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

Percentage Accurate: 58.0% → 98.7%

Time: 5.8s

Alternatives: 19

Speedup: 4.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 10^{+304}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, 81407.94439079006\right)}{\mathsf{fma}\left(x, x, 1878.3557951513571 - 43.3400022514 \cdot x\right)}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
           y)
          x)
         z))
       (+
        (*
         (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
         x)
        47.066876606))
      1e+304)
   (*
    (- x 2.0)
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma
      (fma
       (fma
        (/
         (fma (* x x) x 81407.94439079006)
         (fma x x (- 1878.3557951513571 (* 43.3400022514 x))))
        x
        263.505074721)
       x
       313.399215894)
      x
      47.066876606)))
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+304) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((fma((x * x), x, 81407.94439079006) / fma(x, x, (1878.3557951513571 - (43.3400022514 * x)))), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+304)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(fma(Float64(x * x), x, 81407.94439079006) / fma(x, x, Float64(1878.3557951513571 - Float64(43.3400022514 * x)))), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 1e+304], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(N[(N[(x * x), $MachinePrecision] * x + 81407.94439079006), $MachinePrecision] / N[(x * x + N[(1878.3557951513571 - N[(43.3400022514 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $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))) < 9.9999999999999994e303

   1. Initial program 96.2%

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

   3. Applied rewrites 98.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. flip3-+ N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{x}^{3} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{x}^{3} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      5. unpow3 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{\left(x \cdot x\right) \cdot x} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      6. unpow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{{x}^{2}} \cdot x + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left({x}^{2}, x, {\frac{216700011257}{5000000000}}^{3}\right)}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      8. unpow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{x \cdot x}, x, {\frac{216700011257}{5000000000}}^{3}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{x \cdot x}, x, {\frac{216700011257}{5000000000}}^{3}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      10. metadata-eval N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \color{blue}{\frac{10175993048848756570705281387591593}{125000000000000000000000000000}}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\color{blue}{\mathsf{fma}\left(x, x, \frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      12. *-commutative N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - \color{blue}{\frac{216700011257}{5000000000} \cdot x}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      13. lower--.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \color{blue}{\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - \frac{216700011257}{5000000000} \cdot x}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      14. metadata-eval N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \color{blue}{\frac{46958894878783926720049}{25000000000000000000}} - \frac{216700011257}{5000000000} \cdot x\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. lower-*.f64 98.9

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, 81407.94439079006\right)}{\mathsf{fma}\left(x, x, 1878.3557951513571 - \color{blue}{43.3400022514 \cdot x}\right)}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 98.9%

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{\mathsf{fma}\left(x \cdot x, x, 81407.94439079006\right)}{\mathsf{fma}\left(x, x, 1878.3557951513571 - 43.3400022514 \cdot x\right)}}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   if 9.9999999999999994e303 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.3%

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

   3. Applied rewrites 3.8%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 98.4%

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

Alternative 2: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 10^{+304}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
           y)
          x)
         z))
       (+
        (*
         (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
         x)
        47.066876606))
      1e+304)
   (*
    (- x 2.0)
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma
      (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
      x
      47.066876606)))
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+304) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+304)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 1e+304], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $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))) < 9.9999999999999994e303

   1. Initial program 96.2%

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

   3. Applied rewrites 98.9%

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

   if 9.9999999999999994e303 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.3%

