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

Percentage Accurate: 93.8% → 97.1%

Time: 10.3s

Alternatives: 11

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 97.1% accurate, 0.5× speedup

Math

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

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 (- (+ c (* (/ 1.0 (sqrt a)) (/ z t))) 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 * ((c + ((1.0 / sqrt(a)) * (z / t))) - 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 * ((c + ((1.0d0 / sqrt(a)) * (z / t))) - 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 * ((c + ((1.0 / Math.sqrt(a)) * (z / t))) - 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 * ((c + ((1.0 / math.sqrt(a)) * (z / t))) - 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(Float64(c + Float64(Float64(1.0 / sqrt(a)) * Float64(z / t))) - 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 * ((c + ((1.0 / sqrt(a)) * (z / t))) - 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 * 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]]]

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 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

   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 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 82.4

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

   5. Applied rewrites 82.4%

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

Alternative 2: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \leq 2 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot 0.8333333333333334\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (-
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))
      2e-31)
   (/ x (+ x (* y (exp (* 2.0 (* c 0.8333333333333334))))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2e-31) {
		tmp = x / (x + (y * exp((2.0 * (c * 0.8333333333333334)))));
	} else {
		tmp = 1.0;
	}
	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) :: 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)))))))))) <= 2d-31) then
        tmp = x / (x + (y * exp((2.0d0 * (c * 0.8333333333333334d0)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2e-31) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * 0.8333333333333334)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2e-31:
		tmp = x / (x + (y * math.exp((2.0 * (c * 0.8333333333333334)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0)))))))))) <= 2e-31)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * 0.8333333333333334))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2e-31)
		tmp = x / (x + (y * exp((2.0 * (c * 0.8333333333333334)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-31], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * 0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 2e-31

   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 61.3

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

   5. Applied rewrites 61.3%

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

   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 60.8

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

   8. Applied rewrites 60.8%

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

   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 54.4%

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

   if 2e-31 < (/.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 90.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 96.8%

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

Alternative 3: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \leq 2 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.8333333333333334 \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (-
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))
      2e-31)
   (/ x (+ x (* y (exp (* 2.0 (* -0.8333333333333334 b))))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2e-31) {
		tmp = x / (x + (y * exp((2.0 * (-0.8333333333333334 * b)))));
	} else {
		tmp = 1.0;
	}
	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) :: 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)))))))))) <= 2d-31) then
        tmp = x / (x + (y * exp((2.0d0 * ((-0.8333333333333334d0) * b)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((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)))))))))) <= 2e-31) {
		tmp = x / (x + (y * Math.exp((2.0 * (-0.8333333333333334 * b)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2e-31:
		tmp = x / (x + (y * math.exp((2.0 * (-0.8333333333333334 * b)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0)))))))))) <= 2e-31)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(-0.8333333333333334 * b))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))) <= 2e-31)
		tmp = x / (x + (y * exp((2.0 * (-0.8333333333333334 * b)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e-31], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(-0.8333333333333334 * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 2e-31

   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 61.3

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

   5. Applied rewrites 61.3%

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

   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 50.7

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

   8. Applied rewrites 50.7%

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

   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 44.4

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

   11. Applied rewrites 44.4%

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

   if 2e-31 < (/.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 90.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 96.8%

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

Alternative 4: 78.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 10^{+303}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \end{array} \end{array} \]

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 -5e+49)
     1.0
     (if (<= t_1 1e+303)
       (/ x (+ x (* y (exp (* 2.0 (* c (+ 0.8333333333333334 a)))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))))))

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 <= -5e+49) {
		tmp = 1.0;
	} else if (t_1 <= 1e+303) {
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + a))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	}
	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 <= -5e+49)
		tmp = 1.0;
	elseif (t_1 <= 1e+303)
		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(fma(sqrt(a), z, Float64(0.6666666666666666 * Float64(b - c))) / t))))));
	end
	return 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, -5e+49], 1.0, If[LessEqual[t$95$1, 1e+303], 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[(N[(N[Sqrt[a], $MachinePrecision] * z + N[(0.6666666666666666 * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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))))))) < -5.0000000000000004e49

   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 -5.0000000000000004e49 < (*.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))))))) < 1e303

   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 82.7

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

   5. Applied rewrites 82.7%

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

   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 72.6

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

   8. Applied rewrites 72.6%

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

   if 1e303 < (*.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 83.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      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 69.8

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

   5. Applied rewrites 69.8%

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

Alternative 5: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+287}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

