Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D

Percentage Accurate: 58.1% → 97.0%

Time: 12.4s

Alternatives: 11

Speedup: 8.8×

Specification

Math

\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+
 x
 (/
  (*
   y
   (+
    (*
     (+
      (*
       (+
        (*
         (+ (* z 313060547623/100000000000) 55833770631/5000000000)
         z)
        t)
       z)
      a)
     z)
    b))
  (+
   (*
    (+
     (*
      (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000)
      z)
     119400905721/10000000000)
    z)
   607771387771/1000000000000))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

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)
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
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

Python

def code(x, y, z, t, a, b):
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 313060547623/100000000000), $MachinePrecision] + 55833770631/5000000000), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15234687407/1000000000), $MachinePrecision] * z), $MachinePrecision] + 314690115749/10000000000), $MachinePrecision] * z), $MachinePrecision] + 119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision] + 607771387771/1000000000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.1% accurate, 1.0× speedup

Math

\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+
 x
 (/
  (*
   y
   (+
    (*
     (+
      (*
       (+
        (*
         (+ (* z 313060547623/100000000000) 55833770631/5000000000)
         z)
        t)
       z)
      a)
     z)
    b))
  (+
   (*
    (+
     (*
      (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000)
      z)
     119400905721/10000000000)
    z)
   607771387771/1000000000000))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

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)
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
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

Python

def code(x, y, z, t, a, b):
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 313060547623/100000000000), $MachinePrecision] + 55833770631/5000000000), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15234687407/1000000000), $MachinePrecision] * z), $MachinePrecision] + 314690115749/10000000000), $MachinePrecision] * z), $MachinePrecision] + 119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision] + 607771387771/1000000000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq -5800000000000000039436163143757201408:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1000000000000000043845843045076197354634047651840:\\ \;\;\;\;x + \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\frac{-607771387771}{1000000000000} - \left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z}\right), \left(t \cdot z + a\right), \left(z \cdot y\right), \left(-y\right), b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -5800000000000000039436163143757201408)
    t_1
    (if (<= z 1000000000000000043845843045076197354634047651840)
      (+
       x
       (134-z0z1z2z3z4
        (/
         -1
         (-
          -607771387771/1000000000000
          (*
           (-
            (*
             (-
              (* (- z -15234687407/1000000000) z)
              -314690115749/10000000000)
             z)
            -119400905721/10000000000)
           z)))
        (+ (* t z) a)
        (* z y)
        (- y)
        b))
      t_1))))

Derivation

1. Split input into 2 regimes

2. if z < -5.8e36 or 1e48 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -5.8e36 < z < 1e48

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   6. Applied rewrites 69.5%

      \[\leadsto x + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\frac{-607771387771}{1000000000000} - \left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z}\right), \left(t \cdot z + a\right), \left(z \cdot y\right), \left(-y\right), b\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \leq \infty:\\ \;\;\;\;x + \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}}\right), \left(\left(\left(\frac{-313060547623}{100000000000} \cdot z - \frac{55833770631}{5000000000}\right) \cdot z - t\right) \cdot z - a\right), \left(z \cdot y\right), y, b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{313060547623}{100000000000} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<=
     (+
      x
      (/
       (*
        y
        (+
         (*
          (+
           (*
            (+
             (*
              (+
               (* z 313060547623/100000000000)
               55833770631/5000000000)
              z)
             t)
            z)
           a)
          z)
         b))
       (+
        (*
         (+
          (*
           (+
            (* (+ z 15234687407/1000000000) z)
            314690115749/10000000000)
           z)
          119400905721/10000000000)
         z)
        607771387771/1000000000000)))
     INFINITY)
  (+
   x
   (134-z0z1z2z3z4
    (/
     -1
     (-
      (*
       (-
        (*
         (-
          (* (- z -15234687407/1000000000) z)
          -314690115749/10000000000)
         z)
        -119400905721/10000000000)
       z)
      -607771387771/1000000000000))
    (-
     (*
      (-
       (*
        (- (* -313060547623/100000000000 z) 55833770631/5000000000)
        z)
       t)
      z)
     a)
    (* z y)
    y
    b))
  (+ x (* 313060547623/100000000000 y))))