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

   3. Applied rewrites 3.8%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 98.4%

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

Alternative 3: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{+73}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -14.5:\\ \;\;\;\;t\_0 \cdot \frac{1}{\left(x \cdot x\right) \cdot x}\\ \mathbf{elif}\;x \leq 17:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{t\_0}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{t\_0}{\left(x \cdot x\right) \cdot \left(x \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
          x
          z)))
   (if (<= x -1.12e+73)
     (* 4.16438922228 x)
     (if (<= x -14.5)
       (* t_0 (/ 1.0 (* (* x x) x)))
       (if (<= x 17.0)
         (*
          (- x 2.0)
          (/ t_0 (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
         (if (<= x 1.8e+63)
           (* (- x 2.0) (/ t_0 (* (* x x) (* x x))))
           (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z);
	double tmp;
	if (x <= -1.12e+73) {
		tmp = 4.16438922228 * x;
	} else if (x <= -14.5) {
		tmp = t_0 * (1.0 / ((x * x) * x));
	} else if (x <= 17.0) {
		tmp = (x - 2.0) * (t_0 / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else if (x <= 1.8e+63) {
		tmp = (x - 2.0) * (t_0 / ((x * x) * (x * x)));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z)
	tmp = 0.0
	if (x <= -1.12e+73)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -14.5)
		tmp = Float64(t_0 * Float64(1.0 / Float64(Float64(x * x) * x)));
	elseif (x <= 17.0)
		tmp = Float64(Float64(x - 2.0) * Float64(t_0 / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	elseif (x <= 1.8e+63)
		tmp = Float64(Float64(x - 2.0) * Float64(t_0 / Float64(Float64(x * x) * Float64(x * x))));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision]}, If[LessEqual[x, -1.12e+73], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -14.5], N[(t$95$0 * N[(1.0 / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 17.0], N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$0 / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+63], N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$0 / N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.12e73 or 1.79999999999999999e63 < x

   1. Initial program 0.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 97.6

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

   4. Applied rewrites 97.6%

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

   if -1.12e73 < x < -14.5

   1. Initial program 70.0%

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

   3. Applied rewrites 92.8%

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

   5. Applied rewrites 92.7%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{1}{{x}^{3}}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\color{blue}{{x}^{3}}} \]

      2. pow3 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{x}} \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{x}} \]

      4. lift-*.f64 83.4

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot x} \]

   8. Applied rewrites 83.4%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{1}{\left(x \cdot x\right) \cdot x}} \]

   if -14.5 < x < 17

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.4%

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

   if 17 < x < 1.79999999999999999e63

   1. Initial program 83.6%

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

   3. Applied rewrites 93.8%

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

   4. Taylor expanded in x around inf

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\color{blue}{{x}^{4}}} \]
   5. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{{x}^{2} \cdot \color{blue}{{x}^{2}}} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{{x}^{2} \cdot \color{blue}{{x}^{2}}} \]

      4. unpow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\left(x \cdot x\right) \cdot {\color{blue}{x}}^{2}} \]

      5. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\left(x \cdot x\right) \cdot {\color{blue}{x}}^{2}} \]

      6. unpow2 N/A

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

      7. lower-*.f64 82.2

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

   6. Applied rewrites 82.2%

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

Alternative 4: 96.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)\\ t_1 := t\_0 \cdot \frac{1}{\left(x \cdot x\right) \cdot x}\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{+73}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -14.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 18:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{t\_0}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
          x
          z))
        (t_1 (* t_0 (/ 1.0 (* (* x x) x)))))
   (if (<= x -1.12e+73)
     (* 4.16438922228 x)
     (if (<= x -14.5)
       t_1
       (if (<= x 18.0)
         (*
          (- x 2.0)
          (/ t_0 (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
         (if (<= x 1.8e+63) t_1 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z);
	double t_1 = t_0 * (1.0 / ((x * x) * x));
	double tmp;
	if (x <= -1.12e+73) {
		tmp = 4.16438922228 * x;
	} else if (x <= -14.5) {
		tmp = t_1;
	} else if (x <= 18.0) {
		tmp = (x - 2.0) * (t_0 / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else if (x <= 1.8e+63) {
		tmp = t_1;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z)
	t_1 = Float64(t_0 * Float64(1.0 / Float64(Float64(x * x) * x)))
	tmp = 0.0
	if (x <= -1.12e+73)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -14.5)
		tmp = t_1;
	elseif (x <= 18.0)
		tmp = Float64(Float64(x - 2.0) * Float64(t_0 / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	elseif (x <= 1.8e+63)
		tmp = t_1;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * N[(1.0 / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.12e+73], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -14.5], t$95$1, If[LessEqual[x, 18.0], N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$0 / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+63], t$95$1, N[(4.16438922228 * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.12e73 or 1.79999999999999999e63 < x

