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

Percentage Accurate: 94.2% → 96.9%

Time: 11.4s

Alternatives: 13

Speedup: 1.0×

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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: 94.2% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \leq 2:\\ \;\;\;\;\frac{x}{x \cdot \left(1 + \frac{y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot {t}^{-1}\right)\right)}}{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(-b\right)\right)}}\\ \end{array} \end{array} \]

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))))))))))
      2.0)
   (/
    x
    (*
     x
     (+
      1.0
      (/
       (*
        y
        (pow
         (exp 2.0)
         (-
          (* (/ z t) (sqrt (+ a t)))
          (*
           (- b c)
           (- (+ 0.8333333333333334 a) (* 0.6666666666666666 (pow t -1.0)))))))
       x))))
   (/ 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 ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2.0) {
		tmp = x / (x * (1.0 + ((y * pow(exp(2.0), (((z / t) * sqrt((a + t))) - ((b - c) * ((0.8333333333333334 + a) - (0.6666666666666666 * pow(t, -1.0))))))) / x)));
	} else {
		tmp = x / (x + (y * exp((2.0 * (a * -b)))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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)))))))))) <= 2.0d0) then
        tmp = x / (x * (1.0d0 + ((y * (exp(2.0d0) ** (((z / t) * sqrt((a + t))) - ((b - c) * ((0.8333333333333334d0 + a) - (0.6666666666666666d0 * (t ** (-1.0d0)))))))) / x)))
    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 ((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)))))))))) <= 2.0) {
		tmp = x / (x * (1.0 + ((y * Math.pow(Math.exp(2.0), (((z / t) * Math.sqrt((a + t))) - ((b - c) * ((0.8333333333333334 + a) - (0.6666666666666666 * Math.pow(t, -1.0))))))) / x)));
	} 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 (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)))))))))) <= 2.0:
		tmp = x / (x * (1.0 + ((y * math.pow(math.exp(2.0), (((z / t) * math.sqrt((a + t))) - ((b - c) * ((0.8333333333333334 + a) - (0.6666666666666666 * math.pow(t, -1.0))))))) / x)))
	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 (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)))))))))) <= 2.0)
		tmp = Float64(x / Float64(x * Float64(1.0 + Float64(Float64(y * (exp(2.0) ^ Float64(Float64(Float64(z / t) * sqrt(Float64(a + t))) - Float64(Float64(b - c) * Float64(Float64(0.8333333333333334 + a) - Float64(0.6666666666666666 * (t ^ -1.0))))))) / x))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(-b)))))));
	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)))))))))) <= 2.0)
		tmp = x / (x * (1.0 + ((y * (exp(2.0) ^ (((z / t) * sqrt((a + t))) - ((b - c) * ((0.8333333333333334 + a) - (0.6666666666666666 * (t ^ -1.0))))))) / x)));
	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[(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], 2.0], N[(x / N[(x * N[(1.0 + N[(N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] * N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(0.8333333333333334 + a), $MachinePrecision] - N[(0.6666666666666666 * N[Power[t, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.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 99.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   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 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 77.6

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

   8. Applied rewrites 77.6%

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

   9. Taylor expanded in b around inf

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

       1. lower-*.f64 85.2

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

   11. Applied rewrites 85.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \leq 2:\\ \;\;\;\;\frac{x}{x \cdot \left(1 + \frac{y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot {t}^{-1}\right)\right)}}{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(-b\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (-
               (/ (* z (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 (* 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((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 * (a * -b)))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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 * (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((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 * (a * -b)))));
	}
	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 * (a * -b)))))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (((z * 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 * (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[(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[(a * (-b)), $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 99.6%

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

   if 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 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 77.6

