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

Percentage Accurate: 57.4% → 97.1%

Time: 6.9s

Alternatives: 32

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\left(1 + \frac{x \cdot 4.16438922228}{78.6994924154}\right) \cdot 78.6994924154, x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{t\_0}, \left(x - 2\right) \cdot \frac{z}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
   (if (<=
        (/
         (*
          (- x 2.0)
          (+
           (*
            (+
             (*
              (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416)
              x)
             y)
            x)
           z))
         (+
          (*
           (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
           x)
          47.066876606))
        2e+255)
     (fma
      (fma
       (fma
        (* (+ 1.0 (/ (* x 4.16438922228) 78.6994924154)) 78.6994924154)
        x
        137.519416416)
       x
       y)
      (/ (* (- x 2.0) x) t_0)
      (* (- x 2.0) (/ z t_0)))
     (*
      -1.0
      (*
       x
       (-
        (*
         -1.0
         (/
          (-
           (*
            -1.0
            (/
             (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414)
             x))
           110.1139242984811)
          x))
        4.16438922228))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+255) {
		tmp = fma(fma(fma(((1.0 + ((x * 4.16438922228) / 78.6994924154)) * 78.6994924154), x, 137.519416416), x, y), (((x - 2.0) * x) / t_0), ((x - 2.0) * (z / t_0)));
	} else {
		tmp = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+255)
		tmp = fma(fma(fma(Float64(Float64(1.0 + Float64(Float64(x * 4.16438922228) / 78.6994924154)) * 78.6994924154), x, 137.519416416), x, y), Float64(Float64(Float64(x - 2.0) * x) / t_0), Float64(Float64(x - 2.0) * Float64(z / t_0)));
	else
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 2e+255], N[(N[(N[(N[(N[(1.0 + N[(N[(x * 4.16438922228), $MachinePrecision] / 78.6994924154), $MachinePrecision]), $MachinePrecision] * 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * N[(N[(N[(x - 2.0), $MachinePrecision] * x), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(x - 2.0), $MachinePrecision] * N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $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))) < 1.99999999999999998e255

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. sum-to-mult N/A

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

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

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

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

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

      8. lower-unsound-/.f64 61.2%

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

   5. Applied rewrites 61.2%

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

   if 1.99999999999999998e255 < (/.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 57.4%

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

   3. Applied rewrites 61.2%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 49.1%

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

Alternative 2: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), \frac{\left(x - 2\right) \cdot x}{t\_0}, \left(x - 2\right) \cdot \frac{z}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
   (if (<=
        (/
         (*
          (- x 2.0)
          (+
           (*
            (+
             (*
              (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416)
              x)
             y)
            x)
           z))
         (+
          (*
           (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
           x)
          47.066876606))
        2e+255)
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      (/ (* (- x 2.0) x) t_0)
      (* (- x 2.0) (/ z t_0)))
     (*
      -1.0
      (*
       x
       (-
        (*
         -1.0
         (/
          (-
           (*
            -1.0
            (/
             (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414)
             x))
           110.1139242984811)
          x))
        4.16438922228))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+255) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), (((x - 2.0) * x) / t_0), ((x - 2.0) * (z / t_0)));
	} else {
		tmp = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+255)
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), Float64(Float64(Float64(x - 2.0) * x) / t_0), Float64(Float64(x - 2.0) * Float64(z / t_0)));
	else
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 2e+255], N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * N[(N[(N[(x - 2.0), $MachinePrecision] * x), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(x - 2.0), $MachinePrecision] * N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $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))) < 1.99999999999999998e255

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   if 1.99999999999999998e255 < (/.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 57.4%

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

   3. Applied rewrites 61.2%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 49.1%

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

Alternative 3: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{x - 2}{t\_0}, \left(x - 2\right) \cdot \left(x \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right)}{t\_0}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
   (if (<=
        (/
         (*
          (- x 2.0)
          (+
           (*
            (+
             (*
              (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416)
              x)
             y)
            x)
           z))
         (+
          (*
           (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
           x)
          47.066876606))
        2e+255)
     (fma
      z
      (/ (- x 2.0) t_0)
      (*
       (- x 2.0)
       (*
        x
        (/
         (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
         t_0))))
     (*
      -1.0
      (*
       x
       (-
        (*
         -1.0
         (/
          (-
           (*
            -1.0
            (/
             (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414)
             x))
           110.1139242984811)
          x))
        4.16438922228))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+255) {
		tmp = fma(z, ((x - 2.0) / t_0), ((x - 2.0) * (x * (fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y) / t_0))));
	} else {
		tmp = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+255)
		tmp = fma(z, Float64(Float64(x - 2.0) / t_0), Float64(Float64(x - 2.0) * Float64(x * Float64(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y) / t_0))));
	else
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 2e+255], N[(z * N[(N[(x - 2.0), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(x - 2.0), $MachinePrecision] * N[(x * N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $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))) < 1.99999999999999998e255

   1. Initial program 57.4%

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

   3. Applied rewrites 61.0%

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

   if 1.99999999999999998e255 < (/.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 57.4%

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

   3. Applied rewrites 61.2%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 49.1%

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

Alternative 4: 97.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{x - 2}}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \end{array} \]

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))
      2e+255)
   (*
    (fma
     (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
     x
     z)
    (/
     1.0
     (/
      (fma
       (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
       x
       47.066876606)
      (- x 2.0))))
   (*
    -1.0
    (*
     x
     (-
      (*
       -1.0
       (/
        (-
         (*
          -1.0
          (/ (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414) x))
         110.1139242984811)
        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)) <= 2e+255) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * (1.0 / (fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606) / (x - 2.0)));
	} else {
		tmp = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / 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)) <= 2e+255)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(1.0 / Float64(fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606) / Float64(x - 2.0))));
	else
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / 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], 2e+255], N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(1.0 / N[(N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision] / N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $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))) < 1.99999999999999998e255

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. div-flip N/A

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

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

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

      6. lower-unsound-/.f64 60.2%

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

   7. Applied rewrites 60.2%

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

   if 1.99999999999999998e255 < (/.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 57.4%

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

   3. Applied rewrites 61.2%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 49.1%

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

Alternative 5: 96.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{2 - x}{-47.066876606 - \mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \end{array} \]