   1. Initial program 0.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 97.6

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

   4. Applied rewrites 97.6%

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

   if -1.12e73 < x < -14.5 or 18 < x < 1.79999999999999999e63

   1. Initial program 76.5%

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

   3. Applied rewrites 93.2%

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

   5. Applied rewrites 93.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{1}{{x}^{3}}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\color{blue}{{x}^{3}}} \]

      2. pow3 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{x}} \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{x}} \]

      4. lift-*.f64 82.9

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot x} \]

   8. Applied rewrites 82.9%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{1}{\left(x \cdot x\right) \cdot x}} \]

   if -14.5 < x < 18

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.4%

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{263.505074721}, x, 313.399215894\right), x, 47.066876606\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 96.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot x}\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{+73}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -2.85:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 18.5:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+63}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (fma
           (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
           x
           z)
          (/ 1.0 (* (* x x) x)))))
   (if (<= x -1.12e+73)
     (* 4.16438922228 x)
     (if (<= x -2.85)
       t_0
       (if (<= x 18.5)
         (*
          (- x 2.0)
          (/
           (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
           (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
         (if (<= x 1.8e+63) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * (1.0 / ((x * x) * x));
	double tmp;
	if (x <= -1.12e+73) {
		tmp = 4.16438922228 * x;
	} else if (x <= -2.85) {
		tmp = t_0;
	} else if (x <= 18.5) {
		tmp = (x - 2.0) * (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else if (x <= 1.8e+63) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(1.0 / Float64(Float64(x * x) * x)))
	tmp = 0.0
	if (x <= -1.12e+73)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -2.85)
		tmp = t_0;
	elseif (x <= 18.5)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	elseif (x <= 1.8e+63)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(1.0 / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.12e+73], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -2.85], t$95$0, If[LessEqual[x, 18.5], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+63], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.12e73 or 1.79999999999999999e63 < x

   1. Initial program 0.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 97.6

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

   4. Applied rewrites 97.6%

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

   if -1.12e73 < x < -2.85000000000000009 or 18.5 < x < 1.79999999999999999e63

   1. Initial program 76.7%

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

   3. Applied rewrites 93.3%

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

   5. Applied rewrites 93.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{1}{{x}^{3}}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\color{blue}{{x}^{3}}} \]

      2. pow3 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{x}} \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{x}} \]

      4. lift-*.f64 82.3

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot x} \]

   8. Applied rewrites 82.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{1}{\left(x \cdot x\right) \cdot x}} \]

   if -2.85000000000000009 < x < 18.5

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. flip3-+ N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{x}^{3} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{x}^{3} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      5. unpow3 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{\left(x \cdot x\right) \cdot x} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      6. unpow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{{x}^{2}} \cdot x + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left({x}^{2}, x, {\frac{216700011257}{5000000000}}^{3}\right)}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      8. unpow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{x \cdot x}, x, {\frac{216700011257}{5000000000}}^{3}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{x \cdot x}, x, {\frac{216700011257}{5000000000}}^{3}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      10. metadata-eval N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \color{blue}{\frac{10175993048848756570705281387591593}{125000000000000000000000000000}}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\color{blue}{\mathsf{fma}\left(x, x, \frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      12. *-commutative N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - \color{blue}{\frac{216700011257}{5000000000} \cdot x}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      13. lower--.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \color{blue}{\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - \frac{216700011257}{5000000000} \cdot x}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      14. metadata-eval N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \color{blue}{\frac{46958894878783926720049}{25000000000000000000}} - \frac{216700011257}{5000000000} \cdot x\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. lower-*.f64 99.7

