y * N[(-1.0 - N[(N[(c * -1.3333333333333333), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-96], 1.0, If[LessEqual[t, 5.7e+187], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5e-299 or 4.6e-96 < t < 5.7000000000000004e187

   1. Initial program 98.5%

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

   2. Taylor expanded in t around inf 82.3%

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

      1. associate-*r* 82.3%

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

      2. neg-mul-1 82.3%

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

      3. neg-sub0 82.3%

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

      4. associate--r- 82.3%

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

      5. neg-sub0 82.3%

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

      6. +-commutative 82.3%

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

      7. sub-neg 82.3%

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

      8. *-commutative 82.3%

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

      9. +-commutative 82.3%

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

   4. Simplified 82.3%

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

   5. Taylor expanded in a around 0 78.9%

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

   if -5.5e-299 < t < 2.90000000000000001e-198

   1. Initial program 90.3%

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

   2. Taylor expanded in t around 0 87.1%

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

   3. Taylor expanded in c around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in c around 0 75.0%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + -1.3333333333333333 \cdot \frac{c}{t}\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.0%

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

   8. Simplified 75.0%

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

   if 2.90000000000000001e-198 < t < 4.6e-96

   1. Initial program 94.1%

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

   2. Taylor expanded in a around inf 34.7%

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

   3. Taylor expanded in a around 0 37.5%

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

   4. Taylor expanded in x around inf 57.3%

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

   if 5.7000000000000004e187 < t

   1. Initial program 98.0%

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

   2. Taylor expanded in a around inf 78.9%

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

   3. Taylor expanded in c around 0 71.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-96}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+187}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \end{array} \]

Alternative 10: 71.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{c}{t} \cdot -0.6666666666666666\right)}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= t -7.6e-239)
     t_1
     (if (<= t 6e-51)
       (/ x (+ x (* y (exp (* 2.0 (* (/ c t) -0.6666666666666666))))))
       (if (<= t 2.7e+185)
         (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= -7.6e-239) {
		tmp = t_1;
	} else if (t <= 6e-51) {
		tmp = x / (x + (y * exp((2.0 * ((c / t) * -0.6666666666666666)))));
	} else if (t <= 2.7e+185) {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    if (t <= (-7.6d-239)) then
        tmp = t_1
    else if (t <= 6d-51) then
        tmp = x / (x + (y * exp((2.0d0 * ((c / t) * (-0.6666666666666666d0))))))
    else if (t <= 2.7d+185) then
        tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	double tmp;
	if (t <= -7.6e-239) {
		tmp = t_1;
	} else if (t <= 6e-51) {
		tmp = x / (x + (y * Math.exp((2.0 * ((c / t) * -0.6666666666666666)))));
	} else if (t <= 2.7e+185) {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	tmp = 0
	if t <= -7.6e-239:
		tmp = t_1
	elif t <= 6e-51:
		tmp = x / (x + (y * math.exp((2.0 * ((c / t) * -0.6666666666666666)))))
	elif t <= 2.7e+185:
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))))
	tmp = 0.0
	if (t <= -7.6e-239)
		tmp = t_1;
	elseif (t <= 6e-51)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c / t) * -0.6666666666666666))))));
	elseif (t <= 2.7e+185)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	tmp = 0.0;
	if (t <= -7.6e-239)
		tmp = t_1;
	elseif (t <= 6e-51)
		tmp = x / (x + (y * exp((2.0 * ((c / t) * -0.6666666666666666)))));
	elseif (t <= 2.7e+185)
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e-239], t$95$1, If[LessEqual[t, 6e-51], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c / t), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+185], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.6000000000000004e-239 or 2.70000000000000007e185 < t

   1. Initial program 99.0%

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

   2. Taylor expanded in a around inf 80.8%

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

   if -7.6000000000000004e-239 < t < 6.00000000000000005e-51

   1. Initial program 93.7%

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

   2. Taylor expanded in t around 0 80.1%

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

   3. Taylor expanded in c around inf 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   if 6.00000000000000005e-51 < t < 2.70000000000000007e185