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))
      2e+255)
   (*
    (fma
     (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
     x
     z)
    (/
     (- 2.0 x)
     (-
      -47.066876606
      (* (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894) x))))
   (*
    -1.0
    (*
     x
     (-
      (*
       -1.0
       (/
        (-
         (*
          -1.0
          (/ (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414) x))
         110.1139242984811)
        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)) <= 2e+255) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * ((2.0 - x) / (-47.066876606 - (fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x)));
	} else {
		tmp = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / 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)) <= 2e+255)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(2.0 - x) / Float64(-47.066876606 - Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x))));
	else
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / 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], 2e+255], N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(2.0 - x), $MachinePrecision] / N[(-47.066876606 - N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $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))) < 1.99999999999999998e255

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip-rev N/A

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

      4. frac-2neg N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-negate-rev N/A

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

      8. lower--.f64 N/A

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

      9. lift-fma.f64 N/A

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

      10. add-flip N/A

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

      11. lift-fma.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift--.f64 N/A

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

      14. metadata-eval N/A

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

      15. add-flip N/A

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

      16. sub-negate N/A

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

   7. Applied rewrites 60.2%

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

   if 1.99999999999999998e255 < (/.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 57.4%

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

   3. Applied rewrites 61.2%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 49.1%

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

Alternative 6: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \end{array} \]

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))
      2e+255)
   (*
    (fma
     (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
     x
     z)
    (/
     (- x 2.0)
     (fma
      (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
      x
      47.066876606)))
   (*
    -1.0
    (*
     x
     (-
      (*
       -1.0
       (/
        (-
         (*
          -1.0
          (/ (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414) x))
         110.1139242984811)
        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)) <= 2e+255) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((x - 2.0) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / 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)) <= 2e+255)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(x - 2.0) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / 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], 2e+255], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $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))) < 1.99999999999999998e255

   1. Initial program 57.4%

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

   3. Applied rewrites 60.2%

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

   if 1.99999999999999998e255 < (/.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 57.4%

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

   3. Applied rewrites 61.2%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 49.1%

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

Alternative 7: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -660000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 650000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(\left(x - 1\right) - 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+
           4.16438922228
           (*
            -1.0
            (/
             (+
              101.7851458539211
              (*
               -1.0
               (/
                (+
                 3451.550173699799
                 (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
                x)))
             x)))
          (- x 2.0))))
   (if (<= x -660000.0)
     t_0
     (if (<= x 650000000000.0)
       (*
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (fma
          (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
          x
          47.066876606))
        (- (- x 1.0) 1.0))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -660000.0) {
		tmp = t_0;
	} else if (x <= 650000000000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * ((x - 1.0) - 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -660000.0)
		tmp = t_0;
	elseif (x <= 650000000000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(Float64(x - 1.0) - 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -660000.0], t$95$0, If[LessEqual[x, 650000000000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(N[(x - 1.0), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e5 or 6.5e11 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]

   if -6.6e5 < x < 6.5e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

      1. lift--.f64 N/A

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

      2. metadata-eval N/A

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

      3. associate--r+ N/A

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

      4. lower--.f64 N/A

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

      5. lower--.f64 53.5%

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

   8. Applied rewrites 53.5%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \color{blue}{\left(\left(x - 1\right) - 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -660000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 650000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x - -47.066876606} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+
           4.16438922228
           (*
            -1.0
            (/
             (+
              101.7851458539211
              (*
               -1.0
               (/
                (+
                 3451.550173699799
                 (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
                x)))
             x)))
          (- x 2.0))))
   (if (<= x -660000.0)
     t_0
     (if (<= x 650000000000.0)
       (*
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (-
          (*
           (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
           x)
          -47.066876606))
        (- x 2.0))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -660000.0) {
		tmp = t_0;
	} else if (x <= 650000000000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / ((fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) - -47.066876606)) * (x - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -660000.0)
		tmp = t_0;
	elseif (x <= 650000000000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / Float64(Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x) - -47.066876606)) * Float64(x - 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -660000.0], t$95$0, If[LessEqual[x, 650000000000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision] - -47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e5 or 6.5e11 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]

   if -6.6e5 < x < 6.5e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

      1. lift-fma.f64 N/A

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

      2. add-flip N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. lift--.f64 N/A

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

      6. metadata-eval N/A

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

      7. add-flip N/A

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

      8. lower--.f64 N/A

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

      9. add-flip N/A

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

      10. metadata-eval N/A

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

      11. lift--.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-fma.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. metadata-eval 53.5%

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

   8. Applied rewrites 53.5%

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

Alternative 9: 96.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -660000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 650000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+
           4.16438922228
           (*
            -1.0
            (/
             (+
              101.7851458539211
              (*
               -1.0
               (/
                (+
                 3451.550173699799
                 (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
                x)))
             x)))
          (- x 2.0))))
   (if (<= x -660000.0)
     t_0
     (if (<= x 650000000000.0)
       (/
        (* (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) (- x 2.0))
        (fma
         (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
         x
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -660000.0) {
		tmp = t_0;
	} else if (x <= 650000000000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * (x - 2.0)) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -660000.0)
		tmp = t_0;
	elseif (x <= 650000000000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -660000.0], t$95$0, If[LessEqual[x, 650000000000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e5 or 6.5e11 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]

   if -6.6e5 < x < 6.5e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

      1. lift-*.f64 N/A

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

   8. Applied rewrites 52.5%

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

Alternative 10: 96.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -660000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 650000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+
           4.16438922228
           (*
            -1.0
            (/
             (+
              101.7851458539211
              (*
               -1.0
               (/
                (+
                 3451.550173699799
                 (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
                x)))
             x)))
          (- x 2.0))))
   (if (<= x -660000.0)
     t_0
     (if (<= x 650000000000.0)
       (*
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (fma
          (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
          x
          47.066876606))
        (- x 2.0))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -660000.0) {
		tmp = t_0;
	} else if (x <= 650000000000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -660000.0)
		tmp = t_0;
	elseif (x <= 650000000000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -660000.0], t$95$0, If[LessEqual[x, 650000000000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6e5 or 6.5e11 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]