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))) < +inf.0

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   3. Applied rewrites 61.9%

      \[\leadsto x + \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{-1}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}}\right), \left(\left(\left(\frac{-313060547623}{100000000000} \cdot z - \frac{55833770631}{5000000000}\right) \cdot z - t\right) \cdot z - a\right), \left(z \cdot y\right), y, b\right)} \]

   if +inf.0 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))))

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq -5800000000000000039436163143757201408:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1000000000000000043845843045076197354634047651840:\\ \;\;\;\;x + \left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \left(y \cdot \frac{-1}{\frac{-607771387771}{1000000000000} - \left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -5800000000000000039436163143757201408)
    t_1
    (if (<= z 1000000000000000043845843045076197354634047651840)
      (+
       x
       (*
        (+ (* (+ (* t z) a) z) b)
        (*
         y
         (/
          -1
          (-
           -607771387771/1000000000000
           (*
            (-
             (*
              (-
               (* (- z -15234687407/1000000000) z)
               -314690115749/10000000000)
              z)
             -119400905721/10000000000)
            z))))))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1e+48) {
		tmp = x + (((((t * z) + a) * z) + b) * (y * (-1.0 / (-0.607771387771 - ((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z)))));
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-5.8d+36)) then
        tmp = t_1
    else if (z <= 1d+48) then
        tmp = x + (((((t * z) + a) * z) + b) * (y * ((-1.0d0) / ((-0.607771387771d0) - ((((((z - (-15.234687407d0)) * z) - (-31.4690115749d0)) * z) - (-11.9400905721d0)) * z)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1e+48) {
		tmp = x + (((((t * z) + a) * z) + b) * (y * (-1.0 / (-0.607771387771 - ((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -5.8e+36:
		tmp = t_1
	elif z <= 1e+48:
		tmp = x + (((((t * z) + a) * z) + b) * (y * (-1.0 / (-0.607771387771 - ((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1e+48)
		tmp = Float64(x + Float64(Float64(Float64(Float64(Float64(t * z) + a) * z) + b) * Float64(y * Float64(-1.0 / Float64(-0.607771387771 - Float64(Float64(Float64(Float64(Float64(Float64(z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1e+48)
		tmp = x + (((((t * z) + a) * z) + b) * (y * (-1.0 / (-0.607771387771 - ((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5800000000000000039436163143757201408], t$95$1, If[LessEqual[z, 1000000000000000043845843045076197354634047651840], N[(x + N[(N[(N[(N[(N[(t * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision] * N[(y * N[(-1 / N[(-607771387771/1000000000000 - N[(N[(N[(N[(N[(N[(z - -15234687407/1000000000), $MachinePrecision] * z), $MachinePrecision] - -314690115749/10000000000), $MachinePrecision] * z), $MachinePrecision] - -119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e36 or 1e48 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -5.8e36 < z < 1e48

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. mult-flip N/A

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)\right) \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      3. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)\right)} \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\left(\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot y\right)} \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. associate-*l* N/A

         \[\leadsto x + \color{blue}{\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto x + \left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \color{blue}{\left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)} \]

      8. frac-2neg N/A

         \[\leadsto x + \left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \left(y \cdot \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}\right)\right)}}\right) \]

