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

Percentage Accurate: 59.1% → 98.8%

Time: 7.6s

Alternatives: 26

Speedup: 4.1×

Specification

Math

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

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: 59.1% accurate, 1.0× speedup

Math

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

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: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}{47.066876606}\right) \cdot 47.066876606\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{t\_0}, \left(x - 2\right) \cdot \frac{z}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (+
          1.0
          (/
           (*
            (fma
             (fma (- x -43.3400022514) x 263.505074721)
             x
             313.399215894)
            x)
           47.066876606))
         47.066876606)))
  (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))
       2e+300)
    (fma
     (fma
      (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
      x
      y)
     (/ (* (- x 2.0) x) t_0)
     (* (- x 2.0) (/ z t_0)))
    (-
     (* x 4.16438922228)
     (*
      (-
       (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
       -110.1139242984811)
      1.0)))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 + ((fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) / 47.066876606)) * 47.066876606;
	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)) <= 2e+300) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), (((x - 2.0) * x) / t_0), ((x - 2.0) * (z / t_0)));
	} else {
		tmp = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 + Float64(Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) / 47.066876606)) * 47.066876606)
	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)) <= 2e+300)
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), Float64(Float64(Float64(x - 2.0) * x) / t_0), Float64(Float64(x - 2.0) * Float64(z / t_0)));
	else
		tmp = Float64(Float64(x * 4.16438922228) - Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 + N[(N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision] / 47.066876606), $MachinePrecision]), $MachinePrecision] * 47.066876606), $MachinePrecision]}, 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], 2e+300], N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * N[(N[(N[(x - 2.0), $MachinePrecision] * x), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(x - 2.0), $MachinePrecision] * N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] - N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]), $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))) < 2.0000000000000001e300

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

      1. lift-fma.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. +-commutative N/A

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

      4. sum-to-mult N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}}, \left(x - 2\right) \cdot \frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)}\right) \]

      5. lower-unsound-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}}, \left(x - 2\right) \cdot \frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)}\right) \]

      6. lower-unsound-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right)} \cdot \frac{23533438303}{500000000}}, \left(x - 2\right) \cdot \frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)}\right) \]

      7. lower-unsound-/.f64 62.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}{47.066876606}}\right) \cdot 47.066876606}, \left(x - 2\right) \cdot \frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\right) \]

   5. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}{47.066876606}\right) \cdot 47.066876606}}, \left(x - 2\right) \cdot \frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\right) \]
   6. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}, \left(x - 2\right) \cdot \frac{z}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}}}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}, \left(x - 2\right) \cdot \frac{z}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x} + \frac{23533438303}{500000000}}\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}, \left(x - 2\right) \cdot \frac{z}{\color{blue}{\frac{23533438303}{500000000} + \mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}}\right) \]

      4. sum-to-mult N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}, \left(x - 2\right) \cdot \frac{z}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}}\right) \]

      5. lower-unsound-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}, \left(x - 2\right) \cdot \frac{z}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}}\right) \]

      6. lower-unsound-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right) \cdot \frac{23533438303}{500000000}}, \left(x - 2\right) \cdot \frac{z}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - \frac{-216700011257}{5000000000}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right) \cdot x}{\frac{23533438303}{500000000}}\right)} \cdot \frac{23533438303}{500000000}}\right) \]

      7. lower-unsound-/.f64 62.4%

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}{47.066876606}\right) \cdot 47.066876606}, \left(x - 2\right) \cdot \frac{z}{\left(1 + \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}{47.066876606}}\right) \cdot 47.066876606}\right) \]

   7. Applied rewrites 62.4%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}{47.066876606}\right) \cdot 47.066876606}, \left(x - 2\right) \cdot \frac{z}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}{47.066876606}\right) \cdot 47.066876606}}\right) \]

   if 2.0000000000000001e300 < (/.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 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{t\_0}, \left(x - 2\right) \cdot \frac{z}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (fma
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x
         47.066876606)))
  (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))
       2e+300)
    (fma
     (fma
      (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
      x
      y)
     (/ (* (- x 2.0) x) t_0)
     (* (- x 2.0) (/ z t_0)))
    (-
     (* x 4.16438922228)
     (*
      (-
       (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
       -110.1139242984811)
      1.0)))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	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)) <= 2e+300) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), (((x - 2.0) * x) / t_0), ((x - 2.0) * (z / t_0)));
	} else {
		tmp = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	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)) <= 2e+300)
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), Float64(Float64(Float64(x - 2.0) * x) / t_0), Float64(Float64(x - 2.0) * Float64(z / t_0)));
	else
		tmp = Float64(Float64(x * 4.16438922228) - Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, 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], 2e+300], N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * N[(N[(N[(x - 2.0), $MachinePrecision] * x), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(x - 2.0), $MachinePrecision] * N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] - N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]), $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))) < 2.0000000000000001e300

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   if 2.0000000000000001e300 < (/.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 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.4% accurate, 0.5× speedup

Math

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

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))
     INFINITY)
  (*
   (/
    (fma
     (fma
      (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
      x
      y)
     x
     z)
    (fma
     (fma (fma (- x -43.3400022514) 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)) <= ((double) INFINITY)) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((x - -43.3400022514), 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)) <= Inf)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(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], Infinity], 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[(x - -43.3400022514), $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))) < +inf.0

