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

Percentage Accurate: 58.0% → 99.4%

Time: 7.5s

Alternatives: 20

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.4× speedup

Math

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

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))
        INFINITY)
     (fma
      (fma (fma (* x x) 4.16438922228 (fma 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)) <= ((double) INFINITY)) {
		tmp = fma(fma(fma((x * x), 4.16438922228, fma(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)) <= Inf)
		tmp = fma(fma(fma(Float64(x * x), 4.16438922228, fma(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], Infinity], N[(N[(N[(N[(x * x), $MachinePrecision] * 4.16438922228 + N[(78.6994924154 * x + 137.519416416), $MachinePrecision]), $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))) < +inf.0

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

      1. lift-fma.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-fma.f64 N/A

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

      4. add-flip N/A

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

      5. *-commutative N/A

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

      6. add-flip N/A

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

      7. distribute-rgt-in N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 61.8

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

   5. Applied rewrites 61.8%

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

   if +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   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 48.2%

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

Alternative 2: 99.4% accurate, 0.4× speedup

Math

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

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))
        INFINITY)
     (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)) <= ((double) INFINITY)) {
		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)) <= Inf)
		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], Infinity], 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))) < +inf.0

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   if +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   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 48.2%

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

Alternative 3: 99.4% accurate, 0.4× speedup

Math

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

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))
        INFINITY)
     (fma
      (/ z t_0)
      (- x 2.0)
      (*
       (*
        x
        (/
         (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
         t_0))
       (- 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 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)) <= ((double) INFINITY)) {
		tmp = fma((z / t_0), (x - 2.0), ((x * (fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y) / t_0)) * (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)
	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)) <= Inf)
		tmp = fma(Float64(z / t_0), Float64(x - 2.0), Float64(Float64(x * Float64(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y) / t_0)) * 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_] := 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], Infinity], N[(N[(z / t$95$0), $MachinePrecision] * N[(x - 2.0), $MachinePrecision] + N[(N[(x * N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $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))) < +inf.0

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   if +inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   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 48.2%

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

Alternative 4: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+275}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \end{array} \end{array} \]

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+275)
   (*
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma
      (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
      x
      47.066876606))
    (- x 2.0))
   (*
    -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+275) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = -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+275)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(-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+275], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(-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))) < 1.99999999999999992e275

   1. Initial program 58.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   3. Applied rewrites 61.0%

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

   if 1.99999999999999992e275 < (/.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 58.0%

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

   3. Applied rewrites 61.8%

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

   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 48.2%

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

Alternative 5: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{if}\;x \leq -100:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 72:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(263.505074721 \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          -1.0
          (*
           x
           (-
            (*
             -1.0
             (/
              (-
               (*
                -1.0
                (/
                 (- (* -1.0 (/ (- y 130977.50649958357) x)) 3655.1204654076414)
                 x))
               110.1139242984811)
              x))
            4.16438922228)))))
   (if (<= x -100.0)
     t_0
     (if (<= x 72.0)
       (/
        (*
         (- x 2.0)
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z))
        (+ (* (+ (* 263.505074721 x) 313.399215894) x) 47.066876606))
       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 <= -100.0) {
		tmp = t_0;
	} else if (x <= 72.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((((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 = (-1.0d0) * (x * (((-1.0d0) * ((((-1.0d0) * ((((-1.0d0) * ((y - 130977.50649958357d0) / x)) - 3655.1204654076414d0) / x)) - 110.1139242984811d0) / x)) - 4.16438922228d0))
    if (x <= (-100.0d0)) then
        tmp = t_0
    else if (x <= 72.0d0) then
        tmp = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z)) / ((((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 = -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 <= -100.0) {
		tmp = t_0;
	} else if (x <= 72.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228))
	tmp = 0
	if x <= -100.0:
		tmp = t_0
	elif x <= 72.0:
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606)
	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 <= -100.0)
		tmp = t_0;
	elseif (x <= 72.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(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 = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	tmp = 0.0;
	if (x <= -100.0)
		tmp = t_0;
	elseif (x <= 72.0)
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((((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[(-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, -100.0], t$95$0, If[LessEqual[x, 72.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -100 or 72 < x