   6. Applied rewrites 63.1%

      \[\leadsto x + \color{blue}{\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \left(y \cdot \frac{-1}{\frac{-607771387771}{1000000000000} - \left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq -5800000000000000039436163143757201408:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1000000000000000043845843045076197354634047651840:\\ \;\;\;\;\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \frac{y}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -5800000000000000039436163143757201408)
    t_1
    (if (<= z 1000000000000000043845843045076197354634047651840)
      (+
       (*
        (+ (* (+ (* t z) a) z) b)
        (/
         y
         (-
          (*
           (-
            (*
             (-
              (* (- z -15234687407/1000000000) z)
              -314690115749/10000000000)
             z)
            -119400905721/10000000000)
           z)
          -607771387771/1000000000000)))
       x)
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1e+48) {
		tmp = (((((t * z) + a) * z) + b) * (y / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771))) + x;
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-5.8d+36)) then
        tmp = t_1
    else if (z <= 1d+48) then
        tmp = (((((t * z) + a) * z) + b) * (y / (((((((z - (-15.234687407d0)) * z) - (-31.4690115749d0)) * z) - (-11.9400905721d0)) * z) - (-0.607771387771d0)))) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1e+48) {
		tmp = (((((t * z) + a) * z) + b) * (y / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -5.8e+36:
		tmp = t_1
	elif z <= 1e+48:
		tmp = (((((t * z) + a) * z) + b) * (y / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771))) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1e+48)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(t * z) + a) * z) + b) * Float64(y / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771))) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1e+48)
		tmp = (((((t * z) + a) * z) + b) * (y / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771))) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5800000000000000039436163143757201408], t$95$1, If[LessEqual[z, 1000000000000000043845843045076197354634047651840], N[(N[(N[(N[(N[(N[(t * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(N[(N[(N[(N[(N[(N[(z - -15234687407/1000000000), $MachinePrecision] * z), $MachinePrecision] - -314690115749/10000000000), $MachinePrecision] * z), $MachinePrecision] - -119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision] - -607771387771/1000000000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e36 or 1e48 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -5.8e36 < z < 1e48

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x} \]

      3. lower-+.f64 61.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x} \]

   6. Applied rewrites 63.1%

      \[\leadsto \color{blue}{\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \frac{y}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}} + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 95.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq -5800000000000000039436163143757201408:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1000000000000000043845843045076197354634047651840:\\ \;\;\;\;x + \frac{\left(t \cdot z + a\right) \cdot z + b}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -5800000000000000039436163143757201408)
    t_1
    (if (<= z 1000000000000000043845843045076197354634047651840)
      (+
       x
       (*
        (/
         (+ (* (+ (* t z) a) z) b)
         (-
          (*
           (-
            (*
             (-
              (* (- z -15234687407/1000000000) z)
              -314690115749/10000000000)
             z)
            -119400905721/10000000000)
           z)
          -607771387771/1000000000000))
        y))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1e+48) {
		tmp = x + ((((((t * z) + a) * z) + b) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y);
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-5.8d+36)) then
        tmp = t_1
    else if (z <= 1d+48) then
        tmp = x + ((((((t * z) + a) * z) + b) / (((((((z - (-15.234687407d0)) * z) - (-31.4690115749d0)) * z) - (-11.9400905721d0)) * z) - (-0.607771387771d0))) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1e+48) {
		tmp = x + ((((((t * z) + a) * z) + b) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -5.8e+36:
		tmp = t_1
	elif z <= 1e+48:
		tmp = x + ((((((t * z) + a) * z) + b) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1e+48)
		tmp = Float64(x + Float64(Float64(Float64(Float64(Float64(Float64(t * z) + a) * z) + b) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1e+48)
		tmp = x + ((((((t * z) + a) * z) + b) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5800000000000000039436163143757201408], t$95$1, If[LessEqual[z, 1000000000000000043845843045076197354634047651840], N[(x + N[(N[(N[(N[(N[(N[(t * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z - -15234687407/1000000000), $MachinePrecision] * z), $MachinePrecision] - -314690115749/10000000000), $MachinePrecision] * z), $MachinePrecision] - -119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision] - -607771387771/1000000000000), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e36 or 1e48 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -5.8e36 < z < 1e48

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{y \cdot \frac{\left(t \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      4. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{\left(t \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot y} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{\left(t \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot y} \]