   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 83.6%

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

      1. associate-*r* 83.6%

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

      2. neg-mul-1 83.6%

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

      3. neg-sub0 83.6%

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

      4. associate--r- 83.6%

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

      5. neg-sub0 83.6%

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

      6. +-commutative 83.6%

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

      7. sub-neg 83.6%

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

      8. *-commutative 83.6%

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

      9. +-commutative 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in a around 0 85.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{c}{t} \cdot -0.6666666666666666\right)}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 11: 66.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))))
   (if (<= t -5.5e-299)
     t_1
     (if (<= t 2.8e-198)
       (/ x (- x (* y (- -1.0 (/ (* c -1.3333333333333333) t)))))
       (if (<= t 3.9e-96) 1.0 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	double tmp;
	if (t <= -5.5e-299) {
		tmp = t_1;
	} else if (t <= 2.8e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 3.9e-96) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    if (t <= (-5.5d-299)) then
        tmp = t_1
    else if (t <= 2.8d-198) then
        tmp = x / (x - (y * ((-1.0d0) - ((c * (-1.3333333333333333d0)) / t))))
    else if (t <= 3.9d-96) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	double tmp;
	if (t <= -5.5e-299) {
		tmp = t_1;
	} else if (t <= 2.8e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 3.9e-96) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	tmp = 0
	if t <= -5.5e-299:
		tmp = t_1
	elif t <= 2.8e-198:
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))))
	elif t <= 3.9e-96:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))))
	tmp = 0.0
	if (t <= -5.5e-299)
		tmp = t_1;
	elseif (t <= 2.8e-198)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(Float64(c * -1.3333333333333333) / t)))));
	elseif (t <= 3.9e-96)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	tmp = 0.0;
	if (t <= -5.5e-299)
		tmp = t_1;
	elseif (t <= 2.8e-198)
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	elseif (t <= 3.9e-96)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-299], t$95$1, If[LessEqual[t, 2.8e-198], N[(x / N[(x - N[(y * N[(-1.0 - N[(N[(c * -1.3333333333333333), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-96], 1.0, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5e-299 or 3.8999999999999998e-96 < t

   1. Initial program 98.4%

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

   2. Taylor expanded in t around inf 85.3%

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

      1. associate-*r* 85.3%

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

      2. neg-mul-1 85.3%

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

      3. neg-sub0 85.3%

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

      4. associate--r- 85.3%

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

      5. neg-sub0 85.3%

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

      6. +-commutative 85.3%

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

      7. sub-neg 85.3%

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

      8. *-commutative 85.3%

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

      9. +-commutative 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in a around 0 73.8%

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

   if -5.5e-299 < t < 2.7999999999999999e-198

   1. Initial program 90.3%

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

   2. Taylor expanded in t around 0 87.1%

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

   3. Taylor expanded in c around inf 71.9%

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

      1. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in c around 0 75.0%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + -1.3333333333333333 \cdot \frac{c}{t}\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.0%