   if -6.6e5 < x < 6.5e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

Alternative 11: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 540000000000:\\ \;\;\;\;\frac{\left(2 - x\right) \cdot \mathsf{fma}\left(y, x, z\right)}{-47.066876606 - \mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+
           4.16438922228
           (*
            -1.0
            (/
             (+
              101.7851458539211
              (*
               -1.0
               (/
                (+
                 3451.550173699799
                 (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
                x)))
             x)))
          (- x 2.0))))
   (if (<= x -8.0)
     t_0
     (if (<= x 1.75e-7)
       (*
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (fma
          (fma (fma 43.3400022514 x 263.505074721) x 313.399215894)
          x
          47.066876606))
        (- x 2.0))
       (if (<= x 540000000000.0)
         (/
          (* (- 2.0 x) (fma y x z))
          (-
           -47.066876606
           (*
            (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
            x)))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -8.0) {
		tmp = t_0;
	} else if (x <= 1.75e-7) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(fma(43.3400022514, x, 263.505074721), x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else if (x <= 540000000000.0) {
		tmp = ((2.0 - x) * fma(y, x, z)) / (-47.066876606 - (fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -8.0)
		tmp = t_0;
	elseif (x <= 1.75e-7)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(fma(43.3400022514, x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	elseif (x <= 540000000000.0)
		tmp = Float64(Float64(Float64(2.0 - x) * fma(y, x, z)) / Float64(-47.066876606 - Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.0], t$95$0, If[LessEqual[x, 1.75e-7], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(43.3400022514 * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 540000000000.0], N[(N[(N[(2.0 - x), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(-47.066876606 - N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8 or 5.4e11 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]

   if -8 < x < 1.74999999999999992e-7

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{216700011257}{5000000000}}, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 50.7%

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

   if 1.74999999999999992e-7 < x < 5.4e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.0%

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

   6. Applied rewrites 50.0%

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

Alternative 12: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -125:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 540000000000:\\ \;\;\;\;\frac{\left(2 - x\right) \cdot \mathsf{fma}\left(y, x, z\right)}{-47.066876606 - \mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+
           4.16438922228
           (*
            -1.0
            (/
             (+
              101.7851458539211
              (*
               -1.0
               (/
                (+
                 3451.550173699799
                 (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
                x)))
             x)))
          (- x 2.0))))
   (if (<= x -125.0)
     t_0
     (if (<= x 1.75e-7)
       (*
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
        (- x 2.0))
       (if (<= x 540000000000.0)
         (/
          (* (- 2.0 x) (fma y x z))
          (-
           -47.066876606
           (*
            (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
            x)))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -125.0) {
		tmp = t_0;
	} else if (x <= 1.75e-7) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else if (x <= 540000000000.0) {
		tmp = ((2.0 - x) * fma(y, x, z)) / (-47.066876606 - (fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -125.0)
		tmp = t_0;
	elseif (x <= 1.75e-7)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	elseif (x <= 540000000000.0)
		tmp = Float64(Float64(Float64(2.0 - x) * fma(y, x, z)) / Float64(-47.066876606 - Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -125.0], t$95$0, If[LessEqual[x, 1.75e-7], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 540000000000.0], N[(N[(N[(2.0 - x), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(-47.066876606 - N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -125 or 5.4e11 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]

   if -125 < x < 1.74999999999999992e-7

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 49.6%

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

   if 1.74999999999999992e-7 < x < 5.4e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.0%

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

   6. Applied rewrites 50.0%

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

Alternative 13: 96.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := -1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{if}\;x \leq -125:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 540000000000:\\ \;\;\;\;\frac{\left(2 - x\right) \cdot \mathsf{fma}\left(y, x, z\right)}{-47.066876606 - \mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          -1.0
          (*
           x
           (-
            (*
             -1.0
             (/
              (-
               (*
                -1.0
                (/
                 (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414)
                 x))
               110.1139242984811)
              x))
            4.16438922228)))))
   (if (<= x -125.0)
     t_0
     (if (<= x 1.75e-7)
       (*
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
        (- x 2.0))
       (if (<= x 540000000000.0)
         (/
          (* (- 2.0 x) (fma y x z))
          (-
           -47.066876606
           (*
            (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
            x)))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	double tmp;
	if (x <= -125.0) {
		tmp = t_0;
	} else if (x <= 1.75e-7) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else if (x <= 540000000000.0) {
		tmp = ((2.0 - x) * fma(y, x, z)) / (-47.066876606 - (fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(Float64(-1.0 * Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228)))
	tmp = 0.0
	if (x <= -125.0)
		tmp = t_0;
	elseif (x <= 1.75e-7)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	elseif (x <= 540000000000.0)
		tmp = Float64(Float64(Float64(2.0 - x) * fma(y, x, z)) / Float64(-47.066876606 - Float64(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894) * x)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(N[(-1.0 * N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -125.0], t$95$0, If[LessEqual[x, 1.75e-7], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 540000000000.0], N[(N[(N[(2.0 - x), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(-47.066876606 - N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -125 or 5.4e11 < x

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 49.1%

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

   if -125 < x < 1.74999999999999992e-7

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 49.6%

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

   if 1.74999999999999992e-7 < x < 5.4e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.0%

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

   6. Applied rewrites 50.0%

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

Alternative 14: 96.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -136000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 510000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(137.519416416 \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (+
           4.16438922228
           (*
            -1.0
            (/
             (+
              101.7851458539211
              (*
               -1.0
               (/
                (+
                 3451.550173699799
                 (* -1.0 (/ (+ 124074.40615218398 (* -1.0 y)) x)))
                x)))
             x)))
          (- x 2.0))))
   (if (<= x -136000.0)
     t_0
     (if (<= x 510000000000.0)
       (/
        (* (- x 2.0) (+ (* (+ (* 137.519416416 x) y) x) z))
        (+
         (*
          (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
          x)
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -136000.0) {
		tmp = t_0;
	} else if (x <= 510000000000.0) {
		tmp = ((x - 2.0) * ((((137.519416416 * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 + ((-1.0d0) * ((101.7851458539211d0 + ((-1.0d0) * ((3451.550173699799d0 + ((-1.0d0) * ((124074.40615218398d0 + ((-1.0d0) * y)) / x))) / x))) / x))) * (x - 2.0d0)
    if (x <= (-136000.0d0)) then
        tmp = t_0
    else if (x <= 510000000000.0d0) then
        tmp = ((x - 2.0d0) * ((((137.519416416d0 * x) + y) * x) + z)) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	double tmp;
	if (x <= -136000.0) {
		tmp = t_0;
	} else if (x <= 510000000000.0) {
		tmp = ((x - 2.0) * ((((137.519416416 * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0)
	tmp = 0
	if x <= -136000.0:
		tmp = t_0
	elif x <= 510000000000.0:
		tmp = ((x - 2.0) * ((((137.519416416 * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 + Float64(-1.0 * Float64(Float64(101.7851458539211 + Float64(-1.0 * Float64(Float64(3451.550173699799 + Float64(-1.0 * Float64(Float64(124074.40615218398 + Float64(-1.0 * y)) / x))) / x))) / x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -136000.0)
		tmp = t_0;
	elseif (x <= 510000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(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));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 + (-1.0 * ((101.7851458539211 + (-1.0 * ((3451.550173699799 + (-1.0 * ((124074.40615218398 + (-1.0 * y)) / x))) / x))) / x))) * (x - 2.0);
	tmp = 0.0;
	if (x <= -136000.0)
		tmp = t_0;
	elseif (x <= 510000000000.0)
		tmp = ((x - 2.0) * ((((137.519416416 * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 + N[(-1.0 * N[(N[(101.7851458539211 + N[(-1.0 * N[(N[(3451.550173699799 + N[(-1.0 * N[(N[(124074.40615218398 + N[(-1.0 * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -136000.0], t$95$0, If[LessEqual[x, 510000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(137.519416416 * 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], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -136000 or 5.1e11 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   9. Applied rewrites 49.3%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 + -1 \cdot \frac{3451.550173699799 + -1 \cdot \frac{124074.40615218398 + -1 \cdot y}{x}}{x}}{x}\right)} \cdot \left(x - 2\right) \]