   6. Applied rewrites 63.3%

      \[\leadsto x + \color{blue}{\frac{\left(t \cdot z + a\right) \cdot z + b}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}} \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \leq \infty:\\ \;\;\;\;x + \frac{b + \left(a + \left(t + \left(\frac{313060547623}{100000000000} \cdot z - \frac{-55833770631}{5000000000}\right) \cdot z\right) \cdot z\right) \cdot z}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{313060547623}{100000000000} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (if (<=
     (+
      x
      (/
       (*
        y
        (+
         (*
          (+
           (*
            (+
             (*
              (+
               (* z 313060547623/100000000000)
               55833770631/5000000000)
              z)
             t)
            z)
           a)
          z)
         b))
       (+
        (*
         (+
          (*
           (+
            (* (+ z 15234687407/1000000000) z)
            314690115749/10000000000)
           z)
          119400905721/10000000000)
         z)
        607771387771/1000000000000)))
     INFINITY)
  (+
   x
   (*
    (/
     (+
      b
      (*
       (+
        a
        (*
         (+
          t
          (*
           (- (* 313060547623/100000000000 z) -55833770631/5000000000)
           z))
         z))
       z))
     (-
      (*
       (-
        (*
         (-
          (* (- z -15234687407/1000000000) z)
          -314690115749/10000000000)
         z)
        -119400905721/10000000000)
       z)
      -607771387771/1000000000000))
    y))
  (+ x (* 313060547623/100000000000 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= ((double) INFINITY)) {
		tmp = x + (((b + ((a + ((t + (((3.13060547623 * z) - -11.1667541262) * z)) * z)) * z)) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y);
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= Double.POSITIVE_INFINITY) {
		tmp = x + (((b + ((a + ((t + (((3.13060547623 * z) - -11.1667541262) * z)) * z)) * z)) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y);
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= math.inf:
		tmp = x + (((b + ((a + ((t + (((3.13060547623 * z) - -11.1667541262) * z)) * z)) * z)) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y)
	else:
		tmp = x + (3.13060547623 * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= Inf)
		tmp = Float64(x + Float64(Float64(Float64(b + Float64(Float64(a + Float64(Float64(t + Float64(Float64(Float64(3.13060547623 * z) - -11.1667541262) * z)) * z)) * z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y));
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= Inf)
		tmp = x + (((b + ((a + ((t + (((3.13060547623 * z) - -11.1667541262) * z)) * z)) * z)) / (((((((z - -15.234687407) * z) - -31.4690115749) * z) - -11.9400905721) * z) - -0.607771387771)) * y);
	else
		tmp = x + (3.13060547623 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 313060547623/100000000000), $MachinePrecision] + 55833770631/5000000000), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15234687407/1000000000), $MachinePrecision] * z), $MachinePrecision] + 314690115749/10000000000), $MachinePrecision] * z), $MachinePrecision] + 119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision] + 607771387771/1000000000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x + N[(N[(N[(b + N[(N[(a + N[(N[(t + N[(N[(N[(313060547623/100000000000 * z), $MachinePrecision] - -55833770631/5000000000), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z - -15234687407/1000000000), $MachinePrecision] * z), $MachinePrecision] - -314690115749/10000000000), $MachinePrecision] * z), $MachinePrecision] - -119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision] - -607771387771/1000000000000), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))) < +inf.0

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   3. Applied rewrites 60.2%

      \[\leadsto x + \color{blue}{\frac{b + \left(a + \left(t + \left(\frac{313060547623}{100000000000} \cdot z - \frac{-55833770631}{5000000000}\right) \cdot z\right) \cdot z\right) \cdot z}{\left(\left(\left(z - \frac{-15234687407}{1000000000}\right) \cdot z - \frac{-314690115749}{10000000000}\right) \cdot z - \frac{-119400905721}{10000000000}\right) \cdot z - \frac{-607771387771}{1000000000000}} \cdot y} \]

   if +inf.0 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))))