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, 81407.94439079006\right)}{\mathsf{fma}\left(x, x, 1878.3557951513571 - \color{blue}{43.3400022514 \cdot x}\right)}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 99.7%

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{\mathsf{fma}\left(x \cdot x, x, 81407.94439079006\right)}{\mathsf{fma}\left(x, x, 1878.3557951513571 - 43.3400022514 \cdot x\right)}}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 98.5%

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

   9. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{263505074721}{1000000000}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 98.5%

       \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{78.6994924154}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 122:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228))))
   (if (<= x -36.0)
     t_0
     (if (<= x 122.0)
       (/
        (*
         (fma
          (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
          x
          z)
         (- x 2.0))
        (fma
         (fma (fma 43.3400022514 x 263.505074721) x 313.399215894)
         x
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 122.0) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * (x - 2.0)) / fma(fma(fma(43.3400022514, x, 263.505074721), x, 313.399215894), x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 122.0)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / fma(fma(fma(43.3400022514, x, 263.505074721), x, 313.399215894), x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 122.0], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(43.3400022514 * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 122 < x

   1. Initial program 16.5%

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

   3. Applied rewrites 22.4%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 94.0%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)} \]

   if -36 < x < 122

   1. Initial program 99.6%

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.5%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{43.3400022514}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 96.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 80:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228))))
   (if (<= x -5.5)
     t_0
     (if (<= x 80.0)
       (*
        (- x 2.0)
        (/
         (fma
          (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
          x
          z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	double tmp;
	if (x <= -5.5) {
		tmp = t_0;
	} else if (x <= 80.0) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228))
	tmp = 0.0
	if (x <= -5.5)
		tmp = t_0;
	elseif (x <= 80.0)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5], t$95$0, If[LessEqual[x, 80.0], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 80 < x

   1. Initial program 16.6%

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

   3. Applied rewrites 22.5%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 93.9%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)} \]

   if -5.5 < x < 80

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.3%

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{263.505074721}, x, 313.399215894\right), x, 47.066876606\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 92.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 10^{+16}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    (- x 2.0)
    (+ (/ (fma -101.7851458539211 x 3451.550173699799) (* x x)) 4.16438922228))
   (if (<= x 1e+16)
     (*
      (- x 2.0)
      (/
       (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
       (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x - 2.0) * ((fma(-101.7851458539211, x, 3451.550173699799) / (x * x)) + 4.16438922228);
	} else if (x <= 1e+16) {
		tmp = (x - 2.0) * (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(fma(-101.7851458539211, x, 3451.550173699799) / Float64(x * x)) + 4.16438922228));
	elseif (x <= 1e+16)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(-101.7851458539211 * x + 3451.550173699799), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+16], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 16.5%

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

   3. Applied rewrites 22.8%

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

   4. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lower-/.f64 87.5

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   6. Applied rewrites 87.5%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{-12723143231740136880149}{125000000000000000000} \cdot x + \frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      4. pow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x \cdot x} + \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 87.1

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   9. Applied rewrites 87.1%

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   if -5.5 < x < 1e16

   1. Initial program 99.6%

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

   3. Applied rewrites 99.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. flip3-+ N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{x}^{3} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      4. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{x}^{3} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      5. unpow3 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{\left(x \cdot x\right) \cdot x} + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      6. unpow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{{x}^{2}} \cdot x + {\frac{216700011257}{5000000000}}^{3}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left({x}^{2}, x, {\frac{216700011257}{5000000000}}^{3}\right)}}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      8. unpow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{x \cdot x}, x, {\frac{216700011257}{5000000000}}^{3}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{x \cdot x}, x, {\frac{216700011257}{5000000000}}^{3}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      10. metadata-eval N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \color{blue}{\frac{10175993048848756570705281387591593}{125000000000000000000000000000}}\right)}{x \cdot x + \left(\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      11. lower-fma.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\color{blue}{\mathsf{fma}\left(x, x, \frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - x \cdot \frac{216700011257}{5000000000}\right)}}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      12. *-commutative N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - \color{blue}{\frac{216700011257}{5000000000} \cdot x}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      13. lower--.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \color{blue}{\frac{216700011257}{5000000000} \cdot \frac{216700011257}{5000000000} - \frac{216700011257}{5000000000} \cdot x}\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      14. metadata-eval N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, \frac{10175993048848756570705281387591593}{125000000000000000000000000000}\right)}{\mathsf{fma}\left(x, x, \color{blue}{\frac{46958894878783926720049}{25000000000000000000}} - \frac{216700011257}{5000000000} \cdot x\right)}, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. lower-*.f64 99.6