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

   8. Simplified 75.0%

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

   if 2.7999999999999999e-198 < t < 3.8999999999999998e-96

   1. Initial program 94.1%

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

   2. Taylor expanded in a around inf 34.7%

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

   3. Taylor expanded in a around 0 37.5%

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

   4. Taylor expanded in x around inf 57.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-96}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 12: 49.4% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{-305}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 8500000000:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - \left(b - c\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 1.3e-305)
   1.0
   (if (<= t 1.65e-198)
     (/ x (- x (* y (- -1.0 (/ (* c -1.3333333333333333) t)))))
     (if (<= t 1.8e-34)
       1.0
       (if (<= t 8500000000.0)
         (/ x (+ x (* y (- 1.0 (* (- b c) (* 2.0 a))))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.3e-305) {
		tmp = 1.0;
	} else if (t <= 1.65e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 1.8e-34) {
		tmp = 1.0;
	} else if (t <= 8500000000.0) {
		tmp = x / (x + (y * (1.0 - ((b - c) * (2.0 * a)))));
	} 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 <= 1.3d-305) then
        tmp = 1.0d0
    else if (t <= 1.65d-198) then
        tmp = x / (x - (y * ((-1.0d0) - ((c * (-1.3333333333333333d0)) / t))))
    else if (t <= 1.8d-34) then
        tmp = 1.0d0
    else if (t <= 8500000000.0d0) then
        tmp = x / (x + (y * (1.0d0 - ((b - c) * (2.0d0 * a)))))
    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 <= 1.3e-305) {
		tmp = 1.0;
	} else if (t <= 1.65e-198) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else if (t <= 1.8e-34) {
		tmp = 1.0;
	} else if (t <= 8500000000.0) {
		tmp = x / (x + (y * (1.0 - ((b - c) * (2.0 * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 1.3e-305:
		tmp = 1.0
	elif t <= 1.65e-198:
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))))
	elif t <= 1.8e-34:
		tmp = 1.0
	elif t <= 8500000000.0:
		tmp = x / (x + (y * (1.0 - ((b - c) * (2.0 * a)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 1.3e-305)
		tmp = 1.0;
	elseif (t <= 1.65e-198)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(Float64(c * -1.3333333333333333) / t)))));
	elseif (t <= 1.8e-34)
		tmp = 1.0;
	elseif (t <= 8500000000.0)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 - Float64(Float64(b - c) * Float64(2.0 * a))))));
	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 <= 1.3e-305)
		tmp = 1.0;
	elseif (t <= 1.65e-198)
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	elseif (t <= 1.8e-34)
		tmp = 1.0;
	elseif (t <= 8500000000.0)
		tmp = x / (x + (y * (1.0 - ((b - c) * (2.0 * a)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 1.3e-305], 1.0, If[LessEqual[t, 1.65e-198], N[(x / N[(x - N[(y * N[(-1.0 - N[(N[(c * -1.3333333333333333), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-34], 1.0, If[LessEqual[t, 8500000000.0], N[(x / N[(x + N[(y * N[(1.0 - N[(N[(b - c), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.3000000000000001e-305 or 1.65e-198 < t < 1.80000000000000004e-34 or 8.5e9 < t

   1. Initial program 97.6%

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

   2. Taylor expanded in a around inf 66.5%

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

   3. Taylor expanded in a around 0 39.4%

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

   4. Taylor expanded in x around inf 60.4%

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

   if 1.3000000000000001e-305 < t < 1.65e-198

   1. Initial program 89.3%

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

   2. Taylor expanded in t around 0 85.7%

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

   3. Taylor expanded in c around inf 68.9%

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

      1. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in c around 0 79.3%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + -1.3333333333333333 \cdot \frac{c}{t}\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 79.3%