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 93.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq -5800000000000000039436163143757201408:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1099999999999999968955791700918272:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -5800000000000000039436163143757201408)
    t_1
    (if (<= z 1099999999999999968955791700918272)
      (+
       x
       (/
        (* y (+ b (* z (+ a (* t z)))))
        (+
         (*
          (+ (* 314690115749/10000000000 z) 119400905721/10000000000)
          z)
         607771387771/1000000000000)))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1.1e+33) {
		tmp = x + ((y * (b + (z * (a + (t * z))))) / ((((31.4690115749 * z) + 11.9400905721) * z) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-5.8d+36)) then
        tmp = t_1
    else if (z <= 1.1d+33) then
        tmp = x + ((y * (b + (z * (a + (t * z))))) / ((((31.4690115749d0 * z) + 11.9400905721d0) * z) + 0.607771387771d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -5.8e+36) {
		tmp = t_1;
	} else if (z <= 1.1e+33) {
		tmp = x + ((y * (b + (z * (a + (t * z))))) / ((((31.4690115749 * z) + 11.9400905721) * z) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -5.8e+36:
		tmp = t_1
	elif z <= 1.1e+33:
		tmp = x + ((y * (b + (z * (a + (t * z))))) / ((((31.4690115749 * z) + 11.9400905721) * z) + 0.607771387771))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1.1e+33)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(t * z))))) / Float64(Float64(Float64(Float64(31.4690115749 * z) + 11.9400905721) * z) + 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -5.8e+36)
		tmp = t_1;
	elseif (z <= 1.1e+33)
		tmp = x + ((y * (b + (z * (a + (t * z))))) / ((((31.4690115749 * z) + 11.9400905721) * z) + 0.607771387771));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5800000000000000039436163143757201408], t$95$1, If[LessEqual[z, 1099999999999999968955791700918272], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(314690115749/10000000000 * z), $MachinePrecision] + 119400905721/10000000000), $MachinePrecision] * z), $MachinePrecision] + 607771387771/1000000000000), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e36 or 1.1e33 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -5.8e36 < z < 1.1e33

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{\color{blue}{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z} \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \color{blue}{\left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. lower-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t \cdot \left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t} \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \color{blue}{\left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. lower-*.f64 61.4%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot \color{blue}{z}\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   4. Applied rewrites 61.4%

      \[\leadsto x + \frac{\color{blue}{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\left(\color{blue}{\frac{314690115749}{10000000000}} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   6. Step-by-step derivation

   7. Applied rewrites 58.3%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\left(\color{blue}{\frac{314690115749}{10000000000}} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   8. Taylor expanded in y around 0

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   9. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(b + \color{blue}{z \cdot \left(a + t \cdot z\right)}\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(b + z \cdot \color{blue}{\left(a + t \cdot z\right)}\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(b + z \cdot \left(a + \color{blue}{t \cdot z}\right)\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. lower-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(b + z \cdot \left(a + t \cdot \color{blue}{z}\right)\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-*.f64 59.3%

         \[\leadsto x + \frac{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   10. Applied rewrites 59.3%