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x \cdot x, x, 81407.94439079006\right)}{\mathsf{fma}\left(x, x, 1878.3557951513571 - \color{blue}{43.3400022514 \cdot x}\right)}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 99.6%

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{\mathsf{fma}\left(x \cdot x, x, 81407.94439079006\right)}{\mathsf{fma}\left(x, x, 1878.3557951513571 - 43.3400022514 \cdot x\right)}}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 96.1%

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

   9. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{393497462077}{5000000000}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{263505074721}{1000000000}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 96.1%

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

   if 1e16 < x

   1. Initial program 12.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 9: 92.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    (- x 2.0)
    (+ (/ (fma -101.7851458539211 x 3451.550173699799) (* x x)) 4.16438922228))
   (if (<= x 2.0)
     (*
      (fma
       (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
       x
       z)
      (-
       (* (fma -1.787568985856513 x 0.3041881842569256) x)
       0.0424927283095952))
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x - 2.0) * ((fma(-101.7851458539211, x, 3451.550173699799) / (x * x)) + 4.16438922228);
	} else if (x <= 2.0) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952);
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(fma(-101.7851458539211, x, 3451.550173699799) / Float64(x * x)) + 4.16438922228));
	elseif (x <= 2.0)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952));
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(-101.7851458539211 * x + 3451.550173699799), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(N[(-1.787568985856513 * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 16.5%

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

   3. Applied rewrites 22.8%

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

   4. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lower-/.f64 87.5

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   6. Applied rewrites 87.5%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{-12723143231740136880149}{125000000000000000000} \cdot x + \frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      4. pow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x \cdot x} + \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 87.1

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   9. Applied rewrites 87.1%

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   if -5.5 < x < 2

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 98.1

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

   8. Applied rewrites 98.1%

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

   if 2 < x

   1. Initial program 17.4%

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

   3. Applied rewrites 23.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 86.3%

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

Alternative 10: 92.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    (- x 2.0)
    (+ (/ (fma -101.7851458539211 x 3451.550173699799) (* x x)) 4.16438922228))
   (if (<= x 1e+16)
     (*
      (fma
       (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
       x
       z)
      (- (* 0.3041881842569256 x) 0.0424927283095952))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x - 2.0) * ((fma(-101.7851458539211, x, 3451.550173699799) / (x * x)) + 4.16438922228);
	} else if (x <= 1e+16) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((0.3041881842569256 * x) - 0.0424927283095952);
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(fma(-101.7851458539211, x, 3451.550173699799) / Float64(x * x)) + 4.16438922228));
	elseif (x <= 1e+16)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(-101.7851458539211 * x + 3451.550173699799), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+16], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 16.5%

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

   3. Applied rewrites 22.8%

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

   4. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lower-/.f64 87.5

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   6. Applied rewrites 87.5%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{-12723143231740136880149}{125000000000000000000} \cdot x + \frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      4. pow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x \cdot x} + \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 87.1

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   9. Applied rewrites 87.1%

