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

Percentage Accurate: 58.5% → 96.8%

Time: 13.1s

Alternatives: 21

Speedup: 4.4×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

Python

def code(x, y, z):
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 10^{+281}:\\ \;\;\;\;\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
           y)
          x)
         z))
       (+
        (*
         (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
         x)
        47.066876606))
      1e+281)
   (/
    (*
     (- (* x x) 4.0)
     (/
      (fma
       (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
       x
       z)
      (fma
       (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
       x
       47.066876606)))
    (+ 2.0 x))
   (* 4.16438922228 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+281) {
		tmp = (((x * x) - 4.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606))) / (2.0 + x);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+281)
		tmp = Float64(Float64(Float64(Float64(x * x) - 4.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606))) / Float64(2.0 + x));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 1e+281], N[(N[(N[(N[(x * x), $MachinePrecision] - 4.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 + x), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1e281

   1. Initial program 96.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   if 1e281 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 1.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 99.1

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 99.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 10^{+281}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
           y)
          x)
         z))
       (+
        (*
         (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
         x)
        47.066876606))
      1e+281)
   (*
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma
      (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
      x
      47.066876606))
    (- x 2.0))
   (* 4.16438922228 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+281) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+281)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 1e+281], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1e281

   1. Initial program 96.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \cdot \left(x - 2\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \cdot \left(x - 2\right)} \]

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)} \]

   if 1e281 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 1.0%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 99.1

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 99.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+46}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00032:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00046:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (* (- x 2.0) (fma y x z))
          (+
           (*
            (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
            x)
           47.066876606))))
   (if (<= x -2.2e+46)
     (* 4.16438922228 x)
     (if (<= x -0.00032)
       t_0
       (if (<= x 0.00046)
         (*
          (fma
           (+
            (* (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x)
            y)
           x
           z)
          (-
           (*
            (fma
             (- (* 10.238818846568002 x) 1.787568985856513)
             x
             0.3041881842569256)
            x)
           0.0424927283095952))
         (if (<= x 2.4e+29) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * fma(y, x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	double tmp;
	if (x <= -2.2e+46) {
		tmp = 4.16438922228 * x;
	} else if (x <= -0.00032) {
		tmp = t_0;
	} else if (x <= 0.00046) {
		tmp = fma(((fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416) * x) + y), x, z) * ((fma(((10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952);
	} else if (x <= 2.4e+29) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - 2.0) * fma(y, x, z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
	tmp = 0.0
	if (x <= -2.2e+46)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -0.00032)
		tmp = t_0;
	elseif (x <= 0.00046)
		tmp = Float64(fma(Float64(Float64(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416) * x) + y), x, z) * Float64(Float64(fma(Float64(Float64(10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952));
	elseif (x <= 2.4e+29)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+46], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -0.00032], t$95$0, If[LessEqual[x, 0.00046], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(N[(N[(10.238818846568002 * x), $MachinePrecision] - 1.787568985856513), $MachinePrecision] * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+29], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e46 or 2.4000000000000001e29 < x

   1. Initial program 6.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 11.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 97.0

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 97.0%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -2.2e46 < x < -3.20000000000000026e-4 or 4.6000000000000001e-4 < x < 2.4000000000000001e29

   1. Initial program 99.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot y\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(x \cdot y + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\color{blue}{y \cdot x} + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. lower-fma.f64 87.6

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Applied rewrites 87.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   if -3.20000000000000026e-4 < x < 4.6000000000000001e-4

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) + \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\left(\color{blue}{\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) \cdot x} + \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      7. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      8. lower-*.f64 99.3

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{10.238818846568002 \cdot x} - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

   7. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right) \cdot x + y}, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right) \cdot x + y}, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 99.3

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right) \cdot x} + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

      4. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{104109730557}{25000000000} \cdot x + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{393497462077}{5000000000} + \color{blue}{x \cdot \frac{104109730557}{25000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{393497462077}{5000000000} + \color{blue}{x \cdot \frac{104109730557}{25000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \frac{104109730557}{25000000000}} + \frac{393497462077}{5000000000}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      10. lower-fma.f64 99.3

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

   9. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y}, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+46}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00032:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 0.00046:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+46}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00032:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00046:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (/
          (* (- x 2.0) (fma y x z))
          (+
           (*
            (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
            x)
           47.066876606))))
   (if (<= x -2.2e+46)
     (* 4.16438922228 x)
     (if (<= x -0.00032)
       t_0
       (if (<= x 0.00046)
         (*
          (fma
           (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
           x
           z)
          (-
           (*
            (fma
             (- (* 10.238818846568002 x) 1.787568985856513)
             x
             0.3041881842569256)
            x)
           0.0424927283095952))
         (if (<= x 2.4e+29) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * fma(y, x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	double tmp;
	if (x <= -2.2e+46) {
		tmp = 4.16438922228 * x;
	} else if (x <= -0.00032) {
		tmp = t_0;
	} else if (x <= 0.00046) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((fma(((10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952);
	} else if (x <= 2.4e+29) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - 2.0) * fma(y, x, z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
	tmp = 0.0
	if (x <= -2.2e+46)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -0.00032)
		tmp = t_0;
	elseif (x <= 0.00046)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(fma(Float64(Float64(10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952));
	elseif (x <= 2.4e+29)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+46], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -0.00032], t$95$0, If[LessEqual[x, 0.00046], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(N[(N[(10.238818846568002 * x), $MachinePrecision] - 1.787568985856513), $MachinePrecision] * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+29], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e46 or 2.4000000000000001e29 < x