       \[\leadsto x + \frac{y \cdot \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 91.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq \frac{-519460313115661}{590295810358705651712}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1099999999999999968955791700918272:\\ \;\;\;\;x + \frac{1}{\frac{607771387771}{1000000000000}} \cdot \left(\left(z \cdot y\right) \cdot \left(a + t \cdot z\right) + b \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -519460313115661/590295810358705651712)
    t_1
    (if (<= z 1099999999999999968955791700918272)
      (+
       x
       (*
        (/ 1 607771387771/1000000000000)
        (+ (* (* z y) (+ a (* t z))) (* b y))))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.8e-7) {
		tmp = t_1;
	} else if (z <= 1.1e+33) {
		tmp = x + ((1.0 / 0.607771387771) * (((z * y) * (a + (t * z))) + (b * y)));
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-8.8d-7)) then
        tmp = t_1
    else if (z <= 1.1d+33) then
        tmp = x + ((1.0d0 / 0.607771387771d0) * (((z * y) * (a + (t * z))) + (b * y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.8e-7) {
		tmp = t_1;
	} else if (z <= 1.1e+33) {
		tmp = x + ((1.0 / 0.607771387771) * (((z * y) * (a + (t * z))) + (b * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -8.8e-7:
		tmp = t_1
	elif z <= 1.1e+33:
		tmp = x + ((1.0 / 0.607771387771) * (((z * y) * (a + (t * z))) + (b * y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -8.8e-7)
		tmp = t_1;
	elseif (z <= 1.1e+33)
		tmp = Float64(x + Float64(Float64(1.0 / 0.607771387771) * Float64(Float64(Float64(z * y) * Float64(a + Float64(t * z))) + Float64(b * y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -8.8e-7)
		tmp = t_1;
	elseif (z <= 1.1e+33)
		tmp = x + ((1.0 / 0.607771387771) * (((z * y) * (a + (t * z))) + (b * y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -519460313115661/590295810358705651712], t$95$1, If[LessEqual[z, 1099999999999999968955791700918272], N[(x + N[(N[(1 / 607771387771/1000000000000), $MachinePrecision] * N[(N[(N[(z * y), $MachinePrecision] * N[(a + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000004e-7 or 1.1e33 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -8.8000000000000004e-7 < z < 1.1e33

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{\color{blue}{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z} \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \color{blue}{\left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. lower-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t \cdot \left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t} \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \color{blue}{\left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. lower-*.f64 61.4%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot \color{blue}{z}\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   4. Applied rewrites 61.4%

      \[\leadsto x + \frac{\color{blue}{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \color{blue}{\left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lift-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t \cdot \left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. distribute-rgt-in N/A

         \[\leadsto x + \frac{b \cdot y + \left(\left(a \cdot y\right) \cdot z + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot z}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \left(\left(a \cdot y\right) \cdot z + \left(\color{blue}{t} \cdot \left(y \cdot z\right)\right) \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. associate-*r* N/A

         \[\leadsto x + \frac{b \cdot y + \left(a \cdot \left(y \cdot z\right) + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \left(a \cdot \left(y \cdot z\right) + \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      8. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \left(a \cdot \left(y \cdot z\right) + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      9. associate-+r+ N/A

         \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      10. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + z \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      11. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + \color{blue}{z \cdot \left(t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      12. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + \color{blue}{z} \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      13. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      14. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(y \cdot z\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      15. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(y \cdot z\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      16. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(y \cdot z\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      17. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      18. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      19. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      20. lower-*.f64 64.0%

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   6. Applied rewrites 64.0%

      \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \color{blue}{\left(\left(z \cdot y\right) \cdot t\right) \cdot z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   7. Taylor expanded in z around 0

      \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 55.2%

      \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   10. Step-by-step derivation

       1. lift-/.f64 N/A

          \[\leadsto x + \color{blue}{\frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\frac{607771387771}{1000000000000}}} \]

       2. mult-flip N/A

          \[\leadsto x + \color{blue}{\left(\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z\right) \cdot \frac{1}{\frac{607771387771}{1000000000000}}} \]

       3. *-commutative N/A

          \[\leadsto x + \color{blue}{\frac{1}{\frac{607771387771}{1000000000000}} \cdot \left(\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z\right)} \]

       4. lower-*.f64 N/A

          \[\leadsto x + \color{blue}{\frac{1}{\frac{607771387771}{1000000000000}} \cdot \left(\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z\right)} \]

       5. lower-/.f64 55.2%

          \[\leadsto x + \color{blue}{\frac{1}{\frac{607771387771}{1000000000000}}} \cdot \left(\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z\right) \]