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   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 48.2%

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

   if -100 < x < 72

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.6%

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

Alternative 6: 95.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 35:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -36.0)
     t_0
     (if (<= x 35.0)
       (/
        (*
         (- x 2.0)
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z))
        (+ (* 313.399215894 x) 47.066876606))
       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 <= -36.0) {
		tmp = t_0;
	} else if (x <= 35.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + 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 = (-1.0d0) * (x * (((-1.0d0) * ((((-1.0d0) * ((((-1.0d0) * ((y - 130977.50649958357d0) / x)) - 3655.1204654076414d0) / x)) - 110.1139242984811d0) / x)) - 4.16438922228d0))
    if (x <= (-36.0d0)) then
        tmp = t_0
    else if (x <= 35.0d0) then
        tmp = ((x - 2.0d0) * ((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + 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 = -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 <= -36.0) {
		tmp = t_0;
	} else if (x <= 35.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228))
	tmp = 0
	if x <= -36.0:
		tmp = t_0
	elif x <= 35.0:
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / ((313.399215894 * x) + 47.066876606)
	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 <= -36.0)
		tmp = t_0;
	elseif (x <= 35.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -1.0 * (x * ((-1.0 * (((-1.0 * (((-1.0 * ((y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	tmp = 0.0;
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 35.0)
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + 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[(-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, -36.0], t$95$0, If[LessEqual[x, 35.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 35 < x

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   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 48.2%

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

   if -36 < x < 35

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.5%

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

Alternative 7: 95.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 \cdot \left(x \cdot \left(-1 \cdot \frac{-1 \cdot \frac{-1 \cdot \frac{y - 130977.50649958357}{x} - 3655.1204654076414}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x \cdot \left(0.3041881842569256 + -1.787568985856513 \cdot x\right) - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -0.18)
     t_0
     (if (<= x 2.0)
       (*
        (fma
         (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
         x
         z)
        (-
         (* x (+ 0.3041881842569256 (* -1.787568985856513 x)))
         0.0424927283095952))
       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 <= -0.18) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * ((x * (0.3041881842569256 + (-1.787568985856513 * x))) - 0.0424927283095952);
	} 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 <= -0.18)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(x * Float64(0.3041881842569256 + Float64(-1.787568985856513 * x))) - 0.0424927283095952));
	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, -0.18], t$95$0, If[LessEqual[x, 2.0], N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $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 < -0.17999999999999999 or 2 < x

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   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 48.2%

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

   if -0.17999999999999999 < x < 2

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, \frac{104109730557}{25000000000}, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right) \cdot \color{blue}{\left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right)} \]
   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 50.7

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

   8. Applied rewrites 50.7%

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

Alternative 8: 92.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 1.9e+18)
     (*
      (fma
       (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
       x
       z)
      (/ (- x 2.0) (fma 313.399215894 x 47.066876606)))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 1.9e+18) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * ((x - 2.0) / fma(313.399215894, x, 47.066876606));
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		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 <= 1.9e+18)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(x - 2.0) / fma(313.399215894, x, 47.066876606)));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], 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, 1.9e+18], N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 58.0%

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

   2. Taylor expanded in x around -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 45.3

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

   4. Applied rewrites 45.3%

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

   if -36 < x < 1.9e18

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 50.4%

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

   if 1.9e18 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 45.7

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip-rev N/A

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

      7. lower-/.f64 45.7

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

   6. Applied rewrites 45.7%

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

Alternative 9: 92.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -260:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(0.3041881842569256 \cdot x - 0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -260.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 1.9e+18)
     (*
      (fma
       (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
       x
       z)
      (- (* 0.3041881842569256 x) 0.0424927283095952))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -260.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 1.9e+18) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * ((0.3041881842569256 * x) - 0.0424927283095952);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -260.0)
		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 <= 1.9e+18)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -260.0], 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, 1.9e+18], N[(N[(N[(N[(N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -260