   1. Initial program 6.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 11.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 97.0

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 97.0%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -2.2e46 < x < -3.20000000000000026e-4 or 4.6000000000000001e-4 < x < 2.4000000000000001e29

   1. Initial program 99.0%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot y\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(x \cdot y + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\color{blue}{y \cdot x} + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. lower-fma.f64 87.6

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Applied rewrites 87.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   if -3.20000000000000026e-4 < x < 4.6000000000000001e-4

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) + \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\left(\color{blue}{\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) \cdot x} + \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      7. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      8. lower-*.f64 99.3

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{10.238818846568002 \cdot x} - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

   7. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+46}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00032:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 0.00046:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+35} \lor \neg \left(x \leq 5.5 \cdot 10^{+26}\right):\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} + 110.1139242984811}{x} - 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e+35) (not (<= x 5.5e+26)))
   (*
    (- x)
    (-
     (/
      (+
       (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
       110.1139242984811)
      x)
     4.16438922228))
   (/
    (* (- x 2.0) (fma (fma 137.519416416 x y) x z))
    (+
     (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
     47.066876606))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e+35) || !(x <= 5.5e+26)) {
		tmp = -x * (((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) + 110.1139242984811) / x) - 4.16438922228);
	} else {
		tmp = ((x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e+35) || !(x <= 5.5e+26))
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) + 110.1139242984811) / x) - 4.16438922228));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e+35], N[Not[LessEqual[x, 5.5e+26]], $MachinePrecision]], N[((-x) * N[(N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] + 110.1139242984811), $MachinePrecision] / x), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999989e35 or 5.4999999999999997e26 < x

   1. Initial program 9.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 2.9

         \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   5. Applied rewrites 2.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   6. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

   8. Applied rewrites 97.3%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 + \left(-y\right)}{x} - 3655.1204654076414}{-x} - 110.1139242984811}{-x} - 4.16438922228\right)} \]

   if -5.79999999999999989e35 < x < 5.4999999999999997e26

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right) + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\color{blue}{\left(y + \frac{4297481763}{31250000} \cdot x\right) \cdot x} + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(y + \frac{4297481763}{31250000} \cdot x, x, z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\color{blue}{\frac{4297481763}{31250000} \cdot x + y}, x, z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      5. lower-fma.f64 97.6

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(137.519416416, x, y\right)}, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Applied rewrites 97.6%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+35} \lor \neg \left(x \leq 5.5 \cdot 10^{+26}\right):\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} + 110.1139242984811}{x} - 4.16438922228\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} + 110.1139242984811}{x} - 4.16438922228\right)\\ \mathbf{if}\;x \leq -8600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00046:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x)
          (-
           (/
            (+
             (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
             110.1139242984811)
            x)
           4.16438922228))))
   (if (<= x -8600.0)
     t_0
     (if (<= x 0.00046)
       (*
        (fma
         (+ (* (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x) y)
         x
         z)
        (-
         (*
          (fma
           (- (* 10.238818846568002 x) 1.787568985856513)
           x
           0.3041881842569256)
          x)
         0.0424927283095952))
       (if (<= x 5.5e+26)
         (/
          (* (- x 2.0) (fma y x z))
          (+
           (*
            (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
            x)
           47.066876606))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -x * (((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) + 110.1139242984811) / x) - 4.16438922228);
	double tmp;
	if (x <= -8600.0) {
		tmp = t_0;
	} else if (x <= 0.00046) {
		tmp = fma(((fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416) * x) + y), x, z) * ((fma(((10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952);
	} else if (x <= 5.5e+26) {
		tmp = ((x - 2.0) * fma(y, x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) + 110.1139242984811) / x) - 4.16438922228))
	tmp = 0.0
	if (x <= -8600.0)
		tmp = t_0;
	elseif (x <= 0.00046)
		tmp = Float64(fma(Float64(Float64(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416) * x) + y), x, z) * Float64(Float64(fma(Float64(Float64(10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952));
	elseif (x <= 5.5e+26)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(y, x, z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[(N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] + 110.1139242984811), $MachinePrecision] / x), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8600.0], t$95$0, If[LessEqual[x, 0.00046], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(N[(N[(10.238818846568002 * x), $MachinePrecision] - 1.787568985856513), $MachinePrecision] * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+26], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8600 or 5.4999999999999997e26 < x

   1. Initial program 14.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 2.9

         \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   5. Applied rewrites 2.9%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   6. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      2. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right) \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

      4. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right) \]

      5. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{\left(-1 \cdot \frac{y}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{x}\right) - \frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x} - \frac{104109730557}{25000000000}\right)} \]