   if -136000 < x < 5.1e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\color{blue}{\frac{4297481763}{31250000}} \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.4%

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

Alternative 15: 94.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -0.013:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(t\_0, x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{\left(2 - x\right) \cdot \mathsf{fma}\left(y, x, z\right)}{-47.066876606 - t\_0 \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)))
   (if (<= x -7.5e+47)
     (* x 4.16438922228)
     (if (<= x -0.013)
       (* (fma y x z) (/ (- x 2.0) (fma t_0 x 47.066876606)))
       (if (<= x 1.75e-7)
         (*
          (/
           (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
           (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
          (- x 2.0))
         (if (<= x 1.9e+20)
           (/ (* (- 2.0 x) (fma y x z)) (- -47.066876606 (* t_0 x)))
           (* x 4.16438922228)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894);
	double tmp;
	if (x <= -7.5e+47) {
		tmp = x * 4.16438922228;
	} else if (x <= -0.013) {
		tmp = fma(y, x, z) * ((x - 2.0) / fma(t_0, x, 47.066876606));
	} else if (x <= 1.75e-7) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else if (x <= 1.9e+20) {
		tmp = ((2.0 - x) * fma(y, x, z)) / (-47.066876606 - (t_0 * x));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894)
	tmp = 0.0
	if (x <= -7.5e+47)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= -0.013)
		tmp = Float64(fma(y, x, z) * Float64(Float64(x - 2.0) / fma(t_0, x, 47.066876606)));
	elseif (x <= 1.75e-7)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	elseif (x <= 1.9e+20)
		tmp = Float64(Float64(Float64(2.0 - x) * fma(y, x, z)) / Float64(-47.066876606 - Float64(t_0 * x)));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision]}, If[LessEqual[x, -7.5e+47], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, -0.013], N[(N[(y * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(t$95$0 * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-7], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+20], N[(N[(N[(2.0 - x), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(-47.066876606 - N[(t$95$0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.4999999999999999e47 or 1.9e20 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 46.4%

      \[\leadsto x \cdot 4.16438922228 \]

   if -7.4999999999999999e47 < x < -0.0129999999999999994

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 N/A

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

   6. Applied rewrites 51.2%

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

   if -0.0129999999999999994 < x < 1.74999999999999992e-7

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 49.6%

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

   if 1.74999999999999992e-7 < x < 1.9e20

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.0%

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

   6. Applied rewrites 50.0%

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

Alternative 16: 93.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+24}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+47)
   (* x 4.16438922228)
   (if (<= x 1.8e+24)
     (*
      (/
       (fma y x z)
       (fma
        (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
        x
        47.066876606))
      (- x 2.0))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+47) {
		tmp = x * 4.16438922228;
	} else if (x <= 1.8e+24) {
		tmp = (fma(y, x, z) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+47)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 1.8e+24)
		tmp = Float64(Float64(fma(y, x, z) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+47], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 1.8e+24], N[(N[(N[(y * x + z), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4999999999999999e47 or 1.79999999999999992e24 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 46.4%

      \[\leadsto x \cdot 4.16438922228 \]

   if -7.4999999999999999e47 < x < 1.79999999999999992e24

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   6. Applied rewrites 51.3%

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

Alternative 17: 93.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -125:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;\left(z + x \cdot \left(y + x \cdot \left(137.519416416 + 78.6994924154 \cdot x\right)\right)\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 480000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x - 110.1139242984811\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -125.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 3.2e-5)
     (*
      (+ z (* x (+ y (* x (+ 137.519416416 (* 78.6994924154 x))))))
      (-
       (* x (+ 0.3041881842569256 (* -1.787568985856513 x)))
       0.0424927283095952))
     (if (<= x 480000000000.0)
       (/
        (* (- x 2.0) z)
        (+
         (*
          (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
          x)
         47.066876606))
       (- (* 4.16438922228 x) 110.1139242984811)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 3.2e-5) {
		tmp = (z + (x * (y + (x * (137.519416416 + (78.6994924154 * x)))))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else if (x <= 480000000000.0) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	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 <= (-125.0d0)) then
        tmp = (-1.0d0) * (x * (((-1.0d0) * (((3655.1204654076414d0 * (1.0d0 / x)) - 110.1139242984811d0) / x)) - 4.16438922228d0))
    else if (x <= 3.2d-5) then
        tmp = (z + (x * (y + (x * (137.519416416d0 + (78.6994924154d0 * x)))))) * ((x * (0.3041881842569256d0 + ((-1.787568985856513d0) * x))) - 0.0424927283095952d0)
    else if (x <= 480000000000.0d0) then
        tmp = ((x - 2.0d0) * z) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
    else
        tmp = (4.16438922228d0 * x) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 3.2e-5) {
		tmp = (z + (x * (y + (x * (137.519416416 + (78.6994924154 * x)))))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else if (x <= 480000000000.0) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -125.0:
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228))
	elif x <= 3.2e-5:
		tmp = (z + (x * (y + (x * (137.519416416 + (78.6994924154 * x)))))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952)
	elif x <= 480000000000.0:
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)
	else:
		tmp = (4.16438922228 * x) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -125.0)
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	elseif (x <= 3.2e-5)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(78.6994924154 * x)))))) * Float64(Float64(x * Float64(0.3041881842569256 + Float64(-1.787568985856513 * x))) - 0.0424927283095952));
	elseif (x <= 480000000000.0)
		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));
	else
		tmp = Float64(Float64(4.16438922228 * x) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -125.0)
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	elseif (x <= 3.2e-5)
		tmp = (z + (x * (y + (x * (137.519416416 + (78.6994924154 * x)))))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	elseif (x <= 480000000000.0)
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	else
		tmp = (4.16438922228 * x) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -125.0], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-5], N[(N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(78.6994924154 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x * N[(0.3041881842569256 + N[(-1.787568985856513 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 480000000000.0], 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], N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -125