   1. Initial program 58.0%

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

   2. Taylor expanded in x around -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 45.3

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

   4. Applied rewrites 45.3%

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

   if -260 < x < 1.9e18

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 51.9

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

   8. Applied rewrites 51.9%

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

   if 1.9e18 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 45.7

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip-rev N/A

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

      7. lower-/.f64 45.7

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

   6. Applied rewrites 45.7%

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

Alternative 10: 92.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -260:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+18}:\\ \;\;\;\;0.0212463641547976 \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -260.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 1.9e+18)
     (*
      0.0212463641547976
      (*
       (fma
        (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
        x
        z)
       (- x 2.0)))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -260.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 1.9e+18) {
		tmp = 0.0212463641547976 * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * (x - 2.0));
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -260.0)
		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 <= 1.9e+18)
		tmp = Float64(0.0212463641547976 * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(x - 2.0)));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -260.0], 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, 1.9e+18], N[(0.0212463641547976 * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -260

   1. Initial program 58.0%

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

   2. Taylor expanded in x around -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 45.3

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

   4. Applied rewrites 45.3%

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

   if -260 < x < 1.9e18

   1. Initial program 58.0%

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

   3. Applied rewrites 57.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 51.5%

      \[\leadsto \color{blue}{0.0212463641547976} \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)\right) \]

   if 1.9e18 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 45.7

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip-rev N/A

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

      7. lower-/.f64 45.7

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

   6. Applied rewrites 45.7%

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

Alternative 11: 92.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9200:\\ \;\;\;\;-1 \cdot \left(x \cdot \left(-1 \cdot \frac{3655.1204654076414 \cdot \frac{1}{x} - 110.1139242984811}{x} - 4.16438922228\right)\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9200.0)
   (*
    -1.0
    (*
     x
     (-
      (* -1.0 (/ (- (* 3655.1204654076414 (/ 1.0 x)) 110.1139242984811) x))
      4.16438922228)))
   (if (<= x 2.0)
     (*
      (fma
       (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
       x
       z)
      -0.0424927283095952)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9200.0) {
		tmp = -1.0 * (x * ((-1.0 * (((3655.1204654076414 * (1.0 / x)) - 110.1139242984811) / x)) - 4.16438922228));
	} else if (x <= 2.0) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9200.0)
		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 <= 2.0)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9200.0], 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, 2.0], 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[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9200

   1. Initial program 58.0%

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

   2. Taylor expanded in x around -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 45.3

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

   4. Applied rewrites 45.3%

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

   if -9200 < x < 2

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 50.1%

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

   if 2 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 45.7

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip-rev N/A

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

      7. lower-/.f64 45.7

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

   6. Applied rewrites 45.7%

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

Alternative 12: 91.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9200:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9200.0)
   (fma x 4.16438922228 -110.1139242984811)
   (if (<= x 2.0)
     (*
      (fma
       (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
       x
       z)
      -0.0424927283095952)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9200.0) {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	} else if (x <= 2.0) {
		tmp = fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9200.0)
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	elseif (x <= 2.0)
		tmp = Float64(fma(fma(fma(fma(x, 4.16438922228, 78.6994924154), x, 137.519416416), x, y), x, z) * -0.0424927283095952);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9200.0], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision], If[LessEqual[x, 2.0], 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[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9200

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-out N/A

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

      8. associate-*l* N/A

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

      9. lift-/.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-plus N/A

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

      12. metadata-eval N/A

          \[\leadsto x \cdot \frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \cdot {x}^{0} \]

      13. metadata-eval N/A

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

      14. *-rgt-identity N/A

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

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000}}, \mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \]

      16. metadata-eval 45.7

          \[\leadsto \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right) \]

   6. Applied rewrites 45.7%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -110.1139242984811\right) \]

   if -9200 < x < 2

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 50.1%

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

   if 2 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 45.7

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

      4. lift-*.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. mult-flip-rev N/A