   8. Applied rewrites 95.6%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 + \left(-y\right)}{x} - 3655.1204654076414}{-x} - 110.1139242984811}{-x} - 4.16438922228\right)} \]

   if -8600 < x < 4.6000000000000001e-4

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) + \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\left(\color{blue}{\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) \cdot x} + \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      7. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      8. lower-*.f64 98.6

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{10.238818846568002 \cdot x} - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

   7. Applied rewrites 98.6%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right) \cdot x + y}, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right) \cdot x + y}, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 98.6

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right) \cdot x} + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

      4. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{104109730557}{25000000000} \cdot x + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{393497462077}{5000000000} + \color{blue}{x \cdot \frac{104109730557}{25000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{393497462077}{5000000000} + \color{blue}{x \cdot \frac{104109730557}{25000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \frac{104109730557}{25000000000}} + \frac{393497462077}{5000000000}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      10. lower-fma.f64 98.6

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

   9. Applied rewrites 98.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y}, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

   if 4.6000000000000001e-4 < x < 5.4999999999999997e26

   1. Initial program 99.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot y\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(x \cdot y + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(\color{blue}{y \cdot x} + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. lower-fma.f64 96.8

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Applied rewrites 96.8%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(y, x, z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8600:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} + 110.1139242984811}{x} - 4.16438922228\right)\\ \mathbf{elif}\;x \leq 0.00046:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} + 110.1139242984811}{x} - 4.16438922228\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8600:\\ \;\;\;\;\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{t\_0}\\ \mathbf{elif}\;x \leq 0.005:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{x - 2}{t\_0}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
   (if (<= x -1.05e+47)
     (* 4.16438922228 x)
     (if (<= x -8600.0)
       (* (* (- x 2.0) y) (/ x t_0))
       (if (<= x 0.005)
         (*
          (fma
           (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
           x
           z)
          (-
           (* (fma -1.787568985856513 x 0.3041881842569256) x)
           0.0424927283095952))
         (if (<= x 5.5e+26)
           (* (* y x) (/ (- x 2.0) t_0))
           (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double tmp;
	if (x <= -1.05e+47) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8600.0) {
		tmp = ((x - 2.0) * y) * (x / t_0);
	} else if (x <= 0.005) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952);
	} else if (x <= 5.5e+26) {
		tmp = (y * x) * ((x - 2.0) / t_0);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	tmp = 0.0
	if (x <= -1.05e+47)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -8600.0)
		tmp = Float64(Float64(Float64(x - 2.0) * y) * Float64(x / t_0));
	elseif (x <= 0.005)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952));
	elseif (x <= 5.5e+26)
		tmp = Float64(Float64(y * x) * Float64(Float64(x - 2.0) / t_0));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, If[LessEqual[x, -1.05e+47], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -8600.0], N[(N[(N[(x - 2.0), $MachinePrecision] * y), $MachinePrecision] * N[(x / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.005], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(-1.787568985856513 * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+26], N[(N[(y * x), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.05e47 or 5.4999999999999997e26 < x

   1. Initial program 6.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 10.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 97.9

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 97.9%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -1.05e47 < x < -8600

   1. Initial program 90.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot x}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - 2\right)} \cdot y\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \color{blue}{\frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      8. +-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) + \frac{23533438303}{500000000}}} \]

      9. *-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) \cdot x} + \frac{23533438303}{500000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\mathsf{fma}\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right), x, \frac{23533438303}{500000000}\right)}} \]

      11. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) + \frac{156699607947}{500000000}}, x, \frac{23533438303}{500000000}\right)} \]

      12. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) \cdot x} + \frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right), x, \frac{156699607947}{500000000}\right)}, x, \frac{23533438303}{500000000}\right)} \]

      14. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{216700011257}{5000000000} + x\right) + \frac{263505074721}{1000000000}}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left(\frac{216700011257}{5000000000} + x\right) \cdot x} + \frac{263505074721}{1000000000}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      16. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right)}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      17. lower-+.f64 62.2

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{43.3400022514 + x}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 62.2%

      \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   if -8600 < x < 0.0050000000000000001

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x + \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. lower-fma.f64 98.5

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right)} \cdot x - 0.0424927283095952\right) \]

   7. Applied rewrites 98.5%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)} \]

   if 0.0050000000000000001 < x < 5.4999999999999997e26

   1. Initial program 99.4%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(x \cdot y\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(y \cdot x\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. lower-*.f64 53.7

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(y \cdot x\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Applied rewrites 53.7%

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(y \cdot x\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(y \cdot x\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(y \cdot x\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y \cdot x\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{\left(y \cdot x\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(y \cdot x\right) \cdot \left(x - 2\right)}{\color{blue}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\left(y \cdot x\right) \cdot \left(x - 2\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)}} \]