   1. Initial program 59.1%

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

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

   3. Applied rewrites 61.6%

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

   if +inf.0 < (/.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 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \left(x \cdot \frac{-104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 44.3%

      \[\leadsto -1 \cdot \left(x \cdot -4.16438922228\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \frac{-104109730557}{25000000000}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \frac{-104109730557}{25000000000}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\frac{-104109730557}{25000000000} \cdot x\right) \]

      5. distribute-lft-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 44.3%

         \[\leadsto \left(--4.16438922228\right) \cdot x \]

   9. Applied rewrites 44.3%

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

Alternative 4: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;x \cdot 4.16438922228 - \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;\left(y \cdot x + z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 240000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(263.505074721, x, 313.399215894\right) \cdot x - -47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x -10000000000000.0)
  (-
   (* x 4.16438922228)
   (*
    (-
     (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
     -110.1139242984811)
    1.0))
  (if (<= x -5.2e-6)
    (*
     (+ (* y x) z)
     (/
      (- x 2.0)
      (fma
       (fma
        (fma (- x -43.3400022514) x 263.505074721)
        x
        313.399215894)
       x
       47.066876606)))
    (if (<= x 240000000.0)
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (*
            (+
             (* (+ (* x 4.16438922228) 78.6994924154) x)
             137.519416416)
            x)
           y)
          x)
         z))
       (- (* (fma 263.505074721 x 313.399215894) x) -47.066876606))
      (*
       (+
        4.16438922228
        (*
         -1.0
         (/
          (+
           101.7851458539211
           (*
            -1.0
            (/
             (+
              3451.550173699799
              (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
             x)))
          x)))
       (- x 2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0);
	} else if (x <= -5.2e-6) {
		tmp = ((y * x) + z) * ((x - 2.0) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else if (x <= 240000000.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((fma(263.505074721, x, 313.399215894) * x) - -47.066876606);
	} else {
		tmp = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(x * 4.16438922228) - Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0));
	elseif (x <= -5.2e-6)
		tmp = Float64(Float64(Float64(y * x) + z) * Float64(Float64(x - 2.0) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	elseif (x <= 240000000.0)
		tmp = 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(fma(263.505074721, x, 313.399215894) * x) - -47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -10000000000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e-6], N[(N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 240000000.0], 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[(263.505074721 * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e13

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -1e13 < x < -5.2000000000000002e-6

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   8. Applied rewrites 53.3%

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

   if -5.2000000000000002e-6 < x < 2.4e8

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(\color{blue}{\frac{263505074721}{1000000000}}, x, 313.399215894\right) \cdot x - -47.066876606} \]
   5. Step-by-step derivation

   6. Applied rewrites 51.8%

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

   if 2.4e8 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + \color{blue}{-1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}}\right) \cdot \left(x - 2\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + -1 \cdot \color{blue}{\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{\color{blue}{x}}\right) \cdot \left(x - 2\right) \]

   8. Applied rewrites 47.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;\left(y \cdot x + z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 240000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -10000000000000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x -5.2e-6)
      (*
       (+ (* y x) z)
       (/
        (- x 2.0)
        (fma
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x
         47.066876606)))
      (if (<= x 240000000.0)
        (*
         (/
          (fma
           (fma
            (fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
            x
            y)
           x
           z)
          (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
         (- x 2.0))
        (fma x 4.16438922228 (- t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= -5.2e-6) {
		tmp = ((y * x) + z) * ((x - 2.0) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else if (x <= 240000000.0) {
		tmp = (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= -5.2e-6)
		tmp = Float64(Float64(Float64(y * x) + z) * Float64(Float64(x - 2.0) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	elseif (x <= 240000000.0)
		tmp = Float64(Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -10000000000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, -5.2e-6], N[(N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 240000000.0], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e13

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -1e13 < x < -5.2000000000000002e-6

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   8. Applied rewrites 53.3%

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

   if -5.2000000000000002e-6 < x < 2.4e8

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{263505074721}{1000000000}}, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 51.9%

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

   if 2.4e8 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;x \cdot 4.16438922228 - \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;\left(y \cdot x + z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 240000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x -10000000000000.0)
  (-
   (* x 4.16438922228)
   (*
    (-
     (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
     -110.1139242984811)
    1.0))
  (if (<= x -5.2e-6)
    (*
     (+ (* y x) z)
     (/
      (- x 2.0)
      (fma
       (fma
        (fma (- x -43.3400022514) x 263.505074721)
        x
        313.399215894)
       x
       47.066876606)))
    (if (<= x 240000000.0)
      (*
       (/
        (fma
         (fma
          (fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
          x
          y)
         x
         z)
        (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
       (- x 2.0))
      (*
       (+
        4.16438922228
        (*
         -1.0
         (/
          (+
           101.7851458539211
           (*
            -1.0
            (/
             (+
              3451.550173699799
              (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
             x)))
          x)))
       (- x 2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0);
	} else if (x <= -5.2e-6) {
		tmp = ((y * x) + z) * ((x - 2.0) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else if (x <= 240000000.0) {
		tmp = (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(x * 4.16438922228) - Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0));
	elseif (x <= -5.2e-6)
		tmp = Float64(Float64(Float64(y * x) + z) * Float64(Float64(x - 2.0) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	elseif (x <= 240000000.0)
		tmp = Float64(Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -10000000000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e-6], N[(N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 240000000.0], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e13