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

      7. lower-/.f64 45.7

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

   6. Applied rewrites 45.7%

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

Alternative 13: 90.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + -2 \cdot y\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (fma x 4.16438922228 -110.1139242984811)
   (if (<= x 3.9e-14)
     (/
      (fma -2.0 z (* x (+ z (* -2.0 y))))
      (+ (* 313.399215894 x) 47.066876606))
     (fma x 4.16438922228 -110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	} else if (x <= 3.9e-14) {
		tmp = fma(-2.0, z, (x * (z + (-2.0 * y)))) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	elseif (x <= 3.9e-14)
		tmp = Float64(fma(-2.0, z, Float64(x * Float64(z + Float64(-2.0 * y)))) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision], If[LessEqual[x, 3.9e-14], N[(N[(-2.0 * z + N[(x * N[(z + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 3.8999999999999998e-14 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-out N/A

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

      8. associate-*l* N/A

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

      9. lift-/.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-plus N/A

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

      12. metadata-eval N/A

          \[\leadsto x \cdot \frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \cdot {x}^{0} \]

      13. metadata-eval N/A

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

      14. *-rgt-identity N/A

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

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000}}, \mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \]

      16. metadata-eval 45.7

          \[\leadsto \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right) \]

   6. Applied rewrites 45.7%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -110.1139242984811\right) \]

   if -36 < x < 3.8999999999999998e-14

   1. Initial program 58.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{\frac{104109730557}{25000000000} \cdot {x}^{5}}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\frac{104109730557}{25000000000} \cdot \color{blue}{{x}^{5}}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. lower-pow.f64 5.9

         \[\leadsto \frac{4.16438922228 \cdot {x}^{\color{blue}{5}}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   4. Applied rewrites 5.9%

      \[\leadsto \frac{\color{blue}{4.16438922228 \cdot {x}^{5}}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{104109730557}{25000000000} \cdot {x}^{5}}{\color{blue}{\frac{156699607947}{500000000} \cdot x} + \frac{23533438303}{500000000}} \]
   6. Step-by-step derivation

      1. lower-*.f64 3.1

         \[\leadsto \frac{4.16438922228 \cdot {x}^{5}}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 3.1%

      \[\leadsto \frac{4.16438922228 \cdot {x}^{5}}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 48.3

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

   10. Applied rewrites 48.3%

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

Alternative 14: 89.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952, z, x \cdot \left(\mathsf{fma}\left(-0.0424927283095952, y, 0.0212463641547976 \cdot z\right) - -0.28294182010212804 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.18)
   (fma x 4.16438922228 -110.1139242984811)
   (if (<= x 3.9e-14)
     (fma
      -0.0424927283095952
      z
      (*
       x
       (-
        (fma -0.0424927283095952 y (* 0.0212463641547976 z))
        (* -0.28294182010212804 z))))
     (fma x 4.16438922228 -110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.18) {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	} else if (x <= 3.9e-14) {
		tmp = fma(-0.0424927283095952, z, (x * (fma(-0.0424927283095952, y, (0.0212463641547976 * z)) - (-0.28294182010212804 * z))));
	} else {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.18)
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	elseif (x <= 3.9e-14)
		tmp = fma(-0.0424927283095952, z, Float64(x * Float64(fma(-0.0424927283095952, y, Float64(0.0212463641547976 * z)) - Float64(-0.28294182010212804 * z))));
	else
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.18], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision], If[LessEqual[x, 3.9e-14], N[(-0.0424927283095952 * z + N[(x * N[(N[(-0.0424927283095952 * y + N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision] - N[(-0.28294182010212804 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.17999999999999999 or 3.8999999999999998e-14 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-out N/A

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

      8. associate-*l* N/A

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

      9. lift-/.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-plus N/A

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

      12. metadata-eval N/A

          \[\leadsto x \cdot \frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \cdot {x}^{0} \]

      13. metadata-eval N/A

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

      14. *-rgt-identity N/A

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

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000}}, \mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \]

      16. metadata-eval 45.7

          \[\leadsto \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right) \]