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

   8. Simplified 79.3%

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

   if 1.80000000000000004e-34 < t < 8.5e9

   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 74.2%

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

   3. Taylor expanded in a around 0 63.1%

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

      1. associate-*r* 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.3 \cdot 10^{-305}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-198}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 8500000000:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - \left(b - c\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 48.6% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-305}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-198} \lor \neg \left(t \leq 4.4 \cdot 10^{-96}\right) \land t \leq 1200000000:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 1.35e-305)
   1.0
   (if (or (<= t 2.7e-198) (and (not (<= t 4.4e-96)) (<= t 1200000000.0)))
     (/ x (- x (* y (- -1.0 (/ (* c -1.3333333333333333) t)))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.35e-305) {
		tmp = 1.0;
	} else if ((t <= 2.7e-198) || (!(t <= 4.4e-96) && (t <= 1200000000.0))) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= 1.35d-305) then
        tmp = 1.0d0
    else if ((t <= 2.7d-198) .or. (.not. (t <= 4.4d-96)) .and. (t <= 1200000000.0d0)) then
        tmp = x / (x - (y * ((-1.0d0) - ((c * (-1.3333333333333333d0)) / t))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.35e-305) {
		tmp = 1.0;
	} else if ((t <= 2.7e-198) || (!(t <= 4.4e-96) && (t <= 1200000000.0))) {
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 1.35e-305:
		tmp = 1.0
	elif (t <= 2.7e-198) or (not (t <= 4.4e-96) and (t <= 1200000000.0)):
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 1.35e-305)
		tmp = 1.0;
	elseif ((t <= 2.7e-198) || (!(t <= 4.4e-96) && (t <= 1200000000.0)))
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(Float64(c * -1.3333333333333333) / t)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 1.35e-305)
		tmp = 1.0;
	elseif ((t <= 2.7e-198) || (~((t <= 4.4e-96)) && (t <= 1200000000.0)))
		tmp = x / (x - (y * (-1.0 - ((c * -1.3333333333333333) / t))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 1.35e-305], 1.0, If[Or[LessEqual[t, 2.7e-198], And[N[Not[LessEqual[t, 4.4e-96]], $MachinePrecision], LessEqual[t, 1200000000.0]]], N[(x / N[(x - N[(y * N[(-1.0 - N[(N[(c * -1.3333333333333333), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < 1.35e-305 or 2.7000000000000002e-198 < t < 4.39999999999999959e-96 or 1.2e9 < t

   1. Initial program 97.5%

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

   2. Taylor expanded in a around inf 67.1%

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

   3. Taylor expanded in a around 0 38.2%

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

   4. Taylor expanded in x around inf 60.3%

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

   if 1.35e-305 < t < 2.7000000000000002e-198 or 4.39999999999999959e-96 < t < 1.2e9

   1. Initial program 94.6%

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

   2. Taylor expanded in t around 0 66.3%

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

   3. Taylor expanded in c around inf 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in c around 0 69.3%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + -1.3333333333333333 \cdot \frac{c}{t}\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 69.3%

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

   8. Simplified 69.3%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + \frac{-1.3333333333333333 \cdot c}{t}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-305}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-198} \lor \neg \left(t \leq 4.4 \cdot 10^{-96}\right) \land t \leq 1200000000:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c \cdot -1.3333333333333333}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14: 50.8% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+199} \lor \neg \left(y \leq 1.26 \cdot 10^{+141}\right) \land y \leq 2.05 \cdot 10^{+173}:\\ \;\;\;\;0.5 \cdot \frac{x}{a \cdot \left(y \cdot \left(c - b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -1.6e+199) (and (not (<= y 1.26e+141)) (<= y 2.05e+173)))
   (* 0.5 (/ x (* 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 ((y <= -1.6e+199) || (!(y <= 1.26e+141) && (y <= 2.05e+173))) {
		tmp = 0.5 * (x / (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 ((y <= (-1.6d+199)) .or. (.not. (y <= 1.26d+141)) .and. (y <= 2.05d+173)) then
        tmp = 0.5d0 * (x / (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 ((y <= -1.6e+199) || (!(y <= 1.26e+141) && (y <= 2.05e+173))) {
		tmp = 0.5 * (x / (a * (y * (c - b))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -1.6e+199) or (not (y <= 1.26e+141) and (y <= 2.05e+173)):
		tmp = 0.5 * (x / (a * (y * (c - b))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -1.6e+199) || (!(y <= 1.26e+141) && (y <= 2.05e+173)))
		tmp = Float64(0.5 * Float64(x / 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 ((y <= -1.6e+199) || (~((y <= 1.26e+141)) && (y <= 2.05e+173)))
		tmp = 0.5 * (x / (a * (y * (c - b))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -1.6e+199], And[N[Not[LessEqual[y, 1.26e+141]], $MachinePrecision], LessEqual[y, 2.05e+173]]], N[(0.5 * N[(x / N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000003e199 or 1.25999999999999994e141 < y < 2.04999999999999988e173