   11. Applied rewrites 56.6%

       \[\leadsto x + \color{blue}{\frac{1}{\frac{607771387771}{1000000000000}} \cdot \left(\left(z \cdot y\right) \cdot \left(a + t \cdot z\right) + b \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 91.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq \frac{-519460313115661}{590295810358705651712}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1099999999999999968955791700918272:\\ \;\;\;\;\frac{\left(z \cdot y\right) \cdot \left(a + t \cdot z\right) + b \cdot y}{\frac{607771387771}{1000000000000}} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -519460313115661/590295810358705651712)
    t_1
    (if (<= z 1099999999999999968955791700918272)
      (+
       (/
        (+ (* (* z y) (+ a (* t z))) (* b y))
        607771387771/1000000000000)
       x)
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.8e-7) {
		tmp = t_1;
	} else if (z <= 1.1e+33) {
		tmp = ((((z * y) * (a + (t * z))) + (b * y)) / 0.607771387771) + x;
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-8.8d-7)) then
        tmp = t_1
    else if (z <= 1.1d+33) then
        tmp = ((((z * y) * (a + (t * z))) + (b * y)) / 0.607771387771d0) + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.8e-7) {
		tmp = t_1;
	} else if (z <= 1.1e+33) {
		tmp = ((((z * y) * (a + (t * z))) + (b * y)) / 0.607771387771) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -8.8e-7:
		tmp = t_1
	elif z <= 1.1e+33:
		tmp = ((((z * y) * (a + (t * z))) + (b * y)) / 0.607771387771) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -8.8e-7)
		tmp = t_1;
	elseif (z <= 1.1e+33)
		tmp = Float64(Float64(Float64(Float64(Float64(z * y) * Float64(a + Float64(t * z))) + Float64(b * y)) / 0.607771387771) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -8.8e-7)
		tmp = t_1;
	elseif (z <= 1.1e+33)
		tmp = ((((z * y) * (a + (t * z))) + (b * y)) / 0.607771387771) + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -519460313115661/590295810358705651712], t$95$1, If[LessEqual[z, 1099999999999999968955791700918272], N[(N[(N[(N[(N[(z * y), $MachinePrecision] * N[(a + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision] / 607771387771/1000000000000), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000004e-7 or 1.1e33 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -8.8000000000000004e-7 < z < 1.1e33

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{\color{blue}{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z} \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \color{blue}{\left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. lower-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t \cdot \left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t} \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \color{blue}{\left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. lower-*.f64 61.4%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot \color{blue}{z}\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   4. Applied rewrites 61.4%

      \[\leadsto x + \frac{\color{blue}{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \color{blue}{z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \color{blue}{\left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lift-+.f64 N/A

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + \color{blue}{t \cdot \left(y \cdot z\right)}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. distribute-rgt-in N/A

         \[\leadsto x + \frac{b \cdot y + \left(\left(a \cdot y\right) \cdot z + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot z}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \left(\left(a \cdot y\right) \cdot z + \left(\color{blue}{t} \cdot \left(y \cdot z\right)\right) \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. associate-*r* N/A

         \[\leadsto x + \frac{b \cdot y + \left(a \cdot \left(y \cdot z\right) + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \left(a \cdot \left(y \cdot z\right) + \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right) \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      8. lift-*.f64 N/A

         \[\leadsto x + \frac{b \cdot y + \left(a \cdot \left(y \cdot z\right) + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)} \cdot z\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      9. associate-+r+ N/A

         \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + \color{blue}{\left(t \cdot \left(y \cdot z\right)\right) \cdot z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      10. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + z \cdot \color{blue}{\left(t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      11. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + \color{blue}{z \cdot \left(t \cdot \left(y \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      12. lower-+.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + \color{blue}{z} \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      13. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + a \cdot \left(y \cdot z\right)\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      14. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(y \cdot z\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      15. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(y \cdot z\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      16. lift-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(y \cdot z\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      17. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      18. lower-*.f64 N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + z \cdot \left(t \cdot \left(y \cdot z\right)\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      19. *-commutative N/A