   7. Applied rewrites 53.7%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8600:\\ \;\;\;\;\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 0.005:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.005:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (* (- x 2.0) y)
          (/
           x
           (fma
            (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
            x
            47.066876606)))))
   (if (<= x -1.05e+47)
     (* 4.16438922228 x)
     (if (<= x -8600.0)
       t_0
       (if (<= x 0.005)
         (*
          (fma
           (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
           x
           z)
          (-
           (* (fma -1.787568985856513 x 0.3041881842569256) x)
           0.0424927283095952))
         (if (<= x 5.5e+26) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = ((x - 2.0) * y) * (x / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	double tmp;
	if (x <= -1.05e+47) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8600.0) {
		tmp = t_0;
	} else if (x <= 0.005) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952);
	} else if (x <= 5.5e+26) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x - 2.0) * y) * Float64(x / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)))
	tmp = 0.0
	if (x <= -1.05e+47)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -8600.0)
		tmp = t_0;
	elseif (x <= 0.005)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952));
	elseif (x <= 5.5e+26)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] * y), $MachinePrecision] * N[(x / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+47], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -8600.0], t$95$0, If[LessEqual[x, 0.005], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(-1.787568985856513 * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+26], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e47 or 5.4999999999999997e26 < x

   1. Initial program 6.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 10.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 97.9

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 97.9%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -1.05e47 < x < -8600 or 0.0050000000000000001 < x < 5.4999999999999997e26

   1. Initial program 94.3%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot x}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - 2\right)} \cdot y\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \color{blue}{\frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      8. +-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) + \frac{23533438303}{500000000}}} \]

      9. *-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) \cdot x} + \frac{23533438303}{500000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\mathsf{fma}\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right), x, \frac{23533438303}{500000000}\right)}} \]

      11. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) + \frac{156699607947}{500000000}}, x, \frac{23533438303}{500000000}\right)} \]

      12. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) \cdot x} + \frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right), x, \frac{156699607947}{500000000}\right)}, x, \frac{23533438303}{500000000}\right)} \]

      14. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{216700011257}{5000000000} + x\right) + \frac{263505074721}{1000000000}}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left(\frac{216700011257}{5000000000} + x\right) \cdot x} + \frac{263505074721}{1000000000}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      16. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right)}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      17. lower-+.f64 58.3

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{43.3400022514 + x}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 58.3%

      \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   if -8600 < x < 0.0050000000000000001

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x + \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. lower-fma.f64 98.5

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right)} \cdot x - 0.0424927283095952\right) \]

   7. Applied rewrites 98.5%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 91.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8600:\\ \;\;\;\;\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+47)
   (* 4.16438922228 x)
   (if (<= x -8600.0)
     (*
      (* (- x 2.0) y)
      (/
       x
       (fma
        (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
        x
        47.066876606)))
     (if (<= x 2e+22)
       (*
        (fma
         (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
         x
         z)
        (-
         (*
          (fma
           (- (* 10.238818846568002 x) 1.787568985856513)
           x
           0.3041881842569256)
          x)
         0.0424927283095952))
       (* 4.16438922228 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+47) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8600.0) {
		tmp = ((x - 2.0) * y) * (x / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else if (x <= 2e+22) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((fma(((10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+47)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -8600.0)
		tmp = Float64(Float64(Float64(x - 2.0) * y) * Float64(x / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	elseif (x <= 2e+22)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(fma(Float64(Float64(10.238818846568002 * x) - 1.787568985856513), x, 0.3041881842569256) * x) - 0.0424927283095952));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+47], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -8600.0], N[(N[(N[(x - 2.0), $MachinePrecision] * y), $MachinePrecision] * N[(x / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+22], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(N[(N[(10.238818846568002 * x), $MachinePrecision] - 1.787568985856513), $MachinePrecision] * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e47 or 2e22 < x

   1. Initial program 8.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 12.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 96.1

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 96.1%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -1.05e47 < x < -8600

   1. Initial program 90.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot x}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - 2\right)} \cdot y\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \color{blue}{\frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      8. +-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) + \frac{23533438303}{500000000}}} \]

      9. *-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) \cdot x} + \frac{23533438303}{500000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\mathsf{fma}\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right), x, \frac{23533438303}{500000000}\right)}} \]

      11. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) + \frac{156699607947}{500000000}}, x, \frac{23533438303}{500000000}\right)} \]

      12. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) \cdot x} + \frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right), x, \frac{156699607947}{500000000}\right)}, x, \frac{23533438303}{500000000}\right)} \]

      14. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{216700011257}{5000000000} + x\right) + \frac{263505074721}{1000000000}}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left(\frac{216700011257}{5000000000} + x\right) \cdot x} + \frac{263505074721}{1000000000}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      16. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right)}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      17. lower-+.f64 62.2

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{43.3400022514 + x}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 62.2%

      \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   if -8600 < x < 2e22

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) - \frac{1000000000}{23533438303}\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right)\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(x \cdot \left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) + \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\left(\color{blue}{\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}\right) \cdot x} + \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}, x, \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      7. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{\frac{3140446455626174059100348970313144550000000}{306719603372886620352117082586607327396481} \cdot x - \frac{23298017199368982832548000000000}{13033352773350869092174451844127}}, x, \frac{168466327098500000000}{553822718361107519809}\right) \cdot x - \frac{1000000000}{23533438303}\right) \]

      8. lower-*.f64 94.3

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(\color{blue}{10.238818846568002 \cdot x} - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \]