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -1e13 < x < -5.2000000000000002e-6

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   8. Applied rewrites 53.3%

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

   if -5.2000000000000002e-6 < x < 2.4e8

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{263505074721}{1000000000}}, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 51.9%

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

   if 2.4e8 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + \color{blue}{-1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}}\right) \cdot \left(x - 2\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + -1 \cdot \color{blue}{\frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{x}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} + -1 \cdot \frac{\frac{12723143231740136880149}{125000000000000000000} + -1 \cdot \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + -1 \cdot \frac{\frac{387732519225574910908939577061312055388407301}{3125000000000000000000000000000000000000} + -1 \cdot y}{x}}{x}}{\color{blue}{x}}\right) \cdot \left(x - 2\right) \]

   8. Applied rewrites 47.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;\left(y \cdot x + z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 12000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -10000000000000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x -5.2e-6)
      (*
       (+ (* y x) z)
       (/
        (- x 2.0)
        (fma
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x
         47.066876606)))
      (if (<= x 12000000.0)
        (/
         (*
          (- x 2.0)
          (+
           (*
            (+
             (*
              (+
               (* (+ (* x 4.16438922228) 78.6994924154) x)
               137.519416416)
              x)
             y)
            x)
           z))
         (+ (* 313.399215894 x) 47.066876606))
        (fma x 4.16438922228 (- t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= -5.2e-6) {
		tmp = ((y * x) + z) * ((x - 2.0) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else if (x <= 12000000.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= -5.2e-6)
		tmp = Float64(Float64(Float64(y * x) + z) * Float64(Float64(x - 2.0) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	elseif (x <= 12000000.0)
		tmp = 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(313.399215894 * x) + 47.066876606));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -10000000000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, -5.2e-6], N[(N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12000000.0], 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[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e13

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -1e13 < x < -5.2000000000000002e-6

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   8. Applied rewrites 53.3%

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

   if -5.2000000000000002e-6 < x < 1.2e7

   1. Initial program 59.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{\frac{156699607947}{500000000}} \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.8%

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

   if 1.2e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 96.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-6}:\\ \;\;\;\;\left(y \cdot x + z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 12000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -10000000000000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x -5.2e-6)
      (*
       (+ (* y x) z)
       (/
        (- x 2.0)
        (fma
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x
         47.066876606)))
      (if (<= x 12000000.0)
        (*
         (/
          (fma
           (fma
            (fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
            x
            y)
           x
           z)
          (fma 313.399215894 x 47.066876606))
         (- x 2.0))
        (fma x 4.16438922228 (- t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= -5.2e-6) {
		tmp = ((y * x) + z) * ((x - 2.0) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else if (x <= 12000000.0) {
		tmp = (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= -5.2e-6)
		tmp = Float64(Float64(Float64(y * x) + z) * Float64(Float64(x - 2.0) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	elseif (x <= 12000000.0)
		tmp = Float64(Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -10000000000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, -5.2e-6], N[(N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12000000.0], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e13

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -1e13 < x < -5.2000000000000002e-6

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   8. Applied rewrites 53.3%

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

   if -5.2000000000000002e-6 < x < 1.2e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\color{blue}{\frac{156699607947}{500000000}}, x, 47.066876606\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 51.8%

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

   if 1.2e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 95.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq 16000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x - -47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -10000000000000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x 16000000.0)
      (/
       (* (- x 2.0) (+ (* x y) z))
       (-
        (*
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x)
        -47.066876606))
      (fma x 4.16438922228 (- t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= 16000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) - -47.066876606);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= 16000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * y) + z)) / Float64(Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) - -47.066876606));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -10000000000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 16000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e13

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -1e13 < x < 1.6e7

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   if 1.6e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 95.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -10000000000000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq 16000000:\\ \;\;\;\;\left(y \cdot x + z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -10000000000000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x 16000000.0)
      (*
       (+ (* y x) z)
       (/
        (- x 2.0)
        (fma
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x
         47.066876606)))
      (fma x 4.16438922228 (- t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -10000000000000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= 16000000.0) {
		tmp = ((y * x) + z) * ((x - 2.0) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -10000000000000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= 16000000.0)
		tmp = Float64(Float64(Float64(y * x) + z) * Float64(Float64(x - 2.0) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -10000000000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 16000000.0], N[(N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e13

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -1e13 < x < 1.6e7

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   8. Applied rewrites 53.3%