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

   8. Applied rewrites 77.6%

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

   9. Taylor expanded in b around inf

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

       1. lower-*.f64 85.2

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

   11. Applied rewrites 85.2%

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

4. Final simplification 98.9%

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

Alternative 3: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(-b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (*
          2.0
          (-
           (/ (* z (sqrt (+ t a))) t)
           (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))
   (if (<= t_1 -4e+62)
     1.0
     (if (<= t_1 5e+301)
       (/ x (+ x (* y (exp (* 2.0 (* c (+ 0.8333333333333334 a)))))))
       (/ x (+ x (* y (exp (* 2.0 (* (- b) (+ 0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))));
	double tmp;
	if (t_1 <= -4e+62) {
		tmp = 1.0;
	} else if (t_1 <= 5e+301) {
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + a))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (-b * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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 = 2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))
    if (t_1 <= (-4d+62)) then
        tmp = 1.0d0
    else if (t_1 <= 5d+301) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (0.8333333333333334d0 + a))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (-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 t_1 = 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 <= -4e+62) {
		tmp = 1.0;
	} else if (t_1 <= 5e+301) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (0.8333333333333334 + a))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (-b * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 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 <= -4e+62:
		tmp = 1.0
	elif t_1 <= 5e+301:
		tmp = x / (x + (y * math.exp((2.0 * (c * (0.8333333333333334 + a))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (-b * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = 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 <= -4e+62)
		tmp = 1.0;
	elseif (t_1 <= 5e+301)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(0.8333333333333334 + a)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(-b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 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 <= -4e+62)
		tmp = 1.0;
	elseif (t_1 <= 5e+301)
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + a))))));
	else
		tmp = x / (x + (y * exp((2.0 * (-b * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -4e+62], 1.0, If[LessEqual[t$95$1, 5e+301], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[((-b) * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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))))))) < -4.00000000000000014e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   if -4.00000000000000014e62 < (*.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))))))) < 5.0000000000000004e301

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in c around inf

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

      1. metadata-eval N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. metadata-eval 59.8

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

   8. Applied rewrites 59.8%

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

   if 5.0000000000000004e301 < (*.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 80.0%

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

   3. Taylor expanded in t around inf

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

      1. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 49.3

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

   5. Applied rewrites 49.3%

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

   6. Taylor expanded in b around inf

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

      1. metadata-eval N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. metadata-eval 62.7

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

   8. Applied rewrites 62.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \leq -4 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(-b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (*
          2.0
          (-
           (/ (* z (sqrt (+ t a))) t)
           (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))
   (if (<= t_1 -4e+62)
     1.0
     (if (<= t_1 5e+301)
       (/ x (+ x (* y (exp (* 2.0 (* c (+ 0.8333333333333334 a)))))))
       (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))));
	double tmp;
	if (t_1 <= -4e+62) {
		tmp = 1.0;
	} else if (t_1 <= 5e+301) {
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + a))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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 = 2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))
    if (t_1 <= (-4d+62)) then
        tmp = 1.0d0
    else if (t_1 <= 5d+301) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (0.8333333333333334d0 + a))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (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 t_1 = 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 <= -4e+62) {
		tmp = 1.0;
	} else if (t_1 <= 5e+301) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (0.8333333333333334 + a))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 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 <= -4e+62:
		tmp = 1.0
	elif t_1 <= 5e+301:
		tmp = x / (x + (y * math.exp((2.0 * (c * (0.8333333333333334 + a))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = 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 <= -4e+62)
		tmp = 1.0;
	elseif (t_1 <= 5e+301)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(0.8333333333333334 + a)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 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 <= -4e+62)
		tmp = 1.0;
	elseif (t_1 <= 5e+301)
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + a))))));
	else
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -4e+62], 1.0, If[LessEqual[t$95$1, 5e+301], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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))))))) < -4.00000000000000014e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   if -4.00000000000000014e62 < (*.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))))))) < 5.0000000000000004e301

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in c around inf

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

      1. metadata-eval N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. metadata-eval 59.8

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

   8. Applied rewrites 59.8%

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

   if 5.0000000000000004e301 < (*.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 80.0%