   7. Applied rewrites 94.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\mathsf{fma}\left(10.238818846568002 \cdot x - 1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 91.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-13}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+47)
   (* 4.16438922228 x)
   (if (<= x -1.95e-13)
     (*
      (* (- x 2.0) y)
      (/
       x
       (fma
        (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
        x
        47.066876606)))
     (if (<= x 5.5e+26)
       (*
        (fma
         (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
         x
         z)
        (/ (- x 2.0) (fma 313.399215894 x 47.066876606)))
       (* 4.16438922228 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+47) {
		tmp = 4.16438922228 * x;
	} else if (x <= -1.95e-13) {
		tmp = ((x - 2.0) * y) * (x / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else if (x <= 5.5e+26) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((x - 2.0) / fma(313.399215894, x, 47.066876606));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+47)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -1.95e-13)
		tmp = Float64(Float64(Float64(x - 2.0) * y) * Float64(x / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	elseif (x <= 5.5e+26)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(x - 2.0) / fma(313.399215894, x, 47.066876606)));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+47], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -1.95e-13], N[(N[(N[(x - 2.0), $MachinePrecision] * y), $MachinePrecision] * N[(x / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+26], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e47 or 5.4999999999999997e26 < x

   1. Initial program 6.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 10.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 97.9

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 97.9%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -1.05e47 < x < -1.95000000000000002e-13

   1. Initial program 91.5%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot x}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      2. associate-/l* N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(x - 2\right)\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right)} \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \left(\color{blue}{\left(x - 2\right)} \cdot y\right) \cdot \frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \color{blue}{\frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      8. +-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) + \frac{23533438303}{500000000}}} \]

      9. *-commutative N/A

         \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) \cdot x} + \frac{23533438303}{500000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\color{blue}{\mathsf{fma}\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right), x, \frac{23533438303}{500000000}\right)}} \]

      11. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) + \frac{156699607947}{500000000}}, x, \frac{23533438303}{500000000}\right)} \]

      12. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right) \cdot x} + \frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right), x, \frac{156699607947}{500000000}\right)}, x, \frac{23533438303}{500000000}\right)} \]

      14. +-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \left(\frac{216700011257}{5000000000} + x\right) + \frac{263505074721}{1000000000}}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. *-commutative N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left(\frac{216700011257}{5000000000} + x\right) \cdot x} + \frac{263505074721}{1000000000}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      16. lower-fma.f64 N/A

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right)}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      17. lower-+.f64 60.7

          \[\leadsto \left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{43.3400022514 + x}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 60.7%

      \[\leadsto \color{blue}{\left(\left(x - 2\right) \cdot y\right) \cdot \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   if -1.95000000000000002e-13 < x < 5.4999999999999997e26

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\color{blue}{\frac{156699607947}{500000000}}, x, \frac{23533438303}{500000000}\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 93.4%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\color{blue}{313.399215894}, x, 47.066876606\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 92.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900000000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -900000000.0) (not (<= x 2.0)))
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (*
    (fma
     (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
     x
     z)
    (-
     (* (fma -1.787568985856513 x 0.3041881842569256) x)
     0.0424927283095952))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -900000000.0) || !(x <= 2.0)) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -900000000.0) || !(x <= 2.0))
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	else
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -900000000.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(-1.787568985856513 * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9e8 or 2 < x

   1. Initial program 18.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot x \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}}\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{13764240537310136880149}{125000000000000000000}}}{x}\right) \cdot x \]

      6. lower-/.f64 86.9

         \[\leadsto \left(4.16438922228 - \color{blue}{\frac{110.1139242984811}{x}}\right) \cdot x \]

   5. Applied rewrites 86.9%

      \[\leadsto \color{blue}{\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x} \]

   if -9e8 < x < 2

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) \cdot x} - \frac{1000000000}{23533438303}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\left(\frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x + \frac{168466327098500000000}{553822718361107519809}\right)} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. lower-fma.f64 96.1

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right)} \cdot x - 0.0424927283095952\right) \]

   7. Applied rewrites 96.1%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -900000000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900000000:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -900000000.0)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 2e+22)
     (*
      (fma
       (+ (* (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x) y)
       x
       z)
      (- (* 0.3041881842569256 x) 0.0424927283095952))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -900000000.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 2e+22) {
		tmp = fma(((fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416) * x) + y), x, z) * ((0.3041881842569256 * x) - 0.0424927283095952);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -900000000.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 2e+22)
		tmp = Float64(fma(Float64(Float64(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416) * x) + y), x, z) * Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -900000000.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2e+22], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e8

   1. Initial program 15.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot x \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}}\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{13764240537310136880149}{125000000000000000000}}}{x}\right) \cdot x \]

      6. lower-/.f64 87.7

         \[\leadsto \left(4.16438922228 - \color{blue}{\frac{110.1139242984811}{x}}\right) \cdot x \]

   5. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x} \]

   if -9e8 < x < 2e22

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]

      2. lower-*.f64 92.7

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{0.3041881842569256 \cdot x} - 0.0424927283095952\right) \]

   7. Applied rewrites 92.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(0.3041881842569256 \cdot x - 0.0424927283095952\right)} \]
   8. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right) \cdot x + y}, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right) \cdot x + y}, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      3. lower-*.f64 92.7

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right) \cdot x} + y, x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \]

