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

Percentage Accurate: 58.2% → 96.1%

Time: 10.1s

Alternatives: 12

Speedup: 4.1×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \end{array} \]

FPCore

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

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 * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \end{array} \]

FPCore

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

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 * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4000000:\\ \;\;\;\;\mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4000000.0)
   (fma
    y
    (-
     (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
     (/ 36.52704169880642 z))
    x)
   (if (<= z 2.15e+18)
     (+
      x
      (/
       (*
        y
        (+
         (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
         b))
       0.607771387771))
     (fma
      y
      (fma
       (/ (fma (/ (+ 457.9610022158428 t) z) -1.0 36.52704169880642) z)
       -1.0
       3.13060547623)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4000000.0) {
		tmp = fma(y, ((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), x);
	} else if (z <= 2.15e+18) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771);
	} else {
		tmp = fma(y, fma((fma(((457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4000000.0)
		tmp = fma(y, Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), x);
	elseif (z <= 2.15e+18)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771));
	else
		tmp = fma(y, fma(Float64(fma(Float64(Float64(457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4000000.0], N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.15e+18], N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4e6

   1. Initial program 22.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 43.0%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 43.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]
   9. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, x\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, x\right) \]

      4. div-add-rev N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      7. pow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{\color{blue}{z}}, x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{\frac{3652704169880641883561}{100000000000000000000}}{z}, x\right) \]

      11. lower-/.f64 96.2

          \[\leadsto \mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{\color{blue}{z}}, x\right) \]

   10. Applied rewrites 96.2%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}}, x\right) \]

   if -4e6 < z < 2.15e18

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.5%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{0.607771387771}} \]

   if 2.15e18 < z

   1. Initial program 18.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 53.3%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 57.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}}, x\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} + \color{blue}{\frac{313060547623}{100000000000}}, x\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} \cdot -1 + \frac{313060547623}{100000000000}, x\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, \color{blue}{-1}, \frac{313060547623}{100000000000}\right), x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{-1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} \cdot -1 + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      9. lower-+.f64 96.5

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right) \]

   10. Applied rewrites 96.5%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right)}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 95.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          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)))))
   (if (<= t_1 INFINITY)
     t_1
     (fma
      y
      (fma
       (/ (fma (/ (+ 457.9610022158428 t) z) -1.0 36.52704169880642) z)
       -1.0
       3.13060547623)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 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 tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(y, fma((fma(((457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = 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)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(y, fma(Float64(fma(Float64(Float64(457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 3.13060547623), $MachinePrecision] + x), $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 96.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   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 0.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 45.3%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 49.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}}, x\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} + \color{blue}{\frac{313060547623}{100000000000}}, x\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} \cdot -1 + \frac{313060547623}{100000000000}, x\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, \color{blue}{-1}, \frac{313060547623}{100000000000}\right), x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{-1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} \cdot -1 + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      9. lower-+.f64 97.9

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right) \]

   10. Applied rewrites 97.9%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right)}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (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)))
      INFINITY)
   (fma
    y
    (/
     (fma (fma (* z z) (fma 3.13060547623 z 11.1667541262) a) z b)
     (fma
      (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
      z
      0.607771387771))
    x)
   (fma
    y
    (fma
     (/ (fma (/ (+ 457.9610022158428 t) z) -1.0 36.52704169880642) z)
     -1.0
     3.13060547623)
    x)))

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 = fma(y, (fma(fma((z * z), fma(3.13060547623, z, 11.1667541262), a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	} else {
		tmp = fma(y, fma((fma(((457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	}
	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 = fma(y, Float64(fma(fma(Float64(z * z), fma(3.13060547623, z, 11.1667541262), a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	else
		tmp = fma(y, fma(Float64(fma(Float64(Float64(457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	end
	return 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 * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(y * N[(N[(N[(N[(z * z), $MachinePrecision] * N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 3.13060547623), $MachinePrecision] + x), $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 96.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 81.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   8. Applied rewrites 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   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 0.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 45.3%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 49.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}}, x\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} + \color{blue}{\frac{313060547623}{100000000000}}, x\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} \cdot -1 + \frac{313060547623}{100000000000}, x\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, \color{blue}{-1}, \frac{313060547623}{100000000000}\right), x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{-1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} \cdot -1 + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      9. lower-+.f64 97.9