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   if -5.5 < x < 1e16

   1. Initial program 99.6%

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

   3. Applied rewrites 99.6%

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 95.1

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

   8. Applied rewrites 95.1%

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

   if 1e16 < x

   1. Initial program 12.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 11: 91.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    (- x 2.0)
    (+ (/ (fma -101.7851458539211 x 3451.550173699799) (* x x)) 4.16438922228))
   (if (<= x 2.0)
     (*
      (fma
       (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
       x
       z)
      -0.0424927283095952)
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x - 2.0) * ((fma(-101.7851458539211, x, 3451.550173699799) / (x * x)) + 4.16438922228);
	} else if (x <= 2.0) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(fma(-101.7851458539211, x, 3451.550173699799) / Float64(x * x)) + 4.16438922228));
	elseif (x <= 2.0)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952);
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(-101.7851458539211 * x + 3451.550173699799), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * -0.0424927283095952), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 16.5%

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

   3. Applied rewrites 22.8%

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

   4. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lower-/.f64 87.5

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   6. Applied rewrites 87.5%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000} + \frac{-12723143231740136880149}{125000000000000000000} \cdot x}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\frac{-12723143231740136880149}{125000000000000000000} \cdot x + \frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{{x}^{2}} + \frac{104109730557}{25000000000}\right) \]

      4. pow2 N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(\frac{-12723143231740136880149}{125000000000000000000}, x, \frac{2157218858562374472887084159837293}{625000000000000000000000000000}\right)}{x \cdot x} + \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 87.1

         \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   9. Applied rewrites 87.1%

      \[\leadsto \left(x - 2\right) \cdot \left(\frac{\mathsf{fma}\left(-101.7851458539211, x, 3451.550173699799\right)}{x \cdot x} + 4.16438922228\right) \]

   if -5.5 < x < 2

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 96.6%

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

   if 2 < x

   1. Initial program 17.4%

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

   3. Applied rewrites 23.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 86.3%

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

Alternative 12: 91.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x)))
   (if (<= x 2.0)
     (*
      (fma
       (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
       x
       z)
      -0.0424927283095952)
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else if (x <= 2.0) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	elseif (x <= 2.0)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952);
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * -0.0424927283095952), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 16.5%

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

   3. Applied rewrites 22.8%

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

   4. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 87.4

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

   6. Applied rewrites 87.4%

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

   if -5.5 < x < 2

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 96.6%

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

   if 2 < x

   1. Initial program 17.4%

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

   3. Applied rewrites 23.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 86.3%

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

Alternative 13: 89.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.0424927283095952, y, 0.3041881842569256 \cdot z\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x)))
   (if (<= x 0.0002)
     (fma
      (fma -0.0424927283095952 y (* 0.3041881842569256 z))
      x
      (* -0.0424927283095952 z))
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else if (x <= 0.0002) {
		tmp = fma(fma(-0.0424927283095952, y, (0.3041881842569256 * z)), x, (-0.0424927283095952 * z));
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	elseif (x <= 0.0002)
		tmp = fma(fma(-0.0424927283095952, y, Float64(0.3041881842569256 * z)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0002], N[(N[(-0.0424927283095952 * y + N[(0.3041881842569256 * z), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 16.5%

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

   3. Applied rewrites 22.8%

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

   4. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 87.4

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

   6. Applied rewrites 87.4%

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

   if -5.5 < x < 2.0000000000000001e-4

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lower-/.f64 2.9

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   6. Applied rewrites 2.9%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)} \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. flip3-- N/A

         \[\leadsto \color{blue}{\frac{{x}^{3} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)}} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{{x}^{3} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)}} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{{x}^{3} - {2}^{3}}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      5. pow3 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot x\right) \cdot x} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      6. pow2 N/A

         \[\leadsto \frac{\color{blue}{{x}^{2}} \cdot x - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{{x}^{2} \cdot x} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      8. pow2 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot x\right)} \cdot x - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot x\right)} \cdot x - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      10. metadata-eval N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - \color{blue}{8}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\color{blue}{\mathsf{fma}\left(x, x, 2 \cdot 2 + x \cdot 2\right)}} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, \color{blue}{4} + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      13. lower-+.f64 N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, \color{blue}{4 + x \cdot 2}\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      14. lower-*.f64 2.9

