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

Percentage Accurate: 58.5% → 98.5%

Time: 6.0s

Alternatives: 23

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

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))
      5e+304)
   (*
    (- x 2.0)
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (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)) <= 5e+304) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / 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)) <= 5e+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(Float64(Float64(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], 5e+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[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 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))) < 4.9999999999999997e304

   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 98.7%

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

      1. lift-fma.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-+.f64 98.7

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

   5. Applied rewrites 98.7%

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

   if 4.9999999999999997e304 < (/.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 0.5%

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

   3. Applied rewrites 3.9%

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

   4. 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 98.2%

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

Alternative 2: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

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))
      5e+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)) <= 5e+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)) <= 5e+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], 5e+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))) < 4.9999999999999997e304

   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 98.7%

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

   if 4.9999999999999997e304 < (/.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 0.5%

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

   3. Applied rewrites 3.9%

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

   4. 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 98.2%

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

Alternative 3: 96.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot x\right) \cdot x\\ \mathbf{if}\;x \leq -7 \cdot 10^{+21}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 1350000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\frac{y}{t\_0} + \frac{3655.1204654076414}{x \cdot x}\right) + 4.16438922228\right) - \frac{110.1139242984811}{x}\right) - \frac{130977.50649958357}{t\_0}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x x) x)))
   (if (<= x -7e+21)
     (*
      (- x 2.0)
      (+
       (-
        (/
         (+
          (-
           (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
          101.7851458539211)
         x))
       4.16438922228))
     (if (<= x 1350000000.0)
       (/
        (fma (+ (fma (- y 275.038832832) x (* -2.0 y)) z) x (* -2.0 z))
        (+
         (*
          (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
          x)
         47.066876606))
       (*
        (-
         (-
          (+ (+ (/ y t_0) (/ 3655.1204654076414 (* x x))) 4.16438922228)
          (/ 110.1139242984811 x))
         (/ 130977.50649958357 t_0))
        x)))))

C

double code(double x, double y, double z) {
	double t_0 = (x * x) * x;
	double tmp;
	if (x <= -7e+21) {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	} else if (x <= 1350000000.0) {
		tmp = fma((fma((y - 275.038832832), x, (-2.0 * y)) + z), x, (-2.0 * z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (((((y / t_0) + (3655.1204654076414 / (x * x))) + 4.16438922228) - (110.1139242984811 / x)) - (130977.50649958357 / t_0)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * x) * x)
	tmp = 0.0
	if (x <= -7e+21)
		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));
	elseif (x <= 1350000000.0)
		tmp = Float64(fma(Float64(fma(Float64(y - 275.038832832), x, Float64(-2.0 * y)) + z), x, Float64(-2.0 * z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(y / t_0) + Float64(3655.1204654076414 / Float64(x * x))) + 4.16438922228) - Float64(110.1139242984811 / x)) - Float64(130977.50649958357 / t_0)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -7e+21], 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, 1350000000.0], N[(N[(N[(N[(N[(y - 275.038832832), $MachinePrecision] * x + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] * x + N[(-2.0 * 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], N[(N[(N[(N[(N[(N[(y / t$95$0), $MachinePrecision] + N[(3655.1204654076414 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] - N[(130977.50649958357 / t$95$0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7e21

   1. Initial program 11.6%

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

   3. Applied rewrites 17.3%

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

   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 96.4%

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

   if -7e21 < x < 1.35e9

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-2 \cdot z + x \cdot \left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{x \cdot \left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) + \color{blue}{-2 \cdot z}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) \cdot x + \color{blue}{-2} \cdot z}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right), \color{blue}{x}, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      4. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      5. lower-+.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      6. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(x \cdot \left(y - \frac{4297481763}{15625000}\right) + -2 \cdot y\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      7. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(\left(y - \frac{4297481763}{15625000}\right) \cdot x + -2 \cdot y\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      8. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      11. lower-*.f64 97.4

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   4. Applied rewrites 97.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   if 1.35e9 < x

   1. Initial program 15.3%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right) \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{104109730557}{25000000000} + \left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(\frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x} + \frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} \cdot \frac{1}{{x}^{3}}\right)\right) \cdot \color{blue}{x} \]