      4. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{104109730557}{25000000000} \cdot x + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{393497462077}{5000000000} + \color{blue}{x \cdot \frac{104109730557}{25000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{393497462077}{5000000000} + \color{blue}{x \cdot \frac{104109730557}{25000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{x \cdot \frac{104109730557}{25000000000}} + \frac{393497462077}{5000000000}, x, \frac{4297481763}{31250000}\right) \cdot x + y, x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      10. lower-fma.f64 92.7

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right)}, x, 137.519416416\right) \cdot x + y, x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \]

   9. Applied rewrites 92.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right) \cdot x + y}, x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \]

   if 2e22 < x

   1. Initial program 14.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 15.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 93.5

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 93.5%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 92.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900000000:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -900000000.0)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 2e+22)
     (*
      (fma
       (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
       x
       z)
      (- (* 0.3041881842569256 x) 0.0424927283095952))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -900000000.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 2e+22) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((0.3041881842569256 * x) - 0.0424927283095952);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -900000000.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 2e+22)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -900000000.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2e+22], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e8

   1. Initial program 15.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot x \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}}\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{13764240537310136880149}{125000000000000000000}}}{x}\right) \cdot x \]

      6. lower-/.f64 87.7

         \[\leadsto \left(4.16438922228 - \color{blue}{\frac{110.1139242984811}{x}}\right) \cdot x \]

   5. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x} \]

   if -9e8 < x < 2e22

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]

      2. lower-*.f64 92.7

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{0.3041881842569256 \cdot x} - 0.0424927283095952\right) \]

   7. Applied rewrites 92.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(0.3041881842569256 \cdot x - 0.0424927283095952\right)} \]

   if 2e22 < x

   1. Initial program 14.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 15.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 93.5

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 93.5%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 92.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900000000:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -900000000.0)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 2e+22)
     (*
      (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
      (- (* 0.3041881842569256 x) 0.0424927283095952))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -900000000.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 2e+22) {
		tmp = fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * ((0.3041881842569256 * x) - 0.0424927283095952);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -900000000.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 2e+22)
		tmp = Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -900000000.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2e+22], N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e8

   1. Initial program 15.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot x \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}}\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{13764240537310136880149}{125000000000000000000}}}{x}\right) \cdot x \]

      6. lower-/.f64 87.7

         \[\leadsto \left(4.16438922228 - \color{blue}{\frac{110.1139242984811}{x}}\right) \cdot x \]

   5. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x} \]

   if -9e8 < x < 2e22

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]

      2. lower-*.f64 92.7

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{0.3041881842569256 \cdot x} - 0.0424927283095952\right) \]

   7. Applied rewrites 92.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(0.3041881842569256 \cdot x - 0.0424927283095952\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 92.7%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{78.6994924154}, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \]

   if 2e22 < x

   1. Initial program 14.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 15.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 93.5

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 93.5%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 91.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900000000:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -900000000.0)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 2e+22)
     (*
      (fma (fma 137.519416416 x y) x z)
      (- (* 0.3041881842569256 x) 0.0424927283095952))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -900000000.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 2e+22) {
		tmp = fma(fma(137.519416416, x, y), x, z) * ((0.3041881842569256 * x) - 0.0424927283095952);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -900000000.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 2e+22)
		tmp = Float64(fma(fma(137.519416416, x, y), x, z) * Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -900000000.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2e+22], N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e8

   1. Initial program 15.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot x \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}}\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{13764240537310136880149}{125000000000000000000}}}{x}\right) \cdot x \]

      6. lower-/.f64 87.7

         \[\leadsto \left(4.16438922228 - \color{blue}{\frac{110.1139242984811}{x}}\right) \cdot x \]

   5. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x} \]

   if -9e8 < x < 2e22

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]

      2. lower-*.f64 92.7

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{0.3041881842569256 \cdot x} - 0.0424927283095952\right) \]

   7. Applied rewrites 92.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(0.3041881842569256 \cdot x - 0.0424927283095952\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{4297481763}{31250000}}, x, y\right), x, z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 92.3%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{137.519416416}, x, y\right), x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \]

   if 2e22 < x

   1. Initial program 14.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 15.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 93.5

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 93.5%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 89.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -900000000:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -900000000.0)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 2e+22)
     (* (fma y x z) (- (* 0.3041881842569256 x) 0.0424927283095952))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -900000000.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 2e+22) {
		tmp = fma(y, x, z) * ((0.3041881842569256 * x) - 0.0424927283095952);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -900000000.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 2e+22)
		tmp = Float64(fma(y, x, z) * Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -900000000.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2e+22], N[(N[(y * x + z), $MachinePrecision] * N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9e8

   1. Initial program 15.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot x \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}}\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{13764240537310136880149}{125000000000000000000}}}{x}\right) \cdot x \]

      6. lower-/.f64 87.7

         \[\leadsto \left(4.16438922228 - \color{blue}{\frac{110.1139242984811}{x}}\right) \cdot x \]

   5. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x} \]

   if -9e8 < x < 2e22

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \left(x - 2\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right) \cdot \frac{x - 2}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}} \]

   4. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right)} \]

      2. lower-*.f64 92.7

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\color{blue}{0.3041881842569256 \cdot x} - 0.0424927283095952\right) \]