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right) \]

   10. Applied rewrites 97.9%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right)}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 93.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.25e+20)
   (fma
    y
    (-
     (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
     (/ 36.52704169880642 z))
    x)
   (if (<= z 3.8e+18)
     (fma
      y
      (/
       (fma a z b)
       (fma (fma (fma z z 31.4690115749) z 11.9400905721) z 0.607771387771))
      x)
     (fma
      y
      (fma
       (/ (fma (/ (+ 457.9610022158428 t) z) -1.0 36.52704169880642) z)
       -1.0
       3.13060547623)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.25e+20) {
		tmp = fma(y, ((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), x);
	} else if (z <= 3.8e+18) {
		tmp = fma(y, (fma(a, z, b) / fma(fma(fma(z, z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	} else {
		tmp = fma(y, fma((fma(((457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.25e+20)
		tmp = fma(y, Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), x);
	elseif (z <= 3.8e+18)
		tmp = fma(y, Float64(fma(a, z, b) / fma(fma(fma(z, z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	else
		tmp = fma(y, fma(Float64(fma(Float64(Float64(457.9610022158428 + t) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.25e+20], N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.8e+18], N[(y * N[(N[(a * z + b), $MachinePrecision] / N[(N[(N[(z * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e20

   1. Initial program 17.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 40.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 41.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]
   9. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, x\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, x\right) \]

      4. div-add-rev N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      7. pow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{\color{blue}{z}}, x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{\frac{3652704169880641883561}{100000000000000000000}}{z}, x\right) \]

      11. lower-/.f64 98.3

          \[\leadsto \mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{\color{blue}{z}}, x\right) \]

   10. Applied rewrites 98.3%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}}, x\right) \]

   if -2.25e20 < z < 3.8e18

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.0%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 85.9%

       \[\leadsto \mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{z}, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]

   11. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 96.6

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, \color{blue}{z}, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]

   13. Applied rewrites 96.6%

       \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]

   if 3.8e18 < z

   1. Initial program 18.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 53.3%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 57.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}}, x\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} + \color{blue}{\frac{313060547623}{100000000000}}, x\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z} \cdot -1 + \frac{313060547623}{100000000000}, x\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, \color{blue}{-1}, \frac{313060547623}{100000000000}\right), x\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{-1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z} \cdot -1 + \frac{3652704169880641883561}{100000000000000000000}}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}, -1, \frac{3652704169880641883561}{100000000000000000000}\right)}{z}, -1, \frac{313060547623}{100000000000}\right), x\right) \]

      9. lower-+.f64 96.5

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), x\right) \]

   10. Applied rewrites 96.5%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{457.9610022158428 + t}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right)}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 93.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+20} \lor \neg \left(z \leq 3.8 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.25e+20) (not (<= z 3.8e+18)))
   (fma
    y
    (-
     (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
     (/ 36.52704169880642 z))
    x)
   (fma
    y
    (/
     (fma a z b)
     (fma (fma (fma z z 31.4690115749) z 11.9400905721) z 0.607771387771))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.25e+20) || !(z <= 3.8e+18)) {
		tmp = fma(y, ((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), x);
	} else {
		tmp = fma(y, (fma(a, z, b) / fma(fma(fma(z, z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.25e+20) || !(z <= 3.8e+18))
		tmp = fma(y, Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), x);
	else
		tmp = fma(y, Float64(fma(a, z, b) / fma(fma(fma(z, z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.25e+20], N[Not[LessEqual[z, 3.8e+18]], $MachinePrecision]], N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(a * z + b), $MachinePrecision] / N[(N[(N[(z * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e20 or 3.8e18 < z

   1. Initial program 18.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 46.1%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]
   9. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, x\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, x\right) \]

      4. div-add-rev N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      7. pow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, x\right) \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{\color{blue}{z}}, x\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(y, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z \cdot z} + \frac{313060547623}{100000000000}\right) - \frac{\frac{3652704169880641883561}{100000000000000000000}}{z}, x\right) \]