   4. Applied rewrites 94.2%

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

Alternative 4: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq -0.03:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot 4.16438922228\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 75:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(\frac{130977.50649958357}{x} + \left(-\frac{y}{x}\right)\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.1e+23)
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))
   (if (<= x -0.03)
     (/
      (* (- x 2.0) (+ (* (* (* (* x x) x) 4.16438922228) x) z))
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (if (<= x 75.0)
       (/
        (*
         (- x 2.0)
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z))
        (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
       (*
        (- x)
        (-
         (-
          (/
           (-
            (-
             (/
              (- (+ (/ 130977.50649958357 x) (- (/ y x))) 3655.1204654076414)
              x))
            110.1139242984811)
           x))
         4.16438922228))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.1e+23) {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	} else if (x <= -0.03) {
		tmp = ((x - 2.0) * (((((x * x) * x) * 4.16438922228) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else if (x <= 75.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606);
	} else {
		tmp = -x * (-((-((((130977.50649958357 / x) + -(y / x)) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.1e+23)
		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));
	elseif (x <= -0.03)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(x * x) * x) * 4.16438922228) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	elseif (x <= 75.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(130977.50649958357 / x) + Float64(-Float64(y / x))) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.1e+23], 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, -0.03], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision] * 4.16438922228), $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], If[LessEqual[x, 75.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[(N[(N[(130977.50649958357 / x), $MachinePrecision] + (-N[(y / x), $MachinePrecision])), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.09999999999999996e23

   1. Initial program 11.2%

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

   3. Applied rewrites 16.9%

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

   4. 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 96.6%

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

   if -4.09999999999999996e23 < x < -0.029999999999999999

   1. Initial program 93.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\color{blue}{\left(\frac{104109730557}{25000000000} \cdot {x}^{3}\right)} \cdot x + z\right)}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. unpow3 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 52.4

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

   4. Applied rewrites 52.4%

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

   if -0.029999999999999999 < x < 75

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 98.8

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

   4. Applied rewrites 98.8%

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

   if 75 < x

   1. Initial program 17.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 93.0%

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

Alternative 5: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq -0.086:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 75:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(\frac{130977.50649958357}{x} + \left(-\frac{y}{x}\right)\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+21)
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))
   (if (<= x -0.086)
     (*
      (- x 2.0)
      (/
       z
       (fma
        (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894)
        x
        47.066876606)))
     (if (<= x 75.0)
       (/
        (*
         (- x 2.0)
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z))
        (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
       (*
        (- x)
        (-
         (-
          (/
           (-
            (-
             (/
              (- (+ (/ 130977.50649958357 x) (- (/ y x))) 3655.1204654076414)
              x))
            110.1139242984811)
           x))
         4.16438922228))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	} else if (x <= -0.086) {
		tmp = (x - 2.0) * (z / fma(((fma((43.3400022514 + x), x, 263.505074721) * x) + 313.399215894), x, 47.066876606));
	} else if (x <= 75.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606);
	} else {
		tmp = -x * (-((-((((130977.50649958357 / x) + -(y / x)) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+21)
		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));
	elseif (x <= -0.086)
		tmp = Float64(Float64(x - 2.0) * Float64(z / fma(Float64(Float64(fma(Float64(43.3400022514 + x), x, 263.505074721) * x) + 313.399215894), x, 47.066876606)));
	elseif (x <= 75.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(130977.50649958357 / x) + Float64(-Float64(y / x))) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+21], 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, -0.086], N[(N[(x - 2.0), $MachinePrecision] * N[(z / N[(N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 75.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[(N[(N[(130977.50649958357 / x), $MachinePrecision] + (-N[(y / x), $MachinePrecision])), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.8e21

   1. Initial program 11.6%

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

   3. Applied rewrites 17.3%

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

   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 96.4%

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

   if -6.8e21 < x < -0.085999999999999993

   1. Initial program 92.6%

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

   3. Applied rewrites 98.0%

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

      1. lift-fma.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-+.f64 98.0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 32.7%