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      20. lower-*.f64 64.0%

          \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(t \cdot \left(y \cdot z\right)\right) \cdot \color{blue}{z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   6. Applied rewrites 64.0%

      \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \color{blue}{\left(\left(z \cdot y\right) \cdot t\right) \cdot z}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   7. Taylor expanded in z around 0

      \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 55.2%

      \[\leadsto x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   10. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \color{blue}{x + \frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\frac{607771387771}{1000000000000}}} \]

       2. +-commutative N/A

          \[\leadsto \color{blue}{\frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\frac{607771387771}{1000000000000}} + x} \]

       3. lower-+.f64 55.2%

          \[\leadsto \color{blue}{\frac{\left(b \cdot y + \left(z \cdot y\right) \cdot a\right) + \left(\left(z \cdot y\right) \cdot t\right) \cdot z}{\frac{607771387771}{1000000000000}} + x} \]

   11. Applied rewrites 56.5%

       \[\leadsto \color{blue}{\frac{\left(z \cdot y\right) \cdot \left(a + t \cdot z\right) + b \cdot y}{\frac{607771387771}{1000000000000}} + x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 83.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{313060547623}{100000000000} \cdot y\\ \mathbf{if}\;z \leq -33500000000000001048576:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1699999999999999965123967908315136:\\ \;\;\;\;x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (let* ((t_1 (+ x (* 313060547623/100000000000 y))))
  (if (<= z -33500000000000001048576)
    t_1
    (if (<= z 1699999999999999965123967908315136)
      (+ x (* 1000000000000/607771387771 (* b y)))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -3.35e+22) {
		tmp = t_1;
	} else if (z <= 1.7e+33) {
		tmp = x + (1.6453555072203998 * (b * y));
	} else {
		tmp = t_1;
	}
	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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-3.35d+22)) then
        tmp = t_1
    else if (z <= 1.7d+33) then
        tmp = x + (1.6453555072203998d0 * (b * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -3.35e+22) {
		tmp = t_1;
	} else if (z <= 1.7e+33) {
		tmp = x + (1.6453555072203998 * (b * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -3.35e+22:
		tmp = t_1
	elif z <= 1.7e+33:
		tmp = x + (1.6453555072203998 * (b * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -3.35e+22)
		tmp = t_1;
	elseif (z <= 1.7e+33)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(b * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -3.35e+22)
		tmp = t_1;
	elseif (z <= 1.7e+33)
		tmp = x + (1.6453555072203998 * (b * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -33500000000000001048576], t$95$1, If[LessEqual[z, 1699999999999999965123967908315136], N[(x + N[(1000000000000/607771387771 * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3500000000000001e22 or 1.7e33 < z

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.4%

         \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

   4. Applied rewrites 62.4%

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

   if -3.3500000000000001e22 < z < 1.7e33

   1. Initial program 58.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x + \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(b \cdot y\right)} \]

      2. lower-*.f64 59.6%

         \[\leadsto x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 59.6%

      \[\leadsto x + \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 62.4% accurate, 8.8× speedup

Math

\[x + \frac{313060547623}{100000000000} \cdot y \]

FPCore

(FPCore (x y z t a b)
  :precision binary64
  (+ x (* 313060547623/100000000000 y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + (3.13060547623 * y);
}

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)
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
    code = x + (3.13060547623d0 * y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + (3.13060547623 * y);
}

Python

def code(x, y, z, t, a, b):
	return x + (3.13060547623 * y)

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(3.13060547623 * y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + (3.13060547623 * y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(313060547623/100000000000 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.1%

   \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
3. Step-by-step derivation

   1. lower-*.f64 62.4%

      \[\leadsto x + \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]

4. Applied rewrites 62.4%

   \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64
  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))))