   7. Applied rewrites 92.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(0.3041881842569256 \cdot x - 0.0424927283095952\right)} \]

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(z + x \cdot y\right)} \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y + z\right)} \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      2. *-commutative N/A

         \[\leadsto \left(\color{blue}{y \cdot x} + z\right) \cdot \left(\frac{168466327098500000000}{553822718361107519809} \cdot x - \frac{1000000000}{23533438303}\right) \]

      3. lower-fma.f64 85.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z\right)} \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \]

   10. Applied rewrites 85.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z\right)} \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \]

   if 2e22 < x

   1. Initial program 14.2%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 15.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 93.5

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 93.5%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 77.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8600 \lor \neg \left(x \leq 1.3 \cdot 10^{+20}\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 0.3041881842569256, x, -0.0424927283095952 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8600.0) (not (<= x 1.3e+20)))
   (* 4.16438922228 x)
   (fma (* z 0.3041881842569256) x (* -0.0424927283095952 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8600.0) || !(x <= 1.3e+20)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = fma((z * 0.3041881842569256), x, (-0.0424927283095952 * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8600.0) || !(x <= 1.3e+20))
		tmp = Float64(4.16438922228 * x);
	else
		tmp = fma(Float64(z * 0.3041881842569256), x, Float64(-0.0424927283095952 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8600.0], N[Not[LessEqual[x, 1.3e+20]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(N[(z * 0.3041881842569256), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8600 or 1.3e20 < x

   1. Initial program 16.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 20.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 88.0

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 88.0%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -8600 < x < 1.3e20

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right)} \cdot \left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left({x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right) + z\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left({x}^{2}, \frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right), z\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      7. unpow2 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\color{blue}{x \cdot x}, \frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\color{blue}{x \cdot x}, \frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right) + \frac{4297481763}{31250000}}, z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{\left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right) \cdot x} + \frac{4297481763}{31250000}, z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      11. lower-fma.f64 N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{\mathsf{fma}\left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x, x, \frac{4297481763}{31250000}\right)}, z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      12. +-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\color{blue}{\frac{104109730557}{25000000000} \cdot x + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      14. +-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), z\right)}{\color{blue}{x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) + \frac{23533438303}{500000000}}} \]

      15. *-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), z\right)}{\color{blue}{\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) \cdot x} + \frac{23533438303}{500000000}} \]

   5. Applied rewrites 74.0%

      \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1000000000}{23533438303} \cdot z + \color{blue}{x \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.6%

      \[\leadsto \mathsf{fma}\left(z \cdot 0.3041881842569256, \color{blue}{x}, -0.0424927283095952 \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8600 \lor \neg \left(x \leq 1.3 \cdot 10^{+20}\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 0.3041881842569256, x, -0.0424927283095952 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 77.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8600:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 0.3041881842569256, x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8600.0)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 1.3e+20)
     (fma (* z 0.3041881842569256) x (* -0.0424927283095952 z))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8600.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 1.3e+20) {
		tmp = fma((z * 0.3041881842569256), x, (-0.0424927283095952 * z));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8600.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 1.3e+20)
		tmp = fma(Float64(z * 0.3041881842569256), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8600.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 1.3e+20], N[(N[(z * 0.3041881842569256), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8600

   1. Initial program 17.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right) \cdot x} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot x \]

      4. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{\frac{13764240537310136880149}{125000000000000000000} \cdot 1}{x}}\right) \cdot x \]

      5. metadata-eval N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\color{blue}{\frac{13764240537310136880149}{125000000000000000000}}}{x}\right) \cdot x \]

      6. lower-/.f64 85.0

         \[\leadsto \left(4.16438922228 - \color{blue}{\frac{110.1139242984811}{x}}\right) \cdot x \]

   5. Applied rewrites 85.0%

      \[\leadsto \color{blue}{\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x} \]

   if -8600 < x < 1.3e20

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right) \cdot \left(x - 2\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right) \cdot \left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x - 2\right)} \cdot \left(z + {x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right)\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left({x}^{2} \cdot \left(\frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right)\right) + z\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left({x}^{2}, \frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right), z\right)}}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      7. unpow2 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\color{blue}{x \cdot x}, \frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\color{blue}{x \cdot x}, \frac{4297481763}{31250000} + x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{x \cdot \left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right) + \frac{4297481763}{31250000}}, z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      10. *-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{\left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x\right) \cdot x} + \frac{4297481763}{31250000}, z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      11. lower-fma.f64 N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \color{blue}{\mathsf{fma}\left(\frac{393497462077}{5000000000} + \frac{104109730557}{25000000000} \cdot x, x, \frac{4297481763}{31250000}\right)}, z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      12. +-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\color{blue}{\frac{104109730557}{25000000000} \cdot x + \frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      13. lower-fma.f64 N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), z\right)}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} \]

      14. +-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), z\right)}{\color{blue}{x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) + \frac{23533438303}{500000000}}} \]

      15. *-commutative N/A

          \[\leadsto \frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), z\right)}{\color{blue}{\left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right) \cdot x} + \frac{23533438303}{500000000}} \]