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

   if 1.6e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 95.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -51000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 12000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -51000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x -1.5e-7)
      (/
       (* x (* y (- x 2.0)))
       (+
        (*
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x)
        47.066876606))
      (if (<= x 12000000.0)
        (/
         (*
          (- x 2.0)
          (+
           (*
            (+
             (*
              (+
               (* (+ (* x 4.16438922228) 78.6994924154) x)
               137.519416416)
              x)
             y)
            x)
           z))
         47.066876606)
        (fma x 4.16438922228 (- t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -51000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= -1.5e-7) {
		tmp = (x * (y * (x - 2.0))) / ((fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) + 47.066876606);
	} else if (x <= 12000000.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / 47.066876606;
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -51000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= -1.5e-7)
		tmp = Float64(Float64(x * Float64(y * Float64(x - 2.0))) / Float64(Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) + 47.066876606));
	elseif (x <= 12000000.0)
		tmp = 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)) / 47.066876606);
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -51000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, -1.5e-7], N[(N[(x * N[(y * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12000000.0], 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] / 47.066876606), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -51000

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -51000 < x < -1.4999999999999999e-7

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 16.9%

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

   4. Applied rewrites 16.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 16.9%

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. add-flip N/A

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

      8. metadata-eval N/A

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

      9. lift--.f64 N/A

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

      10. lift-fma.f64 16.9%

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

   6. Applied rewrites 16.9%

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

   if -1.4999999999999999e-7 < x < 1.2e7

   1. Initial program 59.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{\frac{23533438303}{500000000}}} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.6%

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

   if 1.2e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 95.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -51000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 12000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -51000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x -1.5e-7)
      (/
       (* x (* y (- x 2.0)))
       (+
        (*
         (fma
          (fma (- x -43.3400022514) x 263.505074721)
          x
          313.399215894)
         x)
        47.066876606))
      (if (<= x 12000000.0)
        (*
         (/
          (fma
           (fma
            (fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
            x
            y)
           x
           z)
          47.066876606)
         (- x 2.0))
        (fma x 4.16438922228 (- t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -51000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= -1.5e-7) {
		tmp = (x * (y * (x - 2.0))) / ((fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) + 47.066876606);
	} else if (x <= 12000000.0) {
		tmp = (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * (x - 2.0);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -51000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= -1.5e-7)
		tmp = Float64(Float64(x * Float64(y * Float64(x - 2.0))) / Float64(Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) + 47.066876606));
	elseif (x <= 12000000.0)
		tmp = Float64(Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * Float64(x - 2.0));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -51000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, -1.5e-7], N[(N[(x * N[(y * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12000000.0], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -51000

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -51000 < x < -1.4999999999999999e-7

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 16.9%

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

   4. Applied rewrites 16.9%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 16.9%

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. add-flip N/A

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

      8. metadata-eval N/A

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

      9. lift--.f64 N/A

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

      10. lift-fma.f64 16.9%

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

   6. Applied rewrites 16.9%

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

   if -1.4999999999999999e-7 < x < 1.2e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\frac{23533438303}{500000000}}} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 52.7%

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

   if 1.2e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 94.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -51000:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{\left(\left(x - 2\right) \cdot y\right) \cdot x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 12000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -51000.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x -1.5e-7)
      (/
       (* (* (- x 2.0) y) x)
       (fma
        (fma
         (fma (- x -43.3400022514) x 263.505074721)
         x
         313.399215894)
        x
        47.066876606))
      (if (<= x 12000000.0)
        (*
         (/
          (fma
           (fma
            (fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
            x
            y)
           x
           z)
          47.066876606)
         (- x 2.0))
        (fma x 4.16438922228 (- t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -51000.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= -1.5e-7) {
		tmp = (((x - 2.0) * y) * x) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	} else if (x <= 12000000.0) {
		tmp = (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * (x - 2.0);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -51000.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= -1.5e-7)
		tmp = Float64(Float64(Float64(Float64(x - 2.0) * y) * x) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	elseif (x <= 12000000.0)
		tmp = Float64(Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * Float64(x - 2.0));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -51000.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, -1.5e-7], N[(N[(N[(N[(x - 2.0), $MachinePrecision] * y), $MachinePrecision] * x), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12000000.0], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -51000

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -51000 < x < -1.4999999999999999e-7

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 16.9%

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

   4. Applied rewrites 16.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 16.9%

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 16.9%

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

      7. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x - 2\right) \cdot y\right) \cdot x}{\mathsf{Rewrite=>}\left(lift-+.f64, \left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}\right)\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x - 2\right) \cdot y\right) \cdot x}{\mathsf{Rewrite=>}\left(lift-*.f64, \left(\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x\right)\right) + \frac{23533438303}{500000000}} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\left(\left(x - 2\right) \cdot y\right) \cdot x}{\mathsf{Rewrite=>}\left(lower-fma.f64, \left(\mathsf{fma}\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)\right)\right)} \]

   6. Applied rewrites 16.9%

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

   if -1.4999999999999999e-7 < x < 1.2e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\frac{23533438303}{500000000}}} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 52.7%

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

   if 1.2e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 94.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -26:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq 12000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -26.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x 12000000.0)
      (*
       (/
        (fma
         (fma
          (fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
          x
          y)
         x
         z)
        47.066876606)
       (- x 2.0))
      (fma x 4.16438922228 (- t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -26.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= 12000000.0) {
		tmp = (fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * (x - 2.0);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -26.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= 12000000.0)
		tmp = Float64(Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * Float64(x - 2.0));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -26.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 12000000.0], N[(N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -26

