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

Percentage Accurate: 93.7% → 96.5%

Time: 16.0s

Alternatives: 8

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
    if (t_1 <= 2.0d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * (((0.8333333333333334d0 + a) - (0.6666666666666666d0 / t)) * c)))))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z, t, a, b, c):
	t_1 = 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)))))))))
	tmp = 0
	if t_1 <= 2.0:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * (((0.8333333333333334 + a) - (0.6666666666666666 / t)) * c)))))
	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(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))))))))))
	tmp = 0.0
	if (t_1 <= 2.0)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(0.8333333333333334 + a) - Float64(0.6666666666666666 / t)) * c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	tmp = 0.0;
	if (t_1 <= 2.0)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * (((0.8333333333333334 + a) - (0.6666666666666666 / t)) * c)))));
	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[(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]}, If[LessEqual[t$95$1, 2.0], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(0.8333333333333334 + a), $MachinePrecision] - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 70.6

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

   5. Applied rewrites 70.6%

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

Alternative 2: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \leq 10^{-11}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (-
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))
      1e-11)
   (/ x (+ x (* y (exp (* 2.0 (* c a))))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 1e-11) {
		tmp = x / (x + (y * exp((2.0 * (c * 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 ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))) <= 1d-11) then
        tmp = x / (x + (y * exp((2.0d0 * (c * 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 ((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)))))))))) <= 1e-11) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 1e-11:
		tmp = x / (x + (y * math.exp((2.0 * (c * a)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0)))))))))) <= 1e-11)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * 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 ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 1e-11)
		tmp = x / (x + (y * exp((2.0 * (c * a)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(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], 1e-11], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 9.99999999999999939e-12

   1. Initial program 98.3%

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

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 68.7

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

   5. Applied rewrites 68.7%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 46.8%

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

   if 9.99999999999999939e-12 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 89.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 95.0%

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

Alternative 3: 78.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} \leq 0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot 0.8333333333333334\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (exp
       (*
        2.0
        (-
         (/ (* z (sqrt (+ t a))) t)
         (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
      0.0)
   1.0
   (/ x (+ x (* y (exp (* 2.0 (* (- c b) 0.8333333333333334))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))) <= 0.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * 0.8333333333333334)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0))))))) <= 0.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * 0.8333333333333334d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))) <= 0.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * 0.8333333333333334)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))) <= 0.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * 0.8333333333333334)))))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))) <= 0.0)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * 0.8333333333333334)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], 0.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * 0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))) < 0.0

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if 0.0 < (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))

   1. Initial program 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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sqrt.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 63.5

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

   5. Applied rewrites 63.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 71.3%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 63.8%

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

Alternative 4: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} \leq 0:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(-a\right) \cdot b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (exp
       (*
        2.0
        (-
         (/ (* z (sqrt (+ t a))) t)
         (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
      0.0)
   1.0
   (/ x (+ x (* y (exp (* 2.0 (* (- a) b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))) <= 0.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * (-a * b)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0))))))) <= 0.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * (-a * b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))) <= 0.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (-a * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))))) <= 0.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * (-a * b)))))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], 0.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[((-a) * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))) < 0.0

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if 0.0 < (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))

   1. Initial program 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. Add Preprocessing

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--r+ N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 65.3

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

   5. Applied rewrites 65.3%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 51.7%

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

Alternative 5: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.105:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(\left(0.8333333333333334 + a\right) - \frac{0.6666666666666666}{t}\right) \cdot c\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \mathsf{fma}\left(\sqrt{{t}^{-1}}, z, \left(-\left(b - c\right)\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.25e+66)
   (/ x (+ x (* y (exp (* 2.0 (* (+ 0.8333333333333334 a) (- c b)))))))
   (if (<= t 1.35e-127)
     (/
      x
      (+
       x
       (*
        y
        (exp (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
     (if (<= t 0.105)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (* (- (+ 0.8333333333333334 a) (/ 0.6666666666666666 t)) c))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (fma
             (sqrt (pow t -1.0))
             z
             (* (- (- b c)) (+ 0.8333333333333334 a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.25e+66) {
		tmp = x / (x + (y * exp((2.0 * ((0.8333333333333334 + a) * (c - b))))));
	} else if (t <= 1.35e-127) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 0.105) {
		tmp = x / (x + (y * exp((2.0 * (((0.8333333333333334 + a) - (0.6666666666666666 / t)) * c)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * fma(sqrt(pow(t, -1.0)), z, (-(b - c) * (0.8333333333333334 + a)))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.25e+66)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(0.8333333333333334 + a) * Float64(c - b)))))));
	elseif (t <= 1.35e-127)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(fma(sqrt(a), z, Float64(0.6666666666666666 * Float64(b - c))) / t))))));
	elseif (t <= 0.105)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(0.8333333333333334 + a) - Float64(0.6666666666666666 / t)) * c))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * fma(sqrt((t ^ -1.0)), z, Float64(Float64(-Float64(b - c)) * Float64(0.8333333333333334 + a))))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.25e+66], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(0.8333333333333334 + a), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-127], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[Sqrt[a], $MachinePrecision] * z + N[(0.6666666666666666 * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.105], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(0.8333333333333334 + a), $MachinePrecision] - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[Sqrt[N[Power[t, -1.0], $MachinePrecision]], $MachinePrecision] * z + N[((-N[(b - c), $MachinePrecision]) * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.24999999999999998e66