      11. lower-/.f64 97.5

          \[\leadsto \mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{\color{blue}{z}}, x\right) \]

   10. Applied rewrites 97.5%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}}, x\right) \]

   if -2.25e20 < z < 3.8e18

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.0%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 86.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 85.9%

       \[\leadsto \mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{z}, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]

   11. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 96.6

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, \color{blue}{z}, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]

   13. Applied rewrites 96.6%

       \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+20} \lor \neg \left(z \leq 3.8 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+24} \lor \neg \left(z \leq 4.1 \cdot 10^{+24}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e+24) (not (<= z 4.1e+24)))
   (fma 3.13060547623 y x)
   (fma
    y
    (/
     (fma a z b)
     (fma (fma (fma z z 31.4690115749) z 11.9400905721) z 0.607771387771))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e+24) || !(z <= 4.1e+24)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma(y, (fma(a, z, b) / fma(fma(fma(z, z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e+24) || !(z <= 4.1e+24))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(y, Float64(fma(a, z, b) / fma(fma(fma(z, z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e+24], N[Not[LessEqual[z, 4.1e+24]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(y * N[(N[(a * z + b), $MachinePrecision] / N[(N[(N[(z * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e24 or 4.1000000000000001e24 < z

   1. Initial program 17.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   5. Applied rewrites 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -2e24 < z < 4.1000000000000001e24

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.4%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   7. Applied rewrites 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 85.4%

       \[\leadsto \mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{z}, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]

   11. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 96.1

          \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, \color{blue}{z}, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]

   13. Applied rewrites 96.1%

       \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+24} \lor \neg \left(z \leq 4.1 \cdot 10^{+24}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -31500000000 \lor \neg \left(z \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(a \cdot z + b\right)}{0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -31500000000.0) (not (<= z 4.5e+18)))
   (fma 3.13060547623 y x)
   (+ x (/ (* y (+ (* a z) b)) 0.607771387771))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -31500000000.0) || !(z <= 4.5e+18)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = x + ((y * ((a * z) + b)) / 0.607771387771);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -31500000000.0) || !(z <= 4.5e+18))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(a * z) + b)) / 0.607771387771));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -31500000000.0], N[Not[LessEqual[z, 4.5e+18]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(x + N[(N[(y * N[(N[(a * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.15e10 or 4.5e18 < z

   1. Initial program 20.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 87.0

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   5. Applied rewrites 87.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -3.15e10 < z < 4.5e18

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.5%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{0.607771387771}} \]

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 97.0%

      \[\leadsto x + \frac{y \cdot \left(\color{blue}{a} \cdot z + b\right)}{0.607771387771} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31500000000 \lor \neg \left(z \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(a \cdot z + b\right)}{0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+24} \lor \neg \left(z \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.52e+24) (not (<= z 4e+18)))
   (fma 3.13060547623 y x)
   (fma (* b y) 1.6453555072203998 x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.52e+24) || !(z <= 4e+18)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma((b * y), 1.6453555072203998, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.52e+24) || !(z <= 4e+18))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(Float64(b * y), 1.6453555072203998, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.52e+24], N[Not[LessEqual[z, 4e+18]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5199999999999999e24 or 4e18 < z

   1. Initial program 17.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   5. Applied rewrites 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.5199999999999999e24 < z < 4e18

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 84.6

         \[\leadsto \mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right) \]

   5. Applied rewrites 84.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+24} \lor \neg \left(z \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+24} \lor \neg \left(z \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998 \cdot b, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.52e+24) (not (<= z 4e+18)))
   (fma 3.13060547623 y x)
   (fma (* 1.6453555072203998 b) y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.52e+24) || !(z <= 4e+18)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma((1.6453555072203998 * b), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.52e+24) || !(z <= 4e+18))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(Float64(1.6453555072203998 * b), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.52e+24], N[Not[LessEqual[z, 4e+18]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(1.6453555072203998 * b), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5199999999999999e24 or 4e18 < z