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 46.3%

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

   4. Applied rewrites 46.3%

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

   if -125 < x < 3.19999999999999986e-5

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 50.0%

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

   8. Applied rewrites 50.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(z + x \cdot \left(y + x \cdot \left(\frac{4297481763}{31250000} + \frac{393497462077}{5000000000} \cdot x\right)\right)\right)} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]
   10. Step-by-step derivation

       1. lower-+.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower-+.f64 N/A

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

       6. lower-*.f64 48.7%

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

   11. Applied rewrites 48.7%

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

   if 3.19999999999999986e-5 < x < 4.8e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 36.0%

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

   if 4.8e11 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

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

Alternative 18: 93.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -0.14:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 480000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x - 110.1139242984811\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.14)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 3.2e-5)
     (*
      (/
       (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
       (fma 313.399215894 x 47.066876606))
      (- x 2.0))
     (if (<= x 480000000000.0)
       (/
        (* (- x 2.0) z)
        (+
         (*
          (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
          x)
         47.066876606))
       (- (* 4.16438922228 x) 110.1139242984811)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.14) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 3.2e-5) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * (x - 2.0);
	} else if (x <= 480000000000.0) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.14)
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	elseif (x <= 3.2e-5)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * Float64(x - 2.0));
	elseif (x <= 480000000000.0)
		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));
	else
		tmp = Float64(Float64(4.16438922228 * x) - 110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.14], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-5], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 480000000000.0], 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], N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.14000000000000001

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 46.3%

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

   4. Applied rewrites 46.3%

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

   if -0.14000000000000001 < x < 3.19999999999999986e-5

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 51.2%

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

   if 3.19999999999999986e-5 < x < 4.8e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 36.0%

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

   if 4.8e11 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

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

Alternative 19: 93.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -125:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-5}:\\ \;\;\;\;\left(z + x \cdot \left(y + 137.519416416 \cdot x\right)\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 480000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x - 110.1139242984811\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -125.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 3.2e-5)
     (*
      (+ z (* x (+ y (* 137.519416416 x))))
      (-
       (* x (+ 0.3041881842569256 (* -1.787568985856513 x)))
       0.0424927283095952))
     (if (<= x 480000000000.0)
       (/
        (* (- x 2.0) z)
        (+
         (*
          (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
          x)
         47.066876606))
       (- (* 4.16438922228 x) 110.1139242984811)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 3.2e-5) {
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else if (x <= 480000000000.0) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	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 <= (-125.0d0)) then
        tmp = (-1.0d0) * (x * (((-1.0d0) * (((3655.1204654076414d0 * (1.0d0 / x)) - 110.1139242984811d0) / x)) - 4.16438922228d0))
    else if (x <= 3.2d-5) then
        tmp = (z + (x * (y + (137.519416416d0 * x)))) * ((x * (0.3041881842569256d0 + ((-1.787568985856513d0) * x))) - 0.0424927283095952d0)
    else if (x <= 480000000000.0d0) then
        tmp = ((x - 2.0d0) * z) / (((((((x + 43.3400022514d0) * x) + 263.505074721d0) * x) + 313.399215894d0) * x) + 47.066876606d0)
    else
        tmp = (4.16438922228d0 * x) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 3.2e-5) {
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else if (x <= 480000000000.0) {
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -125.0:
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228))
	elif x <= 3.2e-5:
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952)
	elif x <= 480000000000.0:
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)
	else:
		tmp = (4.16438922228 * x) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -125.0)
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	elseif (x <= 3.2e-5)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(137.519416416 * x)))) * Float64(Float64(x * Float64(0.3041881842569256 + Float64(-1.787568985856513 * x))) - 0.0424927283095952));
	elseif (x <= 480000000000.0)
		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));
	else
		tmp = Float64(Float64(4.16438922228 * x) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -125.0)
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	elseif (x <= 3.2e-5)
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	elseif (x <= 480000000000.0)
		tmp = ((x - 2.0) * z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	else
		tmp = (4.16438922228 * x) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -125.0], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-5], N[(N[(z + N[(x * N[(y + N[(137.519416416 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x * N[(0.3041881842569256 + N[(-1.787568985856513 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 480000000000.0], 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], N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -125

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 46.3%

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

   4. Applied rewrites 46.3%

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

   if -125 < x < 3.19999999999999986e-5

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 50.0%

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

   8. Applied rewrites 50.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(z + x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)\right)} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]
   10. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \left(z + \color{blue}{x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)}\right) \cdot \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \left(z + x \cdot \color{blue}{\left(y + \frac{4297481763}{31250000} \cdot x\right)}\right) \cdot \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \left(z + x \cdot \left(y + \color{blue}{\frac{4297481763}{31250000} \cdot x}\right)\right) \cdot \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \]

       4. lower-*.f64 49.8%

          \[\leadsto \left(z + x \cdot \left(y + 137.519416416 \cdot \color{blue}{x}\right)\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]

   11. Applied rewrites 49.8%

       \[\leadsto \color{blue}{\left(z + x \cdot \left(y + 137.519416416 \cdot x\right)\right)} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]

   if 3.19999999999999986e-5 < x < 4.8e11

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 36.0%

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

   if 4.8e11 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

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

Alternative 20: 92.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -125:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 2.6:\\ \;\;\;\;\left(z + x \cdot \left(y + 137.519416416 \cdot x\right)\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -125.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 2.6)
     (*
      (+ z (* x (+ y (* 137.519416416 x))))
      (-
       (* x (+ 0.3041881842569256 (* -1.787568985856513 x)))
       0.0424927283095952))
     (*
      (- x 2.0)
      (- 4.16438922228 (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 2.6) {
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else {
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / 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 <= (-125.0d0)) then
        tmp = (-1.0d0) * (x * (((-1.0d0) * (((3655.1204654076414d0 * (1.0d0 / x)) - 110.1139242984811d0) / x)) - 4.16438922228d0))
    else if (x <= 2.6d0) then
        tmp = (z + (x * (y + (137.519416416d0 * x)))) * ((x * (0.3041881842569256d0 + ((-1.787568985856513d0) * x))) - 0.0424927283095952d0)
    else
        tmp = (x - 2.0d0) * (4.16438922228d0 - ((101.7851458539211d0 - (3451.550173699799d0 / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 2.6) {
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else {
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -125.0:
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228))
	elif x <= 2.6:
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952)
	else:
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -125.0)
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	elseif (x <= 2.6)
		tmp = Float64(Float64(z + Float64(x * Float64(y + Float64(137.519416416 * x)))) * Float64(Float64(x * Float64(0.3041881842569256 + Float64(-1.787568985856513 * x))) - 0.0424927283095952));
	else
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -125.0)
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	elseif (x <= 2.6)
		tmp = (z + (x * (y + (137.519416416 * x)))) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	else
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -125.0], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6], N[(N[(z + N[(x * N[(y + N[(137.519416416 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x * N[(0.3041881842569256 + N[(-1.787568985856513 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -125