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

   if -0.085999999999999993 < x < 75

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 98.8

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

   4. Applied rewrites 98.8%

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

   if 75 < x

   1. Initial program 17.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 93.0%

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

Alternative 6: 95.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq -0.00011:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 42:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(\frac{130977.50649958357}{x} + \left(-\frac{y}{x}\right)\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+21)
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))
   (if (<= x -0.00011)
     (/
      (* (- x 2.0) z)
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (if (<= x 42.0)
       (/
        (* (- x 2.0) (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z))
        (fma 313.399215894 x 47.066876606))
       (*
        (- x)
        (-
         (-
          (/
           (-
            (-
             (/
              (- (+ (/ 130977.50649958357 x) (- (/ y x))) 3655.1204654076414)
              x))
            110.1139242984811)
           x))
         4.16438922228))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	} else if (x <= -0.00011) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else if (x <= 42.0) {
		tmp = ((x - 2.0) * fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = -x * (-((-((((130977.50649958357 / x) + -(y / x)) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+21)
		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));
	elseif (x <= -0.00011)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	elseif (x <= 42.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(130977.50649958357 / x) + Float64(-Float64(y / x))) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+21], 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, -0.00011], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 42.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[(N[(N[(130977.50649958357 / x), $MachinePrecision] + (-N[(y / x), $MachinePrecision])), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.8e21

   1. Initial program 11.6%

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

   3. Applied rewrites 17.3%

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

   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 96.4%

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

   if -6.8e21 < x < -1.10000000000000004e-4

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 28.5%

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

   if -1.10000000000000004e-4 < x < 42

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 98.3

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

   7. Applied rewrites 98.3%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. lift-fma.f64 98.6

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

   10. Applied rewrites 98.6%

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

   if 42 < x

   1. Initial program 17.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 93.0%

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

Alternative 7: 95.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -0.00011:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 42:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -6.8e+21)
     t_0
     (if (<= x -0.00011)
       (/
        (* (- x 2.0) z)
        (+
         (*
          (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
          x)
         47.066876606))
       (if (<= x 42.0)
         (/
          (* (- x 2.0) (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z))
          (fma 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 <= -6.8e+21) {
		tmp = t_0;
	} else if (x <= -0.00011) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else if (x <= 42.0) {
		tmp = ((x - 2.0) * fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z)) / fma(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 <= -6.8e+21)
		tmp = t_0;
	elseif (x <= -0.00011)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	elseif (x <= 42.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z)) / fma(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, -6.8e+21], t$95$0, If[LessEqual[x, -0.00011], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 42.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8e21 or 42 < x

   1. Initial program 14.5%

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

   3. Applied rewrites 20.3%

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

   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 94.7%

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

   if -6.8e21 < x < -1.10000000000000004e-4

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 28.5%

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

   if -1.10000000000000004e-4 < x < 42

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 98.3

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

   7. Applied rewrites 98.3%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. lift-fma.f64 98.6

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

   10. Applied rewrites 98.6%

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

Alternative 8: 92.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+21}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00011:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e+21)
   (* 4.16438922228 x)
   (if (<= x -0.00011)
     (/
      (* (- x 2.0) z)
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (if (<= x 60000000.0)
       (/
        (* (- x 2.0) (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z))
        (fma 313.399215894 x 47.066876606))
       (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= -0.00011) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e+21)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -0.00011)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e+21], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -0.00011], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7e21

   1. Initial program 11.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -7e21 < x < -1.10000000000000004e-4

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 28.5%

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

   if -1.10000000000000004e-4 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.5

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

   7. Applied rewrites 97.5%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. lift-fma.f64 97.8

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

   10. Applied rewrites 97.8%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 9: 92.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+21}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00011:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e+21)
   (* 4.16438922228 x)
   (if (<= x -0.00011)
     (/
      (* (- x 2.0) z)
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (if (<= x 60000000.0)
       (/
        (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z))
        (fma 313.399215894 x 47.066876606))
       (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= -0.00011) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e+21)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -0.00011)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e+21], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -0.00011], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7e21

   1. Initial program 11.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -7e21 < x < -1.10000000000000004e-4

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 28.5%

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

   if -1.10000000000000004e-4 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.5

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

   7. Applied rewrites 97.5%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 10: 92.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+22}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00011:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right) \cdot x + 313.399215894, x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e+22)
   (* 4.16438922228 x)
   (if (<= x -0.00011)
     (*
      (- x 2.0)
      (/
       z
       (fma
        (+ (* (fma (+ 43.3400022514 x) x 263.505074721) x) 313.399215894)
        x
        47.066876606)))
     (if (<= x 60000000.0)
       (/
        (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z))
        (fma 313.399215894 x 47.066876606))
       (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e+22) {
		tmp = 4.16438922228 * x;
	} else if (x <= -0.00011) {
		tmp = (x - 2.0) * (z / fma(((fma((43.3400022514 + x), x, 263.505074721) * x) + 313.399215894), x, 47.066876606));
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e+22)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -0.00011)
		tmp = Float64(Float64(x - 2.0) * Float64(z / fma(Float64(Float64(fma(Float64(43.3400022514 + x), x, 263.505074721) * x) + 313.399215894), x, 47.066876606)));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e+22], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -0.00011], N[(N[(x - 2.0), $MachinePrecision] * N[(z / N[(N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8e22