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -26 < x < 1.2e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\color{blue}{\frac{23533438303}{500000000}}} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 52.7%

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

   if 1.2e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 93.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -26:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq 16000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{\mathsf{fma}\left(263.505074721, x, 313.399215894\right) \cdot x - -47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -26.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x 16000000.0)
      (/
       (* (- x 2.0) (+ (* x y) z))
       (- (* (fma 263.505074721 x 313.399215894) x) -47.066876606))
      (fma x 4.16438922228 (- t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -26.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= 16000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((fma(263.505074721, x, 313.399215894) * x) - -47.066876606);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -26.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= 16000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * y) + z)) / Float64(Float64(fma(263.505074721, x, 313.399215894) * x) - -47.066876606));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -26.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 16000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -26

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -26 < x < 1.6e7

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{\mathsf{fma}\left(\color{blue}{\frac{263505074721}{1000000000}}, x, 313.399215894\right) \cdot x - -47.066876606} \]
   8. Step-by-step derivation

   9. Applied rewrites 49.0%

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

   if 1.6e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 93.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_0 := \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -30:\\ \;\;\;\;x \cdot 4.16438922228 - t\_0\\ \mathbf{elif}\;x \leq 11000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{313.399215894 \cdot x - -47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -t\_0\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (-
          (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
          -110.1139242984811)
         1.0)))
  (if (<= x -30.0)
    (- (* x 4.16438922228) t_0)
    (if (<= x 11000000.0)
      (/
       (* (- x 2.0) (+ (* x y) z))
       (- (* 313.399215894 x) -47.066876606))
      (fma x 4.16438922228 (- t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0;
	double tmp;
	if (x <= -30.0) {
		tmp = (x * 4.16438922228) - t_0;
	} else if (x <= 11000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	} else {
		tmp = fma(x, 4.16438922228, -t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0.0
	if (x <= -30.0)
		tmp = Float64(Float64(x * 4.16438922228) - t_0);
	elseif (x <= 11000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * y) + z)) / Float64(Float64(313.399215894 * x) - -47.066876606));
	else
		tmp = fma(x, 4.16438922228, Float64(-t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]}, If[LessEqual[x, -30.0], N[(N[(x * 4.16438922228), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 11000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + (-t$95$0)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -30

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -30 < x < 1.1e7

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{\color{blue}{\frac{156699607947}{500000000}} \cdot x - -47.066876606} \]
   8. Step-by-step derivation

   9. Applied rewrites 49.4%

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

   if 1.1e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 93.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 - \left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1\\ \mathbf{if}\;x \leq -30:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 11000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{313.399215894 \cdot x - -47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (-
         (* x 4.16438922228)
         (*
          (-
           (/ (- (/ (- 130977.50649958357 y) x) 3655.1204654076414) x)
           -110.1139242984811)
          1.0))))
  (if (<= x -30.0)
    t_0
    (if (<= x 11000000.0)
      (/
       (* (- x 2.0) (+ (* x y) z))
       (- (* 313.399215894 x) -47.066876606))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0);
	double tmp;
	if (x <= -30.0) {
		tmp = t_0;
	} else if (x <= 11000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((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 = (x * 4.16438922228d0) - ((((((130977.50649958357d0 - y) / x) - 3655.1204654076414d0) / x) - (-110.1139242984811d0)) * 1.0d0)
    if (x <= (-30.0d0)) then
        tmp = t_0
    else if (x <= 11000000.0d0) then
        tmp = ((x - 2.0d0) * ((x * y) + z)) / ((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 = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0);
	double tmp;
	if (x <= -30.0) {
		tmp = t_0;
	} else if (x <= 11000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0)
	tmp = 0
	if x <= -30.0:
		tmp = t_0
	elif x <= 11000000.0:
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * 4.16438922228) - Float64(Float64(Float64(Float64(Float64(Float64(130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0))
	tmp = 0.0
	if (x <= -30.0)
		tmp = t_0;
	elseif (x <= 11000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * y) + z)) / Float64(Float64(313.399215894 * x) - -47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * 4.16438922228) - ((((((130977.50649958357 - y) / x) - 3655.1204654076414) / x) - -110.1139242984811) * 1.0);
	tmp = 0.0;
	if (x <= -30.0)
		tmp = t_0;
	elseif (x <= 11000000.0)
		tmp = ((x - 2.0) * ((x * y) + z)) / ((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[(x * 4.16438922228), $MachinePrecision] - N[(N[(N[(N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision] - -110.1139242984811), $MachinePrecision] * 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -30.0], t$95$0, If[LessEqual[x, 11000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -30 or 1.1e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   8. Applied rewrites 47.1%

      \[\leadsto x \cdot 4.16438922228 - \color{blue}{\left(\frac{\frac{130977.50649958357 - y}{x} - 3655.1204654076414}{x} - -110.1139242984811\right) \cdot 1} \]

   if -30 < x < 1.1e7

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{\color{blue}{\frac{156699607947}{500000000}} \cdot x - -47.066876606} \]
   8. Step-by-step derivation