   1. Initial program 17.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   5. Applied rewrites 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.5199999999999999e24 < z < 4e18

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.4%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 84.6

         \[\leadsto \mathsf{fma}\left(1.6453555072203998 \cdot b, y, x\right) \]

   8. Applied rewrites 84.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1.6453555072203998 \cdot b, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+24} \lor \neg \left(z \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998 \cdot b, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-21} \lor \neg \left(z \leq 4.6 \cdot 10^{-51}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7e-21) (not (<= z 4.6e-51))) (fma 3.13060547623 y x) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7e-21) || !(z <= 4.6e-51)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7e-21) || !(z <= 4.6e-51))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7e-21], N[Not[LessEqual[z, 4.6e-51]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000007e-21 or 4.60000000000000004e-51 < z

   1. Initial program 27.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 81.9

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   5. Applied rewrites 81.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -7.0000000000000007e-21 < z < 4.60000000000000004e-51

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 51.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-21} \lor \neg \left(z \leq 4.6 \cdot 10^{-51}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.5% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-190} \lor \neg \left(x \leq 1.45 \cdot 10^{-114}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -3.6e-190) (not (<= x 1.45e-114))) x (* 3.13060547623 y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.6e-190) || !(x <= 1.45e-114)) {
		tmp = x;
	} else {
		tmp = 3.13060547623 * y;
	}
	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) :: tmp
    if ((x <= (-3.6d-190)) .or. (.not. (x <= 1.45d-114))) then
        tmp = x
    else
        tmp = 3.13060547623d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -3.6e-190) || !(x <= 1.45e-114)) {
		tmp = x;
	} else {
		tmp = 3.13060547623 * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -3.6e-190) or not (x <= 1.45e-114):
		tmp = x
	else:
		tmp = 3.13060547623 * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -3.6e-190) || !(x <= 1.45e-114))
		tmp = x;
	else
		tmp = Float64(3.13060547623 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -3.6e-190) || ~((x <= 1.45e-114)))
		tmp = x;
	else
		tmp = 3.13060547623 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -3.6e-190], N[Not[LessEqual[x, 1.45e-114]], $MachinePrecision]], x, N[(3.13060547623 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.60000000000000007e-190 or 1.44999999999999998e-114 < x

   1. Initial program 66.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 60.7%

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

   if -3.60000000000000007e-190 < x < 1.44999999999999998e-114

   1. Initial program 57.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 47.2

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   5. Applied rewrites 47.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 45.2

         \[\leadsto 3.13060547623 \cdot y \]

   8. Applied rewrites 45.2%

      \[\leadsto 3.13060547623 \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-190} \lor \neg \left(x \leq 1.45 \cdot 10^{-114}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;3.13060547623 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.1% accurate, 79.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.9%

   \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Applied rewrites 48.9%

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

Developer Target 1: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z)))
           (/ y 1.0)))))
   (if (< z -6.499344996252632e+53)
     t_1
     (if (< z 7.066965436914287e+59)
       (+
        x
        (/
         y
         (/
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771)
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	} 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 - (36.527041698806414d0 / z)) + (t / (z * z))) * (y / 1.0d0))
    if (z < (-6.499344996252632d+53)) then
        tmp = t_1
    else if (z < 7.066965436914287d+59) then
        tmp = x + (y / ((((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0) / ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0))
	tmp = 0
	if z < -6.499344996252632e+53:
		tmp = t_1
	elif z < 7.066965436914287e+59:
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(3.13060547623 - Float64(36.527041698806414 / z)) + Float64(t / Float64(z * z))) * Float64(y / 1.0)))
	tmp = 0.0
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	tmp = 0.0;
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(3.13060547623 - N[(36.527041698806414 / z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -6.499344996252632e+53], t$95$1, If[Less[z, 7.066965436914287e+59], N[(x + N[(y / N[(N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025037 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -649934499625263200000000000000000000000000000000000000) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))) (if (< z 706696543691428700000000000000000000000000000000000000000000) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (+ (* (+ (* (+ (* (+ (* z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)))) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))))))

  (+ 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))))