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 -5e+49)
     1.0
     (if (<= t_1 4e+287)
       (/ 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 <= -5e+49) {
		tmp = 1.0;
	} else if (t_1 <= 4e+287) {
		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 <= (-5d+49)) then
        tmp = 1.0d0
    else if (t_1 <= 4d+287) 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 <= -5e+49) {
		tmp = 1.0;
	} else if (t_1 <= 4e+287) {
		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 <= -5e+49:
		tmp = 1.0
	elif t_1 <= 4e+287:
		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 <= -5e+49)
		tmp = 1.0;
	elseif (t_1 <= 4e+287)
		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 <= -5e+49)
		tmp = 1.0;
	elseif (t_1 <= 4e+287)
		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, -5e+49], 1.0, If[LessEqual[t$95$1, 4e+287], 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))))))) < -5.0000000000000004e49

   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 -5.0000000000000004e49 < (*.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))))))) < 4.0000000000000003e287

   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 85.7

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

   5. Applied rewrites 85.7%

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

   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 73.4

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

   8. Applied rewrites 73.4%

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

   if 4.0000000000000003e287 < (*.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 85.5%

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

   3. Taylor expanded in t around inf

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

      1. 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 39.0

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

   5. Applied rewrites 39.0%

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

   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 67.0

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

   8. Applied rewrites 67.0%

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

Alternative 6: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \leq -4.4 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

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))))))
      -4.4e+56)
   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)))))) <= -4.4e+56) {
		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)))))) <= (-4.4d+56)) 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)))))) <= -4.4e+56) {
		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)))))) <= -4.4e+56:
		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)))))) <= -4.4e+56)
		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)))))) <= -4.4e+56)
		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], -4.4e+56], 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))))))) < -4.40000000000000032e56

   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 -4.40000000000000032e56 < (*.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 93.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 63.8

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

   5. Applied rewrites 63.8%

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

   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 67.7

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

   8. Applied rewrites 67.7%

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

Alternative 7: 91.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(\left(c + \frac{1}{\sqrt{a}} \cdot \frac{z}{t}\right) - b\right)\right)}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \frac{-0.6666666666666666}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{1}{\sqrt{t}} \cdot z - \left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.3e-255)
   (/
    x
    (+ x (* y (exp (* 2.0 (* a (- (+ c (* (/ 1.0 (sqrt a)) (/ z t))) b)))))))
   (if (<= t 8.5e-56)
     (/
      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 <= -3.3e-255) {
		tmp = x / (x + (y * exp((2.0 * (a * ((c + ((1.0 / sqrt(a)) * (z / t))) - b))))));
	} else if (t <= 8.5e-56) {
		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;
}

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 (t <= (-3.3d-255)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * ((c + ((1.0d0 / sqrt(a)) * (z / t))) - b))))))
    else if (t <= 8.5d-56) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((-0.6666666666666666d0) / t)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (((1.0d0 / sqrt(t)) * z) - ((0.8333333333333334d0 + a) * (b - c)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.3e-255) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * ((c + ((1.0 / Math.sqrt(a)) * (z / t))) - b))))));
	} else if (t <= 8.5e-56) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * (-0.6666666666666666 / t)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (((1.0 / Math.sqrt(t)) * z) - ((0.8333333333333334 + a) * (b - c)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.3e-255:
		tmp = x / (x + (y * math.exp((2.0 * (a * ((c + ((1.0 / math.sqrt(a)) * (z / t))) - b))))))
	elif t <= 8.5e-56:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * (-0.6666666666666666 / t)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (((1.0 / math.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 <= -3.3e-255)
		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 <= 8.5e-56)
		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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.3e-255)
		tmp = x / (x + (y * exp((2.0 * (a * ((c + ((1.0 / sqrt(a)) * (z / t))) - b))))));
	elseif (t <= 8.5e-56)
		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)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.3e-255], 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, 8.5e-56], 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 3 regimes

2. if t < -3.29999999999999988e-255

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(\left(c + \sqrt{\frac{1}{a}} \cdot \frac{z}{t}\right) - b\right)\right)}}} \]
   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 98.1

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

   5. Applied rewrites 98.1%

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

   if -3.29999999999999988e-255 < t < 8.49999999999999932e-56

   1. Initial program 93.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. 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 88.4

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

   5. Applied rewrites 88.4%

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

   if 8.49999999999999932e-56 < t

   1. Initial program 98.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. 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 97.7