   9. Applied rewrites 49.4%

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

Alternative 18: 90.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -40:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811 + \frac{\frac{130977.50649958357}{x} - 3655.1204654076414}{x}}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 22000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{313.399215894 \cdot x - -47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x -40.0)
  (*
   (-
    4.16438922228
    (/
     (+
      110.1139242984811
      (/ (- (/ 130977.50649958357 x) 3655.1204654076414) x))
     x))
   x)
  (if (<= x 22000000.0)
    (/
     (* (- x 2.0) (+ (* x y) z))
     (- (* 313.399215894 x) -47.066876606))
    (* (- 4.16438922228 (* 101.7851458539211 (/ 1.0 x))) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -40.0) {
		tmp = (4.16438922228 - ((110.1139242984811 + (((130977.50649958357 / x) - 3655.1204654076414) / x)) / x)) * x;
	} else if (x <= 22000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	} else {
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (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 <= (-40.0d0)) then
        tmp = (4.16438922228d0 - ((110.1139242984811d0 + (((130977.50649958357d0 / x) - 3655.1204654076414d0) / x)) / x)) * x
    else if (x <= 22000000.0d0) then
        tmp = ((x - 2.0d0) * ((x * y) + z)) / ((313.399215894d0 * x) - (-47.066876606d0))
    else
        tmp = (4.16438922228d0 - (101.7851458539211d0 * (1.0d0 / x))) * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -40.0) {
		tmp = (4.16438922228 - ((110.1139242984811 + (((130977.50649958357 / x) - 3655.1204654076414) / x)) / x)) * x;
	} else if (x <= 22000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	} else {
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -40.0:
		tmp = (4.16438922228 - ((110.1139242984811 + (((130977.50649958357 / x) - 3655.1204654076414) / x)) / x)) * x
	elif x <= 22000000.0:
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606)
	else:
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -40.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(110.1139242984811 + Float64(Float64(Float64(130977.50649958357 / x) - 3655.1204654076414) / x)) / x)) * x);
	elseif (x <= 22000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * y) + z)) / Float64(Float64(313.399215894 * x) - -47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(101.7851458539211 * Float64(1.0 / x))) * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -40.0)
		tmp = (4.16438922228 - ((110.1139242984811 + (((130977.50649958357 / x) - 3655.1204654076414) / x)) / x)) * x;
	elseif (x <= 22000000.0)
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	else
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -40.0], N[(N[(4.16438922228 - N[(N[(110.1139242984811 + N[(N[(N[(130977.50649958357 / x), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 22000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(101.7851458539211 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -40

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   7. Taylor expanded in y around 0

      \[\leadsto \left(4.16438922228 - \frac{110.1139242984811 + \frac{\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000}}{x} - 3655.1204654076414}{x}}{x}\right) \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 44.2%

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

   if -40 < x < 2.2e7

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{\color{blue}{\frac{156699607947}{500000000}} \cdot x - -47.066876606} \]
   8. Step-by-step derivation

   9. Applied rewrites 49.4%

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

   if 2.2e7 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \color{blue}{\frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 44.3%

         \[\leadsto \left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{\color{blue}{x}}\right) \cdot \left(x - 2\right) \]

   8. Applied rewrites 44.3%

      \[\leadsto \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 90.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -40:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811 + \frac{-3655.1204654076414}{x}}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 22000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{313.399215894 \cdot x - -47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x -40.0)
  (*
   (-
    4.16438922228
    (/ (+ 110.1139242984811 (/ -3655.1204654076414 x)) x))
   x)
  (if (<= x 22000000.0)
    (/
     (* (- x 2.0) (+ (* x y) z))
     (- (* 313.399215894 x) -47.066876606))
    (* (- 4.16438922228 (* 101.7851458539211 (/ 1.0 x))) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -40.0) {
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x;
	} else if (x <= 22000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	} else {
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (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 <= (-40.0d0)) then
        tmp = (4.16438922228d0 - ((110.1139242984811d0 + ((-3655.1204654076414d0) / x)) / x)) * x
    else if (x <= 22000000.0d0) then
        tmp = ((x - 2.0d0) * ((x * y) + z)) / ((313.399215894d0 * x) - (-47.066876606d0))
    else
        tmp = (4.16438922228d0 - (101.7851458539211d0 * (1.0d0 / x))) * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -40.0) {
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x;
	} else if (x <= 22000000.0) {
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	} else {
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -40.0:
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x
	elif x <= 22000000.0:
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606)
	else:
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -40.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(110.1139242984811 + Float64(-3655.1204654076414 / x)) / x)) * x);
	elseif (x <= 22000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * y) + z)) / Float64(Float64(313.399215894 * x) - -47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(101.7851458539211 * Float64(1.0 / x))) * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -40.0)
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x;
	elseif (x <= 22000000.0)
		tmp = ((x - 2.0) * ((x * y) + z)) / ((313.399215894 * x) - -47.066876606);
	else
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -40.0], N[(N[(4.16438922228 - N[(N[(110.1139242984811 + N[(-3655.1204654076414 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 22000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(101.7851458539211 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -40

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   7. Taylor expanded in x around inf

      \[\leadsto \left(4.16438922228 - \frac{110.1139242984811 + \frac{\frac{-2284450290879775841688574159837293}{625000000000000000000000000000}}{x}}{x}\right) \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 44.2%