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, 4 + \color{blue}{x \cdot 2}\right)} \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   8. Applied rewrites 2.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, 4 + x \cdot 2\right)}} \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

   11. Applied rewrites 93.0%

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

   if 2.0000000000000001e-4 < x

   1. Initial program 18.6%

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

   3. Applied rewrites 24.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 85.2%

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

Alternative 14: 89.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 0.0002:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.0424927283095952, y, 0.3041881842569256 \cdot z\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 0.0002)
     (fma
      (fma -0.0424927283095952 y (* 0.3041881842569256 z))
      x
      (* -0.0424927283095952 z))
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 0.0002) {
		tmp = fma(fma(-0.0424927283095952, y, (0.3041881842569256 * z)), x, (-0.0424927283095952 * z));
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 0.0002)
		tmp = fma(fma(-0.0424927283095952, y, Float64(0.3041881842569256 * z)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 0.0002], N[(N[(-0.0424927283095952 * y + N[(0.3041881842569256 * z), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 16.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 87.4

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

   4. Applied rewrites 87.4%

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

   if -5.5 < x < 2.0000000000000001e-4

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\mathsf{neg}\left(\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{2157218858562374472887084159837293}{625000000000000000000000000000} \cdot \frac{1}{x}}{x}\right)\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lower-/.f64 2.9

         \[\leadsto \left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   6. Applied rewrites 2.9%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)} \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. flip3-- N/A

         \[\leadsto \color{blue}{\frac{{x}^{3} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)}} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{{x}^{3} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)}} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      4. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{{x}^{3} - {2}^{3}}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      5. pow3 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot x\right) \cdot x} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      6. pow2 N/A

         \[\leadsto \frac{\color{blue}{{x}^{2}} \cdot x - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\color{blue}{{x}^{2} \cdot x} - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      8. pow2 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot x\right)} \cdot x - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(x \cdot x\right)} \cdot x - {2}^{3}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      10. metadata-eval N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - \color{blue}{8}}{x \cdot x + \left(2 \cdot 2 + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\color{blue}{\mathsf{fma}\left(x, x, 2 \cdot 2 + x \cdot 2\right)}} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      12. metadata-eval N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, \color{blue}{4} + x \cdot 2\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      13. lower-+.f64 N/A

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, \color{blue}{4 + x \cdot 2}\right)} \cdot \left(\left(-\frac{\frac{12723143231740136880149}{125000000000000000000} - \frac{\frac{2157218858562374472887084159837293}{625000000000000000000000000000}}{x}}{x}\right) + \frac{104109730557}{25000000000}\right) \]

      14. lower-*.f64 2.9

          \[\leadsto \frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, 4 + \color{blue}{x \cdot 2}\right)} \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   8. Applied rewrites 2.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot x - 8}{\mathsf{fma}\left(x, x, 4 + x \cdot 2\right)}} \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right) \]

   9. Taylor expanded in x around 0

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

       1. +-commutative N/A

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

   11. Applied rewrites 93.0%

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

   if 2.0000000000000001e-4 < x

   1. Initial program 18.6%

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

   3. Applied rewrites 24.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 85.2%

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

Alternative 15: 75.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 0.0002:\\ \;\;\;\;\left(x - 2\right) \cdot \left(0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-29)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 0.0002)
     (* (- x 2.0) (* 0.0212463641547976 z))
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 0.0002) {
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	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 <= (-7.2d-29)) then
        tmp = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    else if (x <= 0.0002d0) then
        tmp = (x - 2.0d0) * (0.0212463641547976d0 * z)
    else
        tmp = (x - 2.0d0) * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 0.0002) {
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e-29:
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x
	elif x <= 0.0002:
		tmp = (x - 2.0) * (0.0212463641547976 * z)
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e-29)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 0.0002)
		tmp = Float64(Float64(x - 2.0) * Float64(0.0212463641547976 * z));
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.2e-29)
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	elseif (x <= 0.0002)
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e-29], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 0.0002], N[(N[(x - 2.0), $MachinePrecision] * N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999948e-29