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

   3. Taylor expanded in t around inf

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

      1. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 49.3

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

   5. Applied rewrites 49.3%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 62.7

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

   8. Applied rewrites 62.7%

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

Alternative 5: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+62}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot 0.8333333333333334\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.8333333333333334 \cdot b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (*
          2.0
          (-
           (/ (* z (sqrt (+ t a))) t)
           (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))
   (if (<= t_1 -4e+62)
     1.0
     (if (<= t_1 5e+301)
       (/ x (+ x (* y (exp (* 2.0 (* c 0.8333333333333334))))))
       (/ x (+ x (* y (exp (* 2.0 (* -0.8333333333333334 b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))));
	double tmp;
	if (t_1 <= -4e+62) {
		tmp = 1.0;
	} else if (t_1 <= 5e+301) {
		tmp = x / (x + (y * exp((2.0 * (c * 0.8333333333333334)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (-0.8333333333333334 * b)))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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 = 2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))
    if (t_1 <= (-4d+62)) then
        tmp = 1.0d0
    else if (t_1 <= 5d+301) then
        tmp = x / (x + (y * exp((2.0d0 * (c * 0.8333333333333334d0)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((-0.8333333333333334d0) * 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 = 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 <= -4e+62) {
		tmp = 1.0;
	} else if (t_1 <= 5e+301) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * 0.8333333333333334)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (-0.8333333333333334 * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 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 <= -4e+62:
		tmp = 1.0
	elif t_1 <= 5e+301:
		tmp = x / (x + (y * math.exp((2.0 * (c * 0.8333333333333334)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (-0.8333333333333334 * b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = 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 <= -4e+62)
		tmp = 1.0;
	elseif (t_1 <= 5e+301)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * 0.8333333333333334))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(-0.8333333333333334 * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 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 <= -4e+62)
		tmp = 1.0;
	elseif (t_1 <= 5e+301)
		tmp = x / (x + (y * exp((2.0 * (c * 0.8333333333333334)))));
	else
		tmp = x / (x + (y * exp((2.0 * (-0.8333333333333334 * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -4e+62], 1.0, If[LessEqual[t$95$1, 5e+301], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * 0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(-0.8333333333333334 * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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))))))) < -4.00000000000000014e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   if -4.00000000000000014e62 < (*.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))))))) < 5.0000000000000004e301

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in c around inf

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

      1. metadata-eval N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. metadata-eval 59.8

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

   8. Applied rewrites 59.8%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 46.7%

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

   if 5.0000000000000004e301 < (*.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 80.0%

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

   3. Taylor expanded in t around inf

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

      1. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 49.3

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

   5. Applied rewrites 49.3%

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

   6. Taylor expanded in b around inf

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

      1. metadata-eval N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. metadata-eval 62.7

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

   8. Applied rewrites 62.7%

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

   9. Taylor expanded in a around 0

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

       1. lower-*.f64 49.1

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

   11. Applied rewrites 49.1%

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

Alternative 6: 78.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \leq -4 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

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))))))
      -4e+16)
   1.0
   (/ x (+ x (* y (exp (* 2.0 (* 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)))))) <= -4e+16) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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)))))) <= (-4d+16)) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * (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)))))) <= -4e+16) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (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)))))) <= -4e+16:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * (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)))))) <= -4e+16)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(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)))))) <= -4e+16)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((2.0 * (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], -4e+16], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * 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))))))) < -4e16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   if -4e16 < (*.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 90.1%

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

   3. Taylor expanded in t around 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 56.3

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

   8. Applied rewrites 56.3%

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

Alternative 7: 70.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \leq -4 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.8333333333333334 \cdot b\right)}}\\ \end{array} \end{array} \]

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))))))
      -4e+16)
   1.0
   (/ x (+ x (* y (exp (* 2.0 (* -0.8333333333333334 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)))))) <= -4e+16) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * (-0.8333333333333334 * b)))));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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)))))) <= (-4d+16)) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * ((-0.8333333333333334d0) * 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)))))) <= -4e+16) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (-0.8333333333333334 * 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)))))) <= -4e+16:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * (-0.8333333333333334 * 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)))))) <= -4e+16)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(-0.8333333333333334 * 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)))))) <= -4e+16)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((2.0 * (-0.8333333333333334 * 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], -4e+16], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(-0.8333333333333334 * b), $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))))))) < -4e16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   if -4e16 < (*.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 90.1%

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

   3. Taylor expanded in t around 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in b around inf

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

      1. metadata-eval N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. metadata-eval 56.2