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 46.3%

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

   4. Applied rewrites 46.3%

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

   if -125 < x < 2.60000000000000009

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 50.0%

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

   8. Applied rewrites 50.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(z + x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)\right)} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]
   10. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \left(z + \color{blue}{x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)}\right) \cdot \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \]

       2. lower-*.f64 N/A

          \[\leadsto \left(z + x \cdot \color{blue}{\left(y + \frac{4297481763}{31250000} \cdot x\right)}\right) \cdot \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \]

       3. lower-+.f64 N/A

          \[\leadsto \left(z + x \cdot \left(y + \color{blue}{\frac{4297481763}{31250000} \cdot x}\right)\right) \cdot \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \]

       4. lower-*.f64 49.8%

          \[\leadsto \left(z + x \cdot \left(y + 137.519416416 \cdot \color{blue}{x}\right)\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]

   11. Applied rewrites 49.8%

       \[\leadsto \color{blue}{\left(z + x \cdot \left(y + 137.519416416 \cdot x\right)\right)} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]

   if 2.60000000000000009 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.2%

         \[\leadsto \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right) \cdot \left(x - 2\right) \]

   9. Applied rewrites 46.2%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 46.2%

          \[\leadsto \color{blue}{\left(x - 2\right) \cdot \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

       4. lift-+.f64 N/A

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

       5. add-flip N/A

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

       6. lower--.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. mul-1-neg N/A

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

   11. Applied rewrites 46.2%

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

Alternative 21: 92.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -125:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 160:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x - 110.1139242984811\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -125.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 160.0)
     (*
      (/ (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) 47.066876606)
      (- x 2.0))
     (- (* 4.16438922228 x) 110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 160.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / 47.066876606) * (x - 2.0);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -125.0)
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	elseif (x <= 160.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / 47.066876606) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(4.16438922228 * x) - 110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -125.0], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 160.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -125

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 46.3%

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

   4. Applied rewrites 46.3%

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

   if -125 < x < 160

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 49.6%

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

   if 160 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

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

Alternative 22: 92.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -125:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 3.25:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -125.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 3.25)
     (*
      (fma
       (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
       x
       z)
      -0.0424927283095952)
     (*
      (- x 2.0)
      (- 4.16438922228 (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -125.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 3.25) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952;
	} else {
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -125.0)
		tmp = Float64(-1.0 * Float64(x * Float64(Float64(-1.0 * Float64(Float64(Float64(3655.1204654076414 * Float64(1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228)));
	elseif (x <= 3.25)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952);
	else
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -125.0], N[(-1.0 * N[(x * N[(N[(-1.0 * N[(N[(N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.25], N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * -0.0424927283095952), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -125

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 46.3%

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

   4. Applied rewrites 46.3%

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

   if -125 < x < 3.25

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{-1000000000}{23533438303}} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.3%

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

   if 3.25 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.2%

         \[\leadsto \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right) \cdot \left(x - 2\right) \]

   9. Applied rewrites 46.2%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 46.2%

          \[\leadsto \color{blue}{\left(x - 2\right) \cdot \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

       4. lift-+.f64 N/A

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

       5. add-flip N/A

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

       6. lower--.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. mul-1-neg N/A

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

   11. Applied rewrites 46.2%

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

Alternative 23: 91.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right)\\ \mathbf{if}\;x \leq -125:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.25:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (-
           4.16438922228
           (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x)))))
   (if (<= x -125.0)
     t_0
     (if (<= x 3.25)
       (*
        (fma
         (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
         x
         z)
        -0.0424927283095952)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	double tmp;
	if (x <= -125.0) {
		tmp = t_0;
	} else if (x <= 3.25) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)))
	tmp = 0.0
	if (x <= -125.0)
		tmp = t_0;
	elseif (x <= 3.25)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -125.0], t$95$0, If[LessEqual[x, 3.25], N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * -0.0424927283095952), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -125 or 3.25 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.2%

         \[\leadsto \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right) \cdot \left(x - 2\right) \]

   9. Applied rewrites 46.2%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 46.2%

          \[\leadsto \color{blue}{\left(x - 2\right) \cdot \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

       4. lift-+.f64 N/A

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

       5. add-flip N/A

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

       6. lower--.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. mul-1-neg N/A

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

   11. Applied rewrites 46.2%

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

   if -125 < x < 3.25

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\frac{-1000000000}{23533438303}} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.3%

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

Alternative 24: 90.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right)\\ \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.25:\\ \;\;\;\;\left(z + x \cdot y\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (-
           4.16438922228
           (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x)))))
   (if (<= x -0.0068)
     t_0
     (if (<= x 3.25)
       (*
        (+ z (* x y))
        (-
         (* x (+ 0.3041881842569256 (* -1.787568985856513 x)))
         0.0424927283095952))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 3.25) {
		tmp = (z + (x * y)) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - 2.0d0) * (4.16438922228d0 - ((101.7851458539211d0 - (3451.550173699799d0 / x)) / x))
    if (x <= (-0.0068d0)) then
        tmp = t_0
    else if (x <= 3.25d0) then
        tmp = (z + (x * y)) * ((x * (0.3041881842569256d0 + ((-1.787568985856513d0) * x))) - 0.0424927283095952d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 3.25) {
		tmp = (z + (x * y)) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x))
	tmp = 0
	if x <= -0.0068:
		tmp = t_0
	elif x <= 3.25:
		tmp = (z + (x * y)) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)))
	tmp = 0.0
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 3.25)
		tmp = Float64(Float64(z + Float64(x * y)) * Float64(Float64(x * Float64(0.3041881842569256 + Float64(-1.787568985856513 * x))) - 0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 3.25)
		tmp = (z + (x * y)) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0068], t$95$0, If[LessEqual[x, 3.25], N[(N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(N[(x * N[(0.3041881842569256 + N[(-1.787568985856513 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00679999999999999962 or 3.25 < x