   1. Initial program 11.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.2

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

   4. Applied rewrites 91.2%

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

   if -1.8e22 < x < -1.10000000000000004e-4

   1. Initial program 93.6%

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

   3. Applied rewrites 98.2%

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

      1. lift-fma.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. *-commutative N/A

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

      9. *-commutative N/A

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

      10. +-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-+.f64 98.2

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 34.2%

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

   if -1.10000000000000004e-4 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.5

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

   7. Applied rewrites 97.5%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 11: 92.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+22}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -0.00011:\\ \;\;\;\;\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot z\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e+22)
   (* 4.16438922228 x)
   (if (<= x -0.00011)
     (*
      (/
       (- x 2.0)
       (fma
        (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
        x
        47.066876606))
      z)
     (if (<= x 60000000.0)
       (/
        (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z))
        (fma 313.399215894 x 47.066876606))
       (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e+22) {
		tmp = 4.16438922228 * x;
	} else if (x <= -0.00011) {
		tmp = ((x - 2.0) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * z;
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e+22)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -0.00011)
		tmp = Float64(Float64(Float64(x - 2.0) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * z);
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e+22], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -0.00011], N[(N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8e22

   1. Initial program 11.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.2

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

   4. Applied rewrites 91.2%

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

   if -1.8e22 < x < -1.10000000000000004e-4

   1. Initial program 93.6%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. metadata-eval N/A

         \[\leadsto z \cdot \left(\frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} - \frac{2 \cdot 1}{\color{blue}{\frac{23533438303}{500000000}} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}\right) \]

      4. associate-*r/ N/A

         \[\leadsto z \cdot \left(\frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} - 2 \cdot \color{blue}{\frac{1}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}}\right) \]

      5. *-commutative N/A

         \[\leadsto \left(\frac{x}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)} - 2 \cdot \frac{1}{\frac{23533438303}{500000000} + x \cdot \left(\frac{156699607947}{500000000} + x \cdot \left(\frac{263505074721}{1000000000} + x \cdot \left(\frac{216700011257}{5000000000} + x\right)\right)\right)}\right) \cdot \color{blue}{z} \]

   4. Applied rewrites 34.2%

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

   if -1.10000000000000004e-4 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.8

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.5

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

   7. Applied rewrites 97.5%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 12: 92.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -37.0)
   (*
    (- x 2.0)
    (+ (- (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x)) 4.16438922228))
   (if (<= x 60000000.0)
     (/
      (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z))
      (fma 313.399215894 x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -37.0) {
		tmp = (x - 2.0) * (-((101.7851458539211 - (3451.550173699799 / x)) / x) + 4.16438922228);
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -37.0)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)) + 4.16438922228));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -37.0], N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -37

   1. Initial program 16.2%

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

   3. Applied rewrites 21.8%

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

   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 87.9

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

   6. Applied rewrites 87.9%

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

   if -37 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 96.9

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

   7. Applied rewrites 96.9%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 13: 92.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{-2 \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\frac{3655.1204654076414}{x} - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -37.0)
   (*
    (- x 2.0)
    (+ (- (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x)) 4.16438922228))
   (if (<= x 2.0)
     (/
      (* -2.0 (+ (* (fma 137.519416416 x y) x) z))
      (fma 313.399215894 x 47.066876606))
     (*
      (- x)
      (-
       (- (/ (- (/ 3655.1204654076414 x) 110.1139242984811) x))
       4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -37.0) {
		tmp = (x - 2.0) * (-((101.7851458539211 - (3451.550173699799 / x)) / x) + 4.16438922228);
	} else if (x <= 2.0) {
		tmp = (-2.0 * ((fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = -x * (-(((3655.1204654076414 / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -37.0)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)) + 4.16438922228));
	elseif (x <= 2.0)
		tmp = Float64(Float64(-2.0 * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(3655.1204654076414 / x) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -37.0], N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(-2.0 * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -37