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

   8. Applied rewrites 56.2%

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

   9. Taylor expanded in a around 0

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

       1. lower-*.f64 42.6

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

   11. Applied rewrites 42.6%

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

Alternative 8: 94.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(\left(c + \frac{1}{\sqrt{a}} \cdot \frac{z}{t}\right) - b\right)\right)}}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.0004:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \frac{-0.6666666666666666}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{1}{\sqrt{t}} \cdot z - \left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -5.7e-20)
   (/
    x
    (+ x (* y (exp (* 2.0 (* a (- (+ c (* (/ 1.0 (sqrt a)) (/ z t))) b)))))))
   (if (<= t 9e-229)
     (/
      x
      (+
       x
       (*
        y
        (exp (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
     (if (<= t 0.0004)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (/ (* z (sqrt (+ t a))) t)
             (* (- b c) (/ -0.6666666666666666 t))))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (* (/ 1.0 (sqrt t)) z)
             (* (+ 0.8333333333333334 a) (- b c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -5.7e-20) {
		tmp = x / (x + (y * exp((2.0 * (a * ((c + ((1.0 / sqrt(a)) * (z / t))) - b))))));
	} else if (t <= 9e-229) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 0.0004) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * (-0.6666666666666666 / t)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((1.0 / sqrt(t)) * z) - ((0.8333333333333334 + a) * (b - c)))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -5.7e-20)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(Float64(c + Float64(Float64(1.0 / sqrt(a)) * Float64(z / t))) - b)))))));
	elseif (t <= 9e-229)
		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 <= 0.0004)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(-0.6666666666666666 / t))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(1.0 / sqrt(t)) * z) - Float64(Float64(0.8333333333333334 + a) * Float64(b - c))))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -5.7e-20], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(N[(c + N[(N[(1.0 / N[Sqrt[a], $MachinePrecision]), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-229], 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, 0.0004], 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[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(1.0 / N[Sqrt[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[(N[(0.8333333333333334 + a), $MachinePrecision] * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.70000000000000024e-20

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sqrt-div N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -5.70000000000000024e-20 < t < 9.0000000000000004e-229

   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. 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

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

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

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 98.4

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

   5. Applied rewrites 98.4%

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

   if 9.0000000000000004e-229 < t < 4.00000000000000019e-4

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 80.1

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

   5. Applied rewrites 80.1%

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

   if 4.00000000000000019e-4 < 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. 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 9: 91.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(\left(c + \frac{1}{\sqrt{a}} \cdot \frac{z}{t}\right) - b\right)\right)}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-205}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.1:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t}}{t} - \left(b - c\right) \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{1}{\sqrt{t}} \cdot z - \left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -5.7e-20)
   (/
    x
    (+ x (* y (exp (* 2.0 (* a (- (+ c (* (/ 1.0 (sqrt a)) (/ z t))) b)))))))
   (if (<= t 3.5e-205)
     (/
      x
      (+
       x
       (*
        y
        (exp (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
     (if (<= t 0.1)
       (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt t)) t) (* (- b c) a)))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (* (/ 1.0 (sqrt t)) z)
             (* (+ 0.8333333333333334 a) (- b c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -5.7e-20) {
		tmp = x / (x + (y * exp((2.0 * (a * ((c + ((1.0 / sqrt(a)) * (z / t))) - b))))));
	} else if (t <= 3.5e-205) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 0.1) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(t)) / t) - ((b - c) * a))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((1.0 / sqrt(t)) * z) - ((0.8333333333333334 + a) * (b - c)))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -5.7e-20)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(Float64(c + Float64(Float64(1.0 / sqrt(a)) * Float64(z / t))) - b)))))));
	elseif (t <= 3.5e-205)
		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 <= 0.1)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(t)) / t) - Float64(Float64(b - c) * a)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(1.0 / sqrt(t)) * z) - Float64(Float64(0.8333333333333334 + a) * Float64(b - c))))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -5.7e-20], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(N[(c + N[(N[(1.0 / N[Sqrt[a], $MachinePrecision]), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-205], 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, 0.1], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[t], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(1.0 / N[Sqrt[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[(N[(0.8333333333333334 + a), $MachinePrecision] * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.70000000000000024e-20

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sqrt-div N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -5.70000000000000024e-20 < t < 3.5e-205