   6. Applied rewrites 45.7%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -110.1139242984811\right) \]

   if -0.17999999999999999 < x < 3.8999999999999998e-14

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 48.4

         \[\leadsto \mathsf{fma}\left(-0.0424927283095952, z, x \cdot \left(\mathsf{fma}\left(-0.0424927283095952, y, 0.0212463641547976 \cdot z\right) - -0.28294182010212804 \cdot z\right)\right) \]

   6. Applied rewrites 48.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.0424927283095952, z, x \cdot \left(\mathsf{fma}\left(-0.0424927283095952, y, 0.0212463641547976 \cdot z\right) - -0.28294182010212804 \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 77.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;\frac{-2 \cdot z}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35)
   (fma x 4.16438922228 -110.1139242984811)
   (if (<= x 3.9e-14)
     (/ (* -2.0 z) (+ (* 313.399215894 x) 47.066876606))
     (fma x 4.16438922228 -110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	} else if (x <= 3.9e-14) {
		tmp = (-2.0 * z) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35)
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	elseif (x <= 3.9e-14)
		tmp = Float64(Float64(-2.0 * z) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision], If[LessEqual[x, 3.9e-14], N[(N[(-2.0 * z), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001 or 3.8999999999999998e-14 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-out N/A

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

      8. associate-*l* N/A

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

      9. lift-/.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-plus N/A

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

      12. metadata-eval N/A

          \[\leadsto x \cdot \frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \cdot {x}^{0} \]

      13. metadata-eval N/A

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

      14. *-rgt-identity N/A

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

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000}}, \mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \]

      16. metadata-eval 45.7

          \[\leadsto \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right) \]

   6. Applied rewrites 45.7%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -110.1139242984811\right) \]

   if -1.3500000000000001 < x < 3.8999999999999998e-14

   1. Initial program 58.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{\frac{104109730557}{25000000000} \cdot {x}^{5}}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\frac{104109730557}{25000000000} \cdot \color{blue}{{x}^{5}}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]

      2. lower-pow.f64 5.9

         \[\leadsto \frac{4.16438922228 \cdot {x}^{\color{blue}{5}}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   4. Applied rewrites 5.9%

      \[\leadsto \frac{\color{blue}{4.16438922228 \cdot {x}^{5}}}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{104109730557}{25000000000} \cdot {x}^{5}}{\color{blue}{\frac{156699607947}{500000000} \cdot x} + \frac{23533438303}{500000000}} \]
   6. Step-by-step derivation

      1. lower-*.f64 3.1

         \[\leadsto \frac{4.16438922228 \cdot {x}^{5}}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 3.1%

      \[\leadsto \frac{4.16438922228 \cdot {x}^{5}}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{-2 \cdot z}}{\frac{156699607947}{500000000} \cdot x + \frac{23533438303}{500000000}} \]
   9. Step-by-step derivation

      1. lower-*.f64 34.7

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

   10. Applied rewrites 34.7%

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

Alternative 16: 77.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;\left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (fma x 4.16438922228 -110.1139242984811)
   (if (<= x 3.9e-14)
     (* (- (* 0.3041881842569256 x) 0.0424927283095952) z)
     (fma x 4.16438922228 -110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	} else if (x <= 3.9e-14) {
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	} else {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	elseif (x <= 3.9e-14)
		tmp = Float64(Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952) * z);
	else
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision], If[LessEqual[x, 3.9e-14], N[(N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z), $MachinePrecision], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 3.8999999999999998e-14 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-out N/A

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

      8. associate-*l* N/A

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

      9. lift-/.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-plus N/A

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

      12. metadata-eval N/A

          \[\leadsto x \cdot \frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \cdot {x}^{0} \]

      13. metadata-eval N/A

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

      14. *-rgt-identity N/A

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

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000}}, \mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \]

      16. metadata-eval 45.7

          \[\leadsto \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right) \]

   6. Applied rewrites 45.7%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -110.1139242984811\right) \]

   if -5.5 < x < 3.8999999999999998e-14

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 36.5%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