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.2%

         \[\leadsto \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right) \cdot \left(x - 2\right) \]

   9. Applied rewrites 46.2%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 46.2%

          \[\leadsto \color{blue}{\left(x - 2\right) \cdot \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

       4. lift-+.f64 N/A

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

       5. add-flip N/A

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

       6. lower--.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. mul-1-neg N/A

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

   11. Applied rewrites 46.2%

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

   if -0.00679999999999999962 < x < 3.25

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 50.0%

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

   8. Applied rewrites 50.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(z + x \cdot y\right)} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]
   10. Step-by-step derivation

       1. lower-+.f64 N/A

          \[\leadsto \left(z + \color{blue}{x \cdot y}\right) \cdot \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \]

       2. lower-*.f64 47.6%

          \[\leadsto \left(z + x \cdot \color{blue}{y}\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]

   11. Applied rewrites 47.6%

       \[\leadsto \color{blue}{\left(z + x \cdot y\right)} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 78.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 - \frac{3451.550173699799}{x}}{x}\right)\\ \mathbf{elif}\;x \leq 110:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x - 110.1139242984811\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0068)
   (*
    (- x 2.0)
    (- 4.16438922228 (/ (- 101.7851458539211 (/ 3451.550173699799 x)) x)))
   (if (<= x 110.0)
     (/ (* (- x 2.0) z) (+ (* 313.399215894 x) 47.066876606))
     (- (* 4.16438922228 x) 110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0068) {
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	} else if (x <= 110.0) {
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	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 <= (-0.0068d0)) then
        tmp = (x - 2.0d0) * (4.16438922228d0 - ((101.7851458539211d0 - (3451.550173699799d0 / x)) / x))
    else if (x <= 110.0d0) then
        tmp = ((x - 2.0d0) * z) / ((313.399215894d0 * x) + 47.066876606d0)
    else
        tmp = (4.16438922228d0 * x) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0068) {
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	} else if (x <= 110.0) {
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 * x) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0068:
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x))
	elif x <= 110.0:
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606)
	else:
		tmp = (4.16438922228 * x) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0068)
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(3451.550173699799 / x)) / x)));
	elseif (x <= 110.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 * x) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = (x - 2.0) * (4.16438922228 - ((101.7851458539211 - (3451.550173699799 / x)) / x));
	elseif (x <= 110.0)
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606);
	else
		tmp = (4.16438922228 * x) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0068], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 - N[(3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 110.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00679999999999999962

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   6. Applied rewrites 53.5%

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

   7. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.2%

         \[\leadsto \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right) \cdot \left(x - 2\right) \]

   9. Applied rewrites 46.2%

      \[\leadsto \color{blue}{\left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lower-*.f64 46.2%

          \[\leadsto \color{blue}{\left(x - 2\right) \cdot \left(4.16438922228 + -1 \cdot \frac{101.7851458539211 - 3451.550173699799 \cdot \frac{1}{x}}{x}\right)} \]

       4. lift-+.f64 N/A

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

       5. add-flip N/A

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

       6. lower--.f64 N/A

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

       7. lift-*.f64 N/A

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

       8. mul-1-neg N/A

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

   11. Applied rewrites 46.2%

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

   if -0.00679999999999999962 < x < 110

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 51.2%

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 34.9%

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

   if 110 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

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

Alternative 26: 78.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_0 := 4.16438922228 \cdot x - 110.1139242984811\\ \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 110:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* 4.16438922228 x) 110.1139242984811)))
   (if (<= x -0.0068)
     t_0
     (if (<= x 110.0)
       (/ (* (- x 2.0) z) (+ (* 313.399215894 x) 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 110.0) {
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 * x) - 110.1139242984811d0
    if (x <= (-0.0068d0)) then
        tmp = t_0
    else if (x <= 110.0d0) then
        tmp = ((x - 2.0d0) * z) / ((313.399215894d0 * x) + 47.066876606d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 110.0) {
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 * x) - 110.1139242984811
	tmp = 0
	if x <= -0.0068:
		tmp = t_0
	elif x <= 110.0:
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 * x) - 110.1139242984811)
	tmp = 0.0
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 110.0)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 * x) - 110.1139242984811;
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 110.0)
		tmp = ((x - 2.0) * z) / ((313.399215894 * x) + 47.066876606);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[LessEqual[x, -0.0068], t$95$0, If[LessEqual[x, 110.0], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00679999999999999962 or 110 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

      \[\leadsto 4.16438922228 \cdot x - \color{blue}{110.1139242984811} \]

   if -0.00679999999999999962 < x < 110

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 51.2%

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 34.9%

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

Alternative 27: 78.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} t_0 := 4.16438922228 \cdot x - 110.1139242984811\\ \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0078:\\ \;\;\;\;z \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* 4.16438922228 x) 110.1139242984811)))
   (if (<= x -0.0068)
     t_0
     (if (<= x 0.0078)
       (*
        z
        (-
         (* x (+ 0.3041881842569256 (* -1.787568985856513 x)))
         0.0424927283095952))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 0.0078) {
		tmp = z * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 * x) - 110.1139242984811d0
    if (x <= (-0.0068d0)) then
        tmp = t_0
    else if (x <= 0.0078d0) then
        tmp = z * ((x * (0.3041881842569256d0 + ((-1.787568985856513d0) * x))) - 0.0424927283095952d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 0.0078) {
		tmp = z * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 * x) - 110.1139242984811
	tmp = 0
	if x <= -0.0068:
		tmp = t_0
	elif x <= 0.0078:
		tmp = z * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 * x) - 110.1139242984811)
	tmp = 0.0
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 0.0078)
		tmp = Float64(z * Float64(Float64(x * Float64(0.3041881842569256 + Float64(-1.787568985856513 * x))) - 0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 * x) - 110.1139242984811;
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 0.0078)
		tmp = z * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[LessEqual[x, -0.0068], t$95$0, If[LessEqual[x, 0.0078], N[(z * N[(N[(x * N[(0.3041881842569256 + N[(-1.787568985856513 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00679999999999999962 or 0.0077999999999999996 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

      \[\leadsto 4.16438922228 \cdot x - \color{blue}{110.1139242984811} \]