   1. Initial program 16.2%

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

   3. Applied rewrites 21.8%

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

   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 87.9

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

   6. Applied rewrites 87.9%

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

   if -37 < x < 2

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 98.0

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

   4. Applied rewrites 98.0%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.8

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

   7. Applied rewrites 97.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 97.2%

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

   if 2 < x

   1. Initial program 17.4%

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

   2. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

         \[\leadsto \left(-x\right) \cdot \left(\left(\mathsf{neg}\left(\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x}\right)\right) - \frac{104109730557}{25000000000}\right) \]

      7. lower-neg.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\left(-\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x}\right) - \frac{104109730557}{25000000000}\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\left(-\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x}\right) - \frac{104109730557}{25000000000}\right) \]

      9. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\left(-\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot \frac{1}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x}\right) - \frac{104109730557}{25000000000}\right) \]

      10. associate-*r/ N/A

          \[\leadsto \left(-x\right) \cdot \left(\left(-\frac{\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000} \cdot 1}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x}\right) - \frac{104109730557}{25000000000}\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(-x\right) \cdot \left(\left(-\frac{\frac{\frac{2284450290879775841688574159837293}{625000000000000000000000000000}}{x} - \frac{13764240537310136880149}{125000000000000000000}}{x}\right) - \frac{104109730557}{25000000000}\right) \]

      12. lower-/.f64 87.1

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

   4. Applied rewrites 87.1%

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

Alternative 14: 91.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+21)
   (* 4.16438922228 x)
   (if (<= x 60000000.0)
     (/ (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z)) 47.066876606)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / 47.066876606;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+21)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / 47.066876606);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+21], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8e21

   1. Initial program 11.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -6.8e21 < x < 6e7

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 94.5

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

   4. Applied rewrites 94.5%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 94.3

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

   7. Applied rewrites 94.3%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(\frac{4297481763}{31250000}, x, y\right) \cdot x + z\right)}{\frac{23533438303}{500000000}} \]
   9. Step-by-step derivation

   10. Applied rewrites 93.5%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 15: 90.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -37.0)
   (*
    (- x 2.0)
    (+ (- (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x)) 4.16438922228))
   (if (<= x 60000000.0)
     (/ (* (- x 2.0) (fma y x z)) (fma 313.399215894 x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -37.0) {
		tmp = (x - 2.0) * (-((101.7851458539211 - (3451.550173699799 / x)) / x) + 4.16438922228);
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * fma(y, x, z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -37.0)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)) + 4.16438922228));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(y, x, z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -37.0], N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -37

   1. Initial program 16.2%

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

   3. Applied rewrites 21.8%

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

   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 87.9

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

   6. Applied rewrites 87.9%

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

   if -37 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 96.9

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

   7. Applied rewrites 96.9%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot y\right)}}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]

      3. lower-fma.f64 92.3

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

   10. Applied rewrites 92.3%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 16: 77.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0056:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0056)
   (*
    (- x 2.0)
    (+ (- (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x)) 4.16438922228))
   (if (<= x 60000000.0)
     (/ (* (- x 2.0) z) (fma 313.399215894 x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0056) {
		tmp = (x - 2.0) * (-((101.7851458539211 - (3451.550173699799 / x)) / x) + 4.16438922228);
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * z) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0056)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)) + 4.16438922228));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0056], N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00559999999999999994

   1. Initial program 17.3%

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

   3. Applied rewrites 22.9%

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

   4. 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 86.8

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

   6. Applied rewrites 86.8%

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

   if -0.00559999999999999994 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.6

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.4

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

   7. Applied rewrites 97.4%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{z}}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 67.0%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 17: 77.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0056:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\frac{3451.550173699799}{x \cdot x} + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0056)
   (* (- x 2.0) (+ (/ 3451.550173699799 (* x x)) 4.16438922228))
   (if (<= x 60000000.0)
     (/ (* (- x 2.0) z) (fma 313.399215894 x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0056) {
		tmp = (x - 2.0) * ((3451.550173699799 / (x * x)) + 4.16438922228);
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * z) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0056)
		tmp = Float64(Float64(x - 2.0) * Float64(Float64(3451.550173699799 / Float64(x * x)) + 4.16438922228));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0056], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(3451.550173699799 / N[(x * x), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00559999999999999994

   1. Initial program 17.3%

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

   3. Applied rewrites 22.9%

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

   4. 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 86.8

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

   6. Applied rewrites 86.8%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 86.5

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

   9. Applied rewrites 86.5%

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

   if -0.00559999999999999994 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.6