   6. Applied rewrites 37.1%

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

   7. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 35.3

         \[\leadsto \left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \cdot z \]

   9. Applied rewrites 35.3%

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

Alternative 17: 76.9% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (fma x 4.16438922228 -110.1139242984811)
   (if (<= x 3.9e-14)
     (* -0.0424927283095952 z)
     (fma x 4.16438922228 -110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	} else if (x <= 3.9e-14) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	elseif (x <= 3.9e-14)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = fma(x, 4.16438922228, -110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision], If[LessEqual[x, 3.9e-14], N[(-0.0424927283095952 * z), $MachinePrecision], N[(x * 4.16438922228 + -110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 3.8999999999999998e-14 < x

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 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 45.7

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

   4. Applied rewrites 45.7%

      \[\leadsto \color{blue}{x \cdot \left(4.16438922228 - 110.1139242984811 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-flip N/A

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

      4. distribute-rgt-in N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. distribute-lft-neg-out N/A

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

      8. associate-*l* N/A

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

      9. lift-/.f64 N/A

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

      10. inv-pow N/A

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

      11. pow-plus N/A

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

      12. metadata-eval N/A

          \[\leadsto x \cdot \frac{104109730557}{25000000000} + \left(\mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \cdot {x}^{0} \]

      13. metadata-eval N/A

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

      14. *-rgt-identity N/A

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

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{104109730557}{25000000000}}, \mathsf{neg}\left(\frac{13764240537310136880149}{125000000000000000000}\right)\right) \]

      16. metadata-eval 45.7

          \[\leadsto \mathsf{fma}\left(x, 4.16438922228, -110.1139242984811\right) \]

   6. Applied rewrites 45.7%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{4.16438922228}, -110.1139242984811\right) \]

   if -5.5 < x < 3.8999999999999998e-14

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 34.8

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

   4. Applied rewrites 34.8%

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

Alternative 18: 76.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+18}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (* 4.16438922228 x)
   (if (<= x 1.9e+18) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.9e+18) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 1.9d+18) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = 4.16438922228d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.9e+18) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = 4.16438922228 * x
	elif x <= 1.9e+18:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.9e+18)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = 4.16438922228 * x;
	elseif (x <= 1.9e+18)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.9e+18], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 1.9e18 < x

   1. Initial program 58.0%

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

   3. Applied rewrites 61.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 45.4

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

   6. Applied rewrites 45.4%

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

   if -5.5 < x < 1.9e18

   1. Initial program 58.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 34.8

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

   4. Applied rewrites 34.8%

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

Alternative 19: 45.4% accurate, 13.3× speedup

Math

\[\begin{array}{l} \\ 4.16438922228 \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 4.16438922228 x))

C

double code(double x, double y, double z) {
	return 4.16438922228 * x;
}

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 = 4.16438922228d0 * x
end function

Java

public static double code(double x, double y, double z) {
	return 4.16438922228 * x;
}

Python

def code(x, y, z):
	return 4.16438922228 * x

Julia

function code(x, y, z)
	return Float64(4.16438922228 * x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 4.16438922228 * x;
end

Wolfram

code[x_, y_, z_] := N[(4.16438922228 * x), $MachinePrecision]

Derivation

1. Initial program 58.0%

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

3. Applied rewrites 61.8%

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

4. Taylor expanded in x around inf

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

   1. lower-*.f64 45.4

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

6. Applied rewrites 45.4%

   \[\leadsto \color{blue}{4.16438922228 \cdot x} \]
7. Add Preprocessing

Alternative 20: 3.4% accurate, 52.5× speedup

Math

\[\begin{array}{l} \\ -110.1139242984811 \end{array} \]

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 58.0%

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

2. Taylor expanded in x around 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 45.7

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

4. Applied rewrites 45.7%

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

5. Taylor expanded in x around 0

   \[\leadsto \frac{-13764240537310136880149}{125000000000000000000} \]
6. Step-by-step derivation

7. Applied rewrites 3.4%

   \[\leadsto -110.1139242984811 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025143 
(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)))