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sqrt.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 0.0

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

   5. Applied rewrites 0.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 96.2%

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

   if -1.24999999999999998e66 < t < 1.35e-127

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 94.4

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

   5. Applied rewrites 94.4%

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

   if 1.35e-127 < t < 0.104999999999999996

   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. Add Preprocessing

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 76.6

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

   5. Applied rewrites 76.6%

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

   if 0.104999999999999996 < t

   1. Initial program 94.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sqrt.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 99.9

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

   5. Applied rewrites 99.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\mathsf{fma}\left(\sqrt{\frac{1}{t}}, z, \left(-\left(b - c\right)\right) \cdot \left(0.8333333333333334 + a\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.105:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(\left(0.8333333333333334 + a\right) - \frac{0.6666666666666666}{t}\right) \cdot c\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \mathsf{fma}\left(\sqrt{{t}^{-1}}, z, \left(-\left(b - c\right)\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \leq -1 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (*
       2.0
       (-
        (/ (* z (sqrt (+ t a))) t)
        (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))
      -1e+17)
   1.0
   (/ x (+ x (* y (exp (* 2.0 (* (+ 0.8333333333333334 a) (- c b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))) <= -1e+17) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((0.8333333333333334 + a) * (c - b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))) <= (-1d+17)) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * ((0.8333333333333334d0 + a) * (c - b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))) <= -1e+17) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((0.8333333333333334 + a) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))) <= -1e+17:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((0.8333333333333334 + a) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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)))))) <= -1e+17)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(0.8333333333333334 + a) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))) <= -1e+17)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((2.0 * ((0.8333333333333334 + a) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], -1e+17], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(0.8333333333333334 + a), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))) < -1e17

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if -1e17 < (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))

   1. Initial program 89.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sqrt.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 71.5%

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

Alternative 7: 86.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.46:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(\left(0.8333333333333334 + a\right) - \frac{0.6666666666666666}{t}\right) \cdot c\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/ x (+ x (* y (exp (* 2.0 (* (+ 0.8333333333333334 a) (- c b)))))))))
   (if (<= t -1.25e+66)
     t_1
     (if (<= t 1.35e-127)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
       (if (<= t 0.46)
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (* (- (+ 0.8333333333333334 a) (/ 0.6666666666666666 t)) c))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * ((0.8333333333333334 + a) * (c - b))))));
	double tmp;
	if (t <= -1.25e+66) {
		tmp = t_1;
	} else if (t <= 1.35e-127) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 0.46) {
		tmp = x / (x + (y * exp((2.0 * (((0.8333333333333334 + a) - (0.6666666666666666 / t)) * c)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(0.8333333333333334 + a) * Float64(c - b)))))))
	tmp = 0.0
	if (t <= -1.25e+66)
		tmp = t_1;
	elseif (t <= 1.35e-127)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(fma(sqrt(a), z, Float64(0.6666666666666666 * Float64(b - c))) / t))))));
	elseif (t <= 0.46)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(0.8333333333333334 + a) - Float64(0.6666666666666666 / t)) * c))))));
	else
		tmp = t_1;
	end
	return 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[(0.8333333333333334 + a), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+66], t$95$1, If[LessEqual[t, 1.35e-127], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[Sqrt[a], $MachinePrecision] * z + N[(0.6666666666666666 * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.46], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(0.8333333333333334 + a), $MachinePrecision] - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.24999999999999998e66 or 0.46000000000000002 < t

   1. Initial program 94.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-sqrt.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 90.6

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 89.5%

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

   if -1.24999999999999998e66 < t < 1.35e-127

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. fp-cancel-sub-sign-inv N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 94.4

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

   5. Applied rewrites 94.4%

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

   if 1.35e-127 < t < 0.46000000000000002

   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. Add Preprocessing

   3. Taylor expanded in c around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 76.6

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

   5. Applied rewrites 76.6%

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

Alternative 8: 52.2% accurate, 198.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 53.1%

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

Developer Target 1: 95.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024338 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

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

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