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

   5. Applied rewrites 97.7%

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

Alternative 8: 90.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(\left(c + \frac{1}{\sqrt{a}} \cdot \frac{z}{t}\right) - b\right)\right)}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{1}{\sqrt{t}} \cdot z - \left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.15e-107)
   (/
    x
    (+ x (* y (exp (* 2.0 (* a (- (+ c (* (/ 1.0 (sqrt a)) (/ z t))) b)))))))
   (if (<= t 9.2e-158)
     (/
      x
      (+
       x
       (*
        y
        (exp (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
     (if (<= t 4e-56)
       (/
        x
        (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) 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 <= -1.15e-107) {
		tmp = x / (x + (y * exp((2.0 * (a * ((c + ((1.0 / sqrt(a)) * (z / t))) - b))))));
	} else if (t <= 9.2e-158) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 4e-56) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / 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 <= -1.15e-107)
		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 <= 9.2e-158)
		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 <= 4e-56)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / 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, -1.15e-107], 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, 9.2e-158], 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, 4e-56], 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] * 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 < -1.15000000000000002e-107

   1. Initial program 93.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. 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 96.9

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

   5. Applied rewrites 96.9%

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

   if -1.15000000000000002e-107 < t < 9.1999999999999995e-158

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      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 89.6

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

   5. Applied rewrites 89.6%

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

   if 9.1999999999999995e-158 < t < 4.0000000000000002e-56

   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 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 85.7%

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

   if 4.0000000000000002e-56 < t

   1. Initial program 98.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. 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 97.7

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

   5. Applied rewrites 97.7%

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

Alternative 9: 89.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{1}{\sqrt{t}} \cdot z - \left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1e-63)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 9.2e-158)
     (/
      x
      (+
       x
       (*
        y
        (exp (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
     (if (<= t 4e-56)
       (/
        x
        (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) 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 <= -1e-63) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 9.2e-158) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 4e-56) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / 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 <= -1e-63)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 9.2e-158)
		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 <= 4e-56)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / 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, -1e-63], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-158], 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, 4e-56], 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] * 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 < -1.00000000000000007e-63

   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 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 0.0

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

   5. Applied rewrites 0.0%

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

   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 95.8

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

   8. Applied rewrites 95.8%

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

   if -1.00000000000000007e-63 < t < 9.1999999999999995e-158

   1. Initial program 91.7%

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

   3. Taylor expanded in t around 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 89.4

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

   5. Applied rewrites 89.4%

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

   if 9.1999999999999995e-158 < t < 4.0000000000000002e-56

   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 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 85.7%

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

   if 4.0000000000000002e-56 < t

   1. Initial program 98.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. 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 97.7

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

   5. Applied rewrites 97.7%

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

Alternative 10: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\mathsf{fma}\left(\sqrt{a}, z, 0.6666666666666666 \cdot \left(b - c\right)\right)}{t}}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{1}{\sqrt{t}} \cdot z - \left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1e-63)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 6.5e-182)
     (/
      x
      (+
       x
       (*
        y
        (exp (* 2.0 (/ (fma (sqrt a) z (* 0.6666666666666666 (- b c))) t))))))
     (if (<= t 7e-58)
       (/ x (+ x (* y (exp (* 2.0 (* (/ z t) (sqrt (+ a 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 <= -1e-63) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 6.5e-182) {
		tmp = x / (x + (y * exp((2.0 * (fma(sqrt(a), z, (0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 7e-58) {
		tmp = x / (x + (y * exp((2.0 * ((z / t) * sqrt((a + 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 <= -1e-63)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 6.5e-182)
		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 <= 7e-58)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z / t) * sqrt(Float64(a + 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, -1e-63], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-182], 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, 7e-58], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z / t), $MachinePrecision] * N[Sqrt[N[(a + 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 < -1.00000000000000007e-63

   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 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 0.0

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

   5. Applied rewrites 0.0%

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

   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 95.8

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

   8. Applied rewrites 95.8%

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

   if -1.00000000000000007e-63 < t < 6.49999999999999997e-182

   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 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 93.0

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

   5. Applied rewrites 93.0%

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

   if 6.49999999999999997e-182 < t < 6.9999999999999998e-58

   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 z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-sqrt.f64 N/A

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

      4. lower-+.f64 79.2

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

   5. Applied rewrites 79.2%

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

   if 6.9999999999999998e-58 < t

   1. Initial program 98.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. 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 97.0

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

   5. Applied rewrites 97.0%

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

Alternative 11: 51.1% 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 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 x around inf

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

5. Applied rewrites 47.4%

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

Developer Target 1: 95.6% 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 2025032 
(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)))))))))))