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

   if -40 < x < 2.2e7

   1. Initial program 59.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. add-flip N/A

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

      12. lower--.f64 N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval 59.1%

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

   3. Applied rewrites 59.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 52.2%

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

   6. Applied rewrites 52.2%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(x \cdot y + z\right)}{\color{blue}{\frac{156699607947}{500000000}} \cdot x - -47.066876606} \]
   8. Step-by-step derivation

   9. Applied rewrites 49.4%

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

   if 2.2e7 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \color{blue}{\frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 44.3%

         \[\leadsto \left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{\color{blue}{x}}\right) \cdot \left(x - 2\right) \]

   8. Applied rewrites 44.3%

      \[\leadsto \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 77.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -26:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811 + \frac{-3655.1204654076414}{x}}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 21000000:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x -26.0)
  (*
   (-
    4.16438922228
    (/ (+ 110.1139242984811 (/ -3655.1204654076414 x)) x))
   x)
  (if (<= x 21000000.0)
    (* (* 0.0212463641547976 z) (- x 2.0))
    (* (- 4.16438922228 (* 101.7851458539211 (/ 1.0 x))) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -26.0) {
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (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 <= (-26.0d0)) then
        tmp = (4.16438922228d0 - ((110.1139242984811d0 + ((-3655.1204654076414d0) / x)) / x)) * x
    else if (x <= 21000000.0d0) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = (4.16438922228d0 - (101.7851458539211d0 * (1.0d0 / x))) * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -26.0) {
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -26.0:
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x
	elif x <= 21000000.0:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -26.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(110.1139242984811 + Float64(-3655.1204654076414 / x)) / x)) * x);
	elseif (x <= 21000000.0)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(101.7851458539211 * Float64(1.0 / x))) * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -26.0)
		tmp = (4.16438922228 - ((110.1139242984811 + (-3655.1204654076414 / x)) / x)) * x;
	elseif (x <= 21000000.0)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -26.0], N[(N[(4.16438922228 - N[(N[(110.1139242984811 + N[(-3655.1204654076414 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 21000000.0], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(101.7851458539211 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -26

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   7. Taylor expanded in x around inf

      \[\leadsto \left(4.16438922228 - \frac{110.1139242984811 + \frac{\frac{-2284450290879775841688574159837293}{625000000000000000000000000000}}{x}}{x}\right) \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 44.2%

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

   if -26 < x < 2.1e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 36.0%

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

   8. Applied rewrites 36.0%

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

   if 2.1e7 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \color{blue}{\frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 44.3%

         \[\leadsto \left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{\color{blue}{x}}\right) \cdot \left(x - 2\right) \]

   8. Applied rewrites 44.3%

      \[\leadsto \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 76.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -26:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 21000000:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (*
         (- 4.16438922228 (* 101.7851458539211 (/ 1.0 x)))
         (- x 2.0))))
  (if (<= x -26.0)
    t_0
    (if (<= x 21000000.0)
      (* (* 0.0212463641547976 z) (- x 2.0))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} 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 = (4.16438922228d0 - (101.7851458539211d0 * (1.0d0 / x))) * (x - 2.0d0)
    if (x <= (-26.0d0)) then
        tmp = t_0
    else if (x <= 21000000.0d0) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0)
	tmp = 0
	if x <= -26.0:
		tmp = t_0
	elif x <= 21000000.0:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(101.7851458539211 * Float64(1.0 / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 21000000.0)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 - (101.7851458539211 * (1.0 / x))) * (x - 2.0);
	tmp = 0.0;
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 21000000.0)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(101.7851458539211 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -26.0], t$95$0, If[LessEqual[x, 21000000.0], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -26 or 2.1e7 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \color{blue}{\frac{12723143231740136880149}{125000000000000000000} \cdot \frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{12723143231740136880149}{125000000000000000000} \cdot \color{blue}{\frac{1}{x}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 44.3%

         \[\leadsto \left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{\color{blue}{x}}\right) \cdot \left(x - 2\right) \]

   8. Applied rewrites 44.3%

      \[\leadsto \color{blue}{\left(4.16438922228 - 101.7851458539211 \cdot \frac{1}{x}\right)} \cdot \left(x - 2\right) \]

   if -26 < x < 2.1e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 36.0%

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

   8. Applied rewrites 36.0%

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

Alternative 22: 76.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -26:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 21000000:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
  (if (<= x -26.0)
    t_0
    (if (<= x 21000000.0)
      (* (* 0.0212463641547976 z) (- x 2.0))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} 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 = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    if (x <= (-26.0d0)) then
        tmp = t_0
    else if (x <= 21000000.0d0) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 - (110.1139242984811 / x)) * x
	tmp = 0
	if x <= -26.0:
		tmp = t_0
	elif x <= 21000000.0:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 21000000.0)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	tmp = 0.0;
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 21000000.0)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -26.0], t$95$0, If[LessEqual[x, 21000000.0], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -26 or 2.1e7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   6. Applied rewrites 47.1%

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

   7. Taylor expanded in x around inf

      \[\leadsto \left(4.16438922228 - \frac{\frac{13764240537310136880149}{125000000000000000000}}{x}\right) \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 44.6%