   5. Applied rewrites 74.0%

      \[\leadsto \color{blue}{\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(x \cdot x, \mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{-1000000000}{23533438303} \cdot z + \color{blue}{x \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 64.6%

      \[\leadsto \mathsf{fma}\left(z \cdot 0.3041881842569256, \color{blue}{x}, -0.0424927283095952 \cdot z\right) \]

   if 1.3e20 < x

   1. Initial program 15.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 17.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 91.9

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 91.9%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 76.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8600 \lor \neg \left(x \leq 1.3 \cdot 10^{+20}\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8600.0) (not (<= x 1.3e+20)))
   (* 4.16438922228 x)
   (* (* 0.0212463641547976 z) (- x 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8600.0) || !(x <= 1.3e+20)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8600.0d0)) .or. (.not. (x <= 1.3d+20))) then
        tmp = 4.16438922228d0 * x
    else
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8600.0) || !(x <= 1.3e+20)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8600.0) or not (x <= 1.3e+20):
		tmp = 4.16438922228 * x
	else:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8600.0) || !(x <= 1.3e+20))
		tmp = Float64(4.16438922228 * x);
	else
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8600.0) || ~((x <= 1.3e+20)))
		tmp = 4.16438922228 * x;
	else
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8600.0], N[Not[LessEqual[x, 1.3e+20]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8600 or 1.3e20 < x

   1. Initial program 16.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 20.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 88.0

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 88.0%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -8600 < x < 1.3e20

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x \cdot x - 4\right) \cdot \color{blue}{\left(\frac{500000000}{23533438303} \cdot z\right)}}{2 + x} \]
   6. Step-by-step derivation

      1. lower-*.f64 64.4

         \[\leadsto \frac{\left(x \cdot x - 4\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z\right)}}{2 + x} \]

   7. Applied rewrites 64.4%

      \[\leadsto \frac{\left(x \cdot x - 4\right) \cdot \color{blue}{\left(0.0212463641547976 \cdot z\right)}}{2 + x} \]

   9. Applied rewrites 64.4%

      \[\leadsto \color{blue}{\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8600 \lor \neg \left(x \leq 1.3 \cdot 10^{+20}\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 77.0% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8600 \lor \neg \left(x \leq 600000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8600.0) (not (<= x 600000.0)))
   (* 4.16438922228 x)
   (* -0.0424927283095952 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8600.0) || !(x <= 600000.0)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = -0.0424927283095952 * z;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8600.0d0)) .or. (.not. (x <= 600000.0d0))) then
        tmp = 4.16438922228d0 * x
    else
        tmp = (-0.0424927283095952d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8600.0) || !(x <= 600000.0)) {
		tmp = 4.16438922228 * x;
	} else {
		tmp = -0.0424927283095952 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8600.0) or not (x <= 600000.0):
		tmp = 4.16438922228 * x
	else:
		tmp = -0.0424927283095952 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8600.0) || !(x <= 600000.0))
		tmp = Float64(4.16438922228 * x);
	else
		tmp = Float64(-0.0424927283095952 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8600.0) || ~((x <= 600000.0)))
		tmp = 4.16438922228 * x;
	else
		tmp = -0.0424927283095952 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8600.0], N[Not[LessEqual[x, 600000.0]], $MachinePrecision]], N[(4.16438922228 * x), $MachinePrecision], N[(-0.0424927283095952 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8600 or 6e5 < x

   1. Initial program 18.8%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   4. Applied rewrites 22.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x - 4\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}{2 + x}} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000} \cdot x} \]
   6. Step-by-step derivation

      1. lower-*.f64 85.9

         \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   7. Applied rewrites 85.9%

      \[\leadsto \color{blue}{4.16438922228 \cdot x} \]

   if -8600 < x < 6e5

   1. Initial program 99.1%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 65.6

         \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

   5. Applied rewrites 65.6%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8600 \lor \neg \left(x \leq 600000\right):\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 35.3% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ -0.0424927283095952 \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* -0.0424927283095952 z))

C

double code(double x, double y, double z) {
	return -0.0424927283095952 * z;
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (-0.0424927283095952d0) * z
end function

Java

public static double code(double x, double y, double z) {
	return -0.0424927283095952 * z;
}

Python

def code(x, y, z):
	return -0.0424927283095952 * z

Julia

function code(x, y, z)
	return Float64(-0.0424927283095952 * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -0.0424927283095952 * z;
end

Wolfram

code[x_, y_, z_] := N[(-0.0424927283095952 * z), $MachinePrecision]

Derivation

1. Initial program 60.8%

   \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]
4. Step-by-step derivation

   1. lower-*.f64 35.7

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]

5. Applied rewrites 35.7%

   \[\leadsto \color{blue}{-0.0424927283095952 \cdot z} \]
6. Add Preprocessing

Developer Target 1: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024358 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -332612872587000500000000000000000000000000000000000000000000000) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000) (if (< x 94299917145546730000000000000000000000000000000000000000) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (+ (* (+ (+ (* 263505074721/1000000000 x) (+ (* 216700011257/5000000000 (* x x)) (* x (* x x)))) 156699607947/500000000) x) 23533438303/500000000))) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000))))

  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))