   1. Initial program 91.3%

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

   3. Taylor expanded in 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

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

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

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 93.8

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

   5. Applied rewrites 93.8%

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

   if 3.5e-205 < t < 0.10000000000000001

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 71.5%

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

   if 0.10000000000000001 < 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. 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 10: 91.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - c\right) \cdot a\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{a}}{t} - t\_1\right)}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-205}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.1:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t}}{t} - t\_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{1}{\sqrt{t}} \cdot z - \left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (- b c) a)))
   (if (<= t -5.8e-20)
     (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt a)) t) t_1))))))
     (if (<= t 3.5e-205)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
       (if (<= t 0.1)
         (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt t)) t) t_1))))))
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (-
               (* (/ 1.0 (sqrt t)) z)
               (* (+ 0.8333333333333334 a) (- b c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b - c) * a;
	double tmp;
	if (t <= -5.8e-20) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) / t) - t_1)))));
	} else if (t <= 3.5e-205) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 0.1) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(t)) / t) - t_1)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((1.0 / sqrt(t)) * z) - ((0.8333333333333334 + a) * (b - c)))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b - c) * a)
	tmp = 0.0
	if (t <= -5.8e-20)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) / t) - t_1))))));
	elseif (t <= 3.5e-205)
		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 <= 0.1)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(t)) / t) - t_1))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(1.0 / sqrt(t)) * z) - Float64(Float64(0.8333333333333334 + a) * Float64(b - c))))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b - c), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, -5.8e-20], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-205], 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, 0.1], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[t], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(1.0 / N[Sqrt[t], $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[(N[(0.8333333333333334 + a), $MachinePrecision] * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.8e-20

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 94.1%

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

   if -5.8e-20 < t < 3.5e-205

   1. Initial program 91.3%

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

   3. Taylor expanded in 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

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

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

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 93.8

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

   5. Applied rewrites 93.8%

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

   if 3.5e-205 < t < 0.10000000000000001

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 71.5%

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

   if 0.10000000000000001 < 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. 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 11: 75.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -0.84:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot 0.8333333333333334\right)}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= a -0.84)
     t_1
     (if (<= a 5.3e-303)
       (/ x (+ x (* y (exp (* 2.0 (* c 0.8333333333333334))))))
       (if (<= a 1.4e+134)
         (/
          x
          (+
           x
           (*
            y
            (exp
             (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
         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 (a <= -0.84) {
		tmp = t_1;
	} else if (a <= 5.3e-303) {
		tmp = x / (x + (y * exp((2.0 * (c * 0.8333333333333334)))));
	} else if (a <= 1.4e+134) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} 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 (a <= -0.84)
		tmp = t_1;
	elseif (a <= 5.3e-303)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * 0.8333333333333334))))));
	elseif (a <= 1.4e+134)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(fma(sqrt(a), z, Float64(0.6666666666666666 * Float64(b - c))) / t))))));
	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[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.84], t$95$1, If[LessEqual[a, 5.3e-303], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * 0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+134], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.839999999999999969 or 1.3999999999999999e134 < a

   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. 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 91.6

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

   8. Applied rewrites 91.6%

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

   if -0.839999999999999969 < a < 5.2999999999999999e-303

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. sqrt-div N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in c around inf

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

      1. metadata-eval N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. metadata-eval 64.2

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

   8. Applied rewrites 64.2%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 64.2%

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

   if 5.2999999999999999e-303 < a < 1.3999999999999999e134

   1. Initial program 95.7%

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

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

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

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 80.9

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

   5. Applied rewrites 80.9%

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

Alternative 12: 81.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - c\right) \cdot a\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{a}}{t} - t\_1\right)}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-205}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t}}{t} - t\_1\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (- b c) a)))
   (if (<= t -5.8e-20)
     (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt a)) t) t_1))))))
     (if (<= t 3.5e-205)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
       (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt t)) t) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b - c) * a;
	double tmp;
	if (t <= -5.8e-20) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) / t) - t_1)))));
	} else if (t <= 3.5e-205) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(t)) / t) - t_1)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b - c) * a)
	tmp = 0.0
	if (t <= -5.8e-20)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) / t) - t_1))))));
	elseif (t <= 3.5e-205)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(fma(sqrt(a), z, Float64(0.6666666666666666 * Float64(b - c))) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(t)) / t) - t_1))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b - c), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[t, -5.8e-20], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-205], 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], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[t], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8e-20

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 94.1%

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

   if -5.8e-20 < t < 3.5e-205

   1. Initial program 91.3%

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

   3. Taylor expanded in 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

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

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

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-sqrt.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 93.8

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

   5. Applied rewrites 93.8%

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

   if 3.5e-205 < t

   1. Initial program 96.2%

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

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.2%

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

Alternative 13: 52.1% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 50.5%

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    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 2025038 
(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)))))))))))