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

   if -26 < x < 2.1e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 36.0%

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

   8. Applied rewrites 36.0%

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

Alternative 23: 76.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} t_0 := 4.16438922228 \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -26:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 21000000:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (* 4.16438922228 (- x 2.0))))
  (if (<= x -26.0)
    t_0
    (if (<= x 21000000.0)
      (* (* 0.0212463641547976 z) (- x 2.0))
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x - 2.0);
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} 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 = 4.16438922228d0 * (x - 2.0d0)
    if (x <= (-26.0d0)) then
        tmp = t_0
    else if (x <= 21000000.0d0) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x - 2.0);
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 21000000.0) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.16438922228 * (x - 2.0)
	tmp = 0
	if x <= -26.0:
		tmp = t_0
	elif x <= 21000000.0:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.16438922228 * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 21000000.0)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.16438922228 * (x - 2.0);
	tmp = 0.0;
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 21000000.0)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.16438922228 * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -26.0], t$95$0, If[LessEqual[x, 21000000.0], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -26 or 2.1e7 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000}} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 44.4%

      \[\leadsto \color{blue}{4.16438922228} \cdot \left(x - 2\right) \]

   if -26 < x < 2.1e7

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 36.0%

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

   8. Applied rewrites 36.0%

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

Alternative 24: 76.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} t_0 := 4.16438922228 \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -26:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-7}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (* 4.16438922228 (- x 2.0))))
  (if (<= x -26.0)
    t_0
    (if (<= x 2e-7) (* -0.0424927283095952 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x - 2.0);
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 2e-7) {
		tmp = -0.0424927283095952 * z;
	} 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 = 4.16438922228d0 * (x - 2.0d0)
    if (x <= (-26.0d0)) then
        tmp = t_0
    else if (x <= 2d-7) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x - 2.0);
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 2e-7) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.16438922228 * (x - 2.0)
	tmp = 0
	if x <= -26.0:
		tmp = t_0
	elif x <= 2e-7:
		tmp = -0.0424927283095952 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.16438922228 * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 2e-7)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.16438922228 * (x - 2.0);
	tmp = 0.0;
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 2e-7)
		tmp = -0.0424927283095952 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.16438922228 * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -26.0], t$95$0, If[LessEqual[x, 2e-7], N[(-0.0424927283095952 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -26 or 1.9999999999999999e-7 < x

   1. Initial program 59.1%

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

   3. Applied rewrites 62.4%

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

   5. Applied rewrites 61.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{104109730557}{25000000000}} \cdot \left(x - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 44.4%

      \[\leadsto \color{blue}{4.16438922228} \cdot \left(x - 2\right) \]

   if -26 < x < 1.9999999999999999e-7

   1. Initial program 59.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 35.8%

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

   4. Applied rewrites 35.8%

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

Alternative 25: 76.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} t_0 := \left(--4.16438922228\right) \cdot x\\ \mathbf{if}\;x \leq -26:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-7}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (* (- -4.16438922228) x)))
  (if (<= x -26.0)
    t_0
    (if (<= x 2e-7) (* -0.0424927283095952 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(-4.16438922228) * x;
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 2e-7) {
		tmp = -0.0424927283095952 * z;
	} 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 = -(-4.16438922228d0) * x
    if (x <= (-26.0d0)) then
        tmp = t_0
    else if (x <= 2d-7) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -(-4.16438922228) * x;
	double tmp;
	if (x <= -26.0) {
		tmp = t_0;
	} else if (x <= 2e-7) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(-4.16438922228) * x
	tmp = 0
	if x <= -26.0:
		tmp = t_0
	elif x <= 2e-7:
		tmp = -0.0424927283095952 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-(-4.16438922228)) * x)
	tmp = 0.0
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 2e-7)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(-4.16438922228) * x;
	tmp = 0.0;
	if (x <= -26.0)
		tmp = t_0;
	elseif (x <= 2e-7)
		tmp = -0.0424927283095952 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((--4.16438922228) * x), $MachinePrecision]}, If[LessEqual[x, -26.0], t$95$0, If[LessEqual[x, 2e-7], N[(-0.0424927283095952 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -26 or 1.9999999999999999e-7 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{\mathsf{fma}\left(-1, \frac{y}{x}, 130977.50649958357 \cdot \frac{1}{x}\right) - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \left(x \cdot \frac{-104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 44.3%

      \[\leadsto -1 \cdot \left(x \cdot -4.16438922228\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \frac{-104109730557}{25000000000}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(x \cdot \frac{-104109730557}{25000000000}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\frac{-104109730557}{25000000000} \cdot x\right) \]

      5. distribute-lft-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. lower-neg.f64 44.3%

         \[\leadsto \left(--4.16438922228\right) \cdot x \]

   9. Applied rewrites 44.3%

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

   if -26 < x < 1.9999999999999999e-7

   1. Initial program 59.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 35.8%

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

   4. Applied rewrites 35.8%

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

Alternative 26: 35.8% accurate, 13.1× speedup

Math

\[-0.0424927283095952 \cdot z \]

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 59.1%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 35.8%

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

4. Applied rewrites 35.8%

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

Reproduce

herbie shell --seed 2025212 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :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)))