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.4

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

   7. Applied rewrites 97.4%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{z}}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 67.0%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 18: 77.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0056:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0056)
   (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x)))
   (if (<= x 60000000.0)
     (/ (* (- x 2.0) z) (fma 313.399215894 x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0056) {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else if (x <= 60000000.0) {
		tmp = ((x - 2.0) * z) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0056)
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	elseif (x <= 60000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0056], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00559999999999999994

   1. Initial program 17.3%

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

   3. Applied rewrites 22.9%

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

   4. 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 86.7

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

   6. Applied rewrites 86.7%

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

   if -0.00559999999999999994 < x < 6e7

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.6

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.4

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

   7. Applied rewrites 97.4%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{z}}{\mathsf{fma}\left(\frac{156699607947}{500000000}, x, \frac{23533438303}{500000000}\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 67.0%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 19: 76.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 60000000:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 0.3041881842569256, x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+21)
   (* 4.16438922228 x)
   (if (<= x 60000000.0)
     (fma (* z 0.3041881842569256) x (* -0.0424927283095952 z))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 60000000.0) {
		tmp = fma((z * 0.3041881842569256), x, (-0.0424927283095952 * z));
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+21)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 60000000.0)
		tmp = fma(Float64(z * 0.3041881842569256), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+21], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 60000000.0], N[(N[(z * 0.3041881842569256), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8e21

   1. Initial program 11.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -6.8e21 < x < 6e7

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 72.6%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto x \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) + \frac{-1000000000}{23533438303} \cdot \color{blue}{z} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x + \frac{-1000000000}{23533438303} \cdot z \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      4. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{fma}\left(z \cdot \left(\frac{500000000}{23533438303} - \frac{-156699607947000000000}{553822718361107519809}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(z \cdot \left(\frac{500000000}{23533438303} - \frac{-156699607947000000000}{553822718361107519809}\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(z \cdot \frac{168466327098500000000}{553822718361107519809}, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. lift-*.f64 64.7

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

   7. Applied rewrites 64.7%

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

   if 6e7 < x

   1. Initial program 15.7%

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

   2. 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 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 20: 76.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.95:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+21)
   (* 4.16438922228 x)
   (if (<= x 1.95)
     (* -0.0424927283095952 z)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.95) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * 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 <= (-6.8d+21)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 1.95d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.95) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.8e+21:
		tmp = 4.16438922228 * x
	elif x <= 1.95:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+21)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.95)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.8e+21)
		tmp = 4.16438922228 * x;
	elseif (x <= 1.95)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+21], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.95], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8e21

   1. Initial program 11.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -6.8e21 < x < 1.94999999999999996

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 64.9

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

   4. Applied rewrites 64.9%

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

   if 1.94999999999999996 < x

   1. Initial program 17.4%

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

   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 87.0

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

   4. Applied rewrites 87.0%

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

Alternative 21: 76.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.8:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+21)
   (* 4.16438922228 x)
   (if (<= x 1.8) (* -0.0424927283095952 z) (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.8) {
		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 <= (-6.8d+21)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 1.8d0) 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 <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.8) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.8e+21:
		tmp = 4.16438922228 * x
	elif x <= 1.8:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+21)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.8)
		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 <= -6.8e+21)
		tmp = 4.16438922228 * x;
	elseif (x <= 1.8)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+21], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.8], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.8e21

   1. Initial program 11.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -6.8e21 < x < 1.80000000000000004

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 64.9

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

   4. Applied rewrites 64.9%

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

   if 1.80000000000000004 < x

   1. Initial program 17.5%

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

   3. Applied rewrites 23.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 86.6%

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

Alternative 22: 76.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.8e+21)
   (* 4.16438922228 x)
   (if (<= x 2.0) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		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 <= (-6.8d+21)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.0d0) 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 <= -6.8e+21) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.8e+21:
		tmp = 4.16438922228 * x
	elif x <= 2.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.8e+21)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		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 <= -6.8e+21)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.8e+21], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.8e21 or 2 < x

   1. Initial program 14.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 88.8

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

   4. Applied rewrites 88.8%

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

   if -6.8e21 < x < 2

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 64.9

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

   4. Applied rewrites 64.9%

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

Alternative 23: 35.0% accurate, 13.3× 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 58.5%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 35.0

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

4. Applied rewrites 35.0%

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

Reproduce

herbie shell --seed 2025110 
(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)))