   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 51.6%

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

   3. Taylor expanded in a around 0 60.8%

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

      1. associate-*r* 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in a around inf 46.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y \cdot \left(a \cdot \left(c - b\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 49.0%

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

      2. *-commutative 49.0%

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

      3. associate-*r* 58.2%

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

      4. *-commutative 58.2%

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

   8. Simplified 58.2%

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

   if -1.60000000000000003e199 < y < 1.25999999999999994e141 or 2.04999999999999988e173 < y

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 63.4%

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

   3. Taylor expanded in a around 0 40.1%

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

   4. Taylor expanded in x around inf 58.9%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+199} \lor \neg \left(y \leq 1.26 \cdot 10^{+141}\right) \land y \leq 2.05 \cdot 10^{+173}:\\ \;\;\;\;0.5 \cdot \frac{x}{a \cdot \left(y \cdot \left(c - b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15: 50.9% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+199} \lor \neg \left(y \leq 1.36 \cdot 10^{+141}\right) \land y \leq 2.9 \cdot 10^{+173}:\\ \;\;\;\;\frac{0.5}{a} \cdot \frac{x}{y \cdot \left(c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -1.6e+199) (and (not (<= y 1.36e+141)) (<= y 2.9e+173)))
   (* (/ 0.5 a) (/ x (* 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 ((y <= -1.6e+199) || (!(y <= 1.36e+141) && (y <= 2.9e+173))) {
		tmp = (0.5 / a) * (x / (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 ((y <= (-1.6d+199)) .or. (.not. (y <= 1.36d+141)) .and. (y <= 2.9d+173)) then
        tmp = (0.5d0 / a) * (x / (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 ((y <= -1.6e+199) || (!(y <= 1.36e+141) && (y <= 2.9e+173))) {
		tmp = (0.5 / a) * (x / (y * (c - b)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -1.6e+199) or (not (y <= 1.36e+141) and (y <= 2.9e+173)):
		tmp = (0.5 / a) * (x / (y * (c - b)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -1.6e+199) || (!(y <= 1.36e+141) && (y <= 2.9e+173)))
		tmp = Float64(Float64(0.5 / a) * Float64(x / 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 ((y <= -1.6e+199) || (~((y <= 1.36e+141)) && (y <= 2.9e+173)))
		tmp = (0.5 / a) * (x / (y * (c - b)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -1.6e+199], And[N[Not[LessEqual[y, 1.36e+141]], $MachinePrecision], LessEqual[y, 2.9e+173]]], N[(N[(0.5 / a), $MachinePrecision] * N[(x / N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000003e199 or 1.36e141 < y < 2.90000000000000007e173

   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 51.6%

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

   3. Taylor expanded in a around 0 60.8%

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

      1. associate-*r* 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in a around inf 46.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y \cdot \left(a \cdot \left(c - b\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 46.2%

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

      2. associate-*r* 49.0%

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

      3. *-commutative 49.0%

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

      4. associate-*r* 58.2%

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

      5. times-frac 65.1%

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

      6. *-commutative 65.1%

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

   8. Simplified 65.1%

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

   if -1.60000000000000003e199 < y < 1.36e141 or 2.90000000000000007e173 < y

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 63.4%

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

   3. Taylor expanded in a around 0 40.1%

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

   4. Taylor expanded in x around inf 58.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+199} \lor \neg \left(y \leq 1.36 \cdot 10^{+141}\right) \land y \leq 2.9 \cdot 10^{+173}:\\ \;\;\;\;\frac{0.5}{a} \cdot \frac{x}{y \cdot \left(c - b\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16: 51.2% 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 96.8%

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

2. Taylor expanded in a around inf 61.9%

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

3. Taylor expanded in a around 0 40.2%

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

4. Taylor expanded in x around inf 54.9%

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

5. Final simplification 54.9%

   \[\leadsto 1 \]

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 2023274 
(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)))))))))))