   if -0.00679999999999999962 < x < 0.0077999999999999996

   1. Initial program 57.4%

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

   3. Applied rewrites 61.2%

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 50.0%

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

   8. Applied rewrites 50.0%

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

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 35.2%

       \[\leadsto \color{blue}{z} \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 28: 78.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} t_0 := 4.16438922228 \cdot x - 110.1139242984811\\ \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0078:\\ \;\;\;\;\frac{-2 \cdot z}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* 4.16438922228 x) 110.1139242984811)))
   (if (<= x -0.0068)
     t_0
     (if (<= x 0.0078)
       (/ (* -2.0 z) (+ (* 313.399215894 x) 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 0.0078) {
		tmp = (-2.0 * z) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 * x) - 110.1139242984811d0
    if (x <= (-0.0068d0)) then
        tmp = t_0
    else if (x <= 0.0078d0) then
        tmp = ((-2.0d0) * z) / ((313.399215894d0 * x) + 47.066876606d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 0.0078) {
		tmp = (-2.0 * z) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 * x) - 110.1139242984811
	tmp = 0
	if x <= -0.0068:
		tmp = t_0
	elif x <= 0.0078:
		tmp = (-2.0 * z) / ((313.399215894 * x) + 47.066876606)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 * x) - 110.1139242984811)
	tmp = 0.0
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 0.0078)
		tmp = Float64(Float64(-2.0 * z) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 * x) - 110.1139242984811;
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 0.0078)
		tmp = (-2.0 * z) / ((313.399215894 * x) + 47.066876606);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[LessEqual[x, -0.0068], t$95$0, If[LessEqual[x, 0.0078], N[(N[(-2.0 * z), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00679999999999999962 or 0.0077999999999999996 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

      \[\leadsto 4.16438922228 \cdot x - \color{blue}{110.1139242984811} \]

   if -0.00679999999999999962 < x < 0.0077999999999999996

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\color{blue}{\frac{393497462077}{5000000000}} \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   3. Step-by-step derivation

   4. Applied rewrites 52.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 51.2%

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

   7. Applied rewrites 51.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-2 \cdot z}}{313.399215894 \cdot x + 47.066876606} \]
   9. Step-by-step derivation

      1. lower-*.f64 34.6%

         \[\leadsto \frac{-2 \cdot \color{blue}{z}}{313.399215894 \cdot x + 47.066876606} \]

   10. Applied rewrites 34.6%

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

Alternative 29: 78.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} t_0 := 4.16438922228 \cdot x - 110.1139242984811\\ \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0078:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* 4.16438922228 x) 110.1139242984811)))
   (if (<= x -0.0068) t_0 (if (<= x 0.0078) (* -0.0424927283095952 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 0.0078) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 * x) - 110.1139242984811d0
    if (x <= (-0.0068d0)) then
        tmp = t_0
    else if (x <= 0.0078d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 * x) - 110.1139242984811;
	double tmp;
	if (x <= -0.0068) {
		tmp = t_0;
	} else if (x <= 0.0078) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 * x) - 110.1139242984811
	tmp = 0
	if x <= -0.0068:
		tmp = t_0
	elif x <= 0.0078:
		tmp = -0.0424927283095952 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 * x) - 110.1139242984811)
	tmp = 0.0
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 0.0078)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 * x) - 110.1139242984811;
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = t_0;
	elseif (x <= 0.0078)
		tmp = -0.0424927283095952 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 * x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[LessEqual[x, -0.0068], t$95$0, If[LessEqual[x, 0.0078], N[(-0.0424927283095952 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00679999999999999962 or 0.0077999999999999996 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{104109730557}{25000000000} \cdot x - \color{blue}{\frac{13764240537310136880149}{125000000000000000000}} \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \frac{104109730557}{25000000000} \cdot x - \frac{13764240537310136880149}{125000000000000000000} \]

      2. lower-*.f64 46.6%

         \[\leadsto 4.16438922228 \cdot x - 110.1139242984811 \]

   7. Applied rewrites 46.6%

      \[\leadsto 4.16438922228 \cdot x - \color{blue}{110.1139242984811} \]

   if -0.00679999999999999962 < x < 0.0077999999999999996

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 34.7%

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

   4. Applied rewrites 34.7%

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

Alternative 30: 77.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -0.0068:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 3.25:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0068)
   (* x 4.16438922228)
   (if (<= x 3.25) (* -0.0424927283095952 z) (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0068) {
		tmp = x * 4.16438922228;
	} else if (x <= 3.25) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = x * 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 <= (-0.0068d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 3.25d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = x * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0068) {
		tmp = x * 4.16438922228;
	} else if (x <= 3.25) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0068:
		tmp = x * 4.16438922228
	elif x <= 3.25:
		tmp = -0.0424927283095952 * z
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0068)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 3.25)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0068)
		tmp = x * 4.16438922228;
	elseif (x <= 3.25)
		tmp = -0.0424927283095952 * z;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0068], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 3.25], N[(-0.0424927283095952 * z), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.00679999999999999962 or 3.25 < x

   1. Initial program 57.4%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 46.6%

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

   4. Applied rewrites 46.6%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 46.4%

      \[\leadsto x \cdot 4.16438922228 \]

   if -0.00679999999999999962 < x < 3.25

   1. Initial program 57.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 34.7%

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

   4. Applied rewrites 34.7%

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

Alternative 31: 34.7% accurate, 13.3× speedup

Math

\[-0.0424927283095952 \cdot z \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.4%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 34.7%

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

4. Applied rewrites 34.7%

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

Alternative 32: 3.3% accurate, 52.5× speedup

Math

\[-110.1139242984811 \]

FPCore

(FPCore (x y z) :precision binary64 -110.1139242984811)

C

double code(double x, double y, double z) {
	return -110.1139242984811;
}

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 = -110.1139242984811d0
end function

Java

public static double code(double x, double y, double z) {
	return -110.1139242984811;
}

Python

def code(x, y, z):
	return -110.1139242984811

Julia

function code(x, y, z)
	return -110.1139242984811
end

MATLAB

function tmp = code(x, y, z)
	tmp = -110.1139242984811;
end

Wolfram

code[x_, y_, z_] := -110.1139242984811

Derivation

1. Initial program 57.4%

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

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. lower-*.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 46.6%

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

4. Applied rewrites 46.6%

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

5. Taylor expanded in x around 0

   \[\leadsto \frac{-13764240537310136880149}{125000000000000000000} \]
6. Step-by-step derivation

7. Applied rewrites 3.3%

   \[\leadsto -110.1139242984811 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025183 
(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)))