   1. Initial program 24.5%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 79.4

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

   4. Applied rewrites 79.4%

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

   if -7.19999999999999948e-29 < x < 2.0000000000000001e-4

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 68.5

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

   6. Applied rewrites 68.5%

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

   if 2.0000000000000001e-4 < x

   1. Initial program 18.6%

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

   3. Applied rewrites 24.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 85.2%

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

Alternative 16: 75.8% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 0.0002:\\ \;\;\;\;\left(x - 2\right) \cdot \left(0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-29)
   (* 4.16438922228 x)
   (if (<= x 0.0002)
     (* (- x 2.0) (* 0.0212463641547976 z))
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.0002) {
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	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 <= (-7.2d-29)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 0.0002d0) then
        tmp = (x - 2.0d0) * (0.0212463641547976d0 * z)
    else
        tmp = (x - 2.0d0) * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.0002) {
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e-29:
		tmp = 4.16438922228 * x
	elif x <= 0.0002:
		tmp = (x - 2.0) * (0.0212463641547976 * z)
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e-29)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 0.0002)
		tmp = Float64(Float64(x - 2.0) * Float64(0.0212463641547976 * z));
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.2e-29)
		tmp = 4.16438922228 * x;
	elseif (x <= 0.0002)
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e-29], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 0.0002], N[(N[(x - 2.0), $MachinePrecision] * N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999948e-29

   1. Initial program 24.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 79.2

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

   4. Applied rewrites 79.2%

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

   if -7.19999999999999948e-29 < x < 2.0000000000000001e-4

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 68.5

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

   6. Applied rewrites 68.5%

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

   if 2.0000000000000001e-4 < x

   1. Initial program 18.6%

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

   3. Applied rewrites 24.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 85.2%

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

Alternative 17: 75.8% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 0.0002:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-29)
   (* 4.16438922228 x)
   (if (<= x 0.0002) (* -0.0424927283095952 z) (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.0002) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	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 <= (-7.2d-29)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 0.0002d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = (x - 2.0d0) * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.0002) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e-29:
		tmp = 4.16438922228 * x
	elif x <= 0.0002:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e-29)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 0.0002)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.2e-29)
		tmp = 4.16438922228 * x;
	elseif (x <= 0.0002)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e-29], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 0.0002], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999948e-29

   1. Initial program 24.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 79.2

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

   4. Applied rewrites 79.2%

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

   if -7.19999999999999948e-29 < x < 2.0000000000000001e-4

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

   if 2.0000000000000001e-4 < x

   1. Initial program 18.6%

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

   3. Applied rewrites 24.0%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 85.2%

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

Alternative 18: 75.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 50000000000000:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e-29)
   (* 4.16438922228 x)
   (if (<= x 50000000000000.0) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = 4.16438922228 * x;
	} else if (x <= 50000000000000.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	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 <= (-7.2d-29)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 50000000000000.0d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = 4.16438922228d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e-29) {
		tmp = 4.16438922228 * x;
	} else if (x <= 50000000000000.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e-29:
		tmp = 4.16438922228 * x
	elif x <= 50000000000000.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e-29)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 50000000000000.0)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.2e-29)
		tmp = 4.16438922228 * x;
	elseif (x <= 50000000000000.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e-29], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 50000000000000.0], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.19999999999999948e-29 or 5e13 < x

   1. Initial program 19.0%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   if -7.19999999999999948e-29 < x < 5e13

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 66.2

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

   4. Applied rewrites 66.2%

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

Alternative 19: 34.3% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.0%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 34.3

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

4. Applied rewrites 34.3%

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

Reproduce

herbie shell --seed 2025101 
(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)))