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

Percentage Accurate: 58.7% → 99.3%

Time: 5.4s

Alternatives: 21

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: 58.7% 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: 99.3% accurate, 0.4× speedup

Math

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

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)))
     (*
      (-
       (/
        (-
         (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
         101.7851458539211)
        x)
       -4.16438922228)
      (- x 2.0)))))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   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 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

Alternative 2: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 10^{+292}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
           y)
          x)
         z))
       (+
        (*
         (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
         x)
        47.066876606))
      1e+292)
   (*
    (/
     (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))
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+292) {
		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 = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 1e+292)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 1e+292], 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[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 1e292

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   if 1e292 < (/.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 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

Alternative 3: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16500000000:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 340000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + \mathsf{fma}\left(-2, y, x \cdot \left(y - 275.038832832\right)\right)\right)\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\mathsf{fma}\left({x}^{3}, x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -16500000000.0)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 340000000000.0)
     (/
      (fma -2.0 z (* x (+ z (fma -2.0 y (* x (- y 275.038832832))))))
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (* (+ (/ z (fma (pow x 3.0) x 47.066876606)) 4.16438922228) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -16500000000.0) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 340000000000.0) {
		tmp = fma(-2.0, z, (x * (z + fma(-2.0, y, (x * (y - 275.038832832)))))) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = ((z / fma(pow(x, 3.0), x, 47.066876606)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -16500000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 340000000000.0)
		tmp = Float64(fma(-2.0, z, Float64(x * Float64(z + fma(-2.0, y, Float64(x * Float64(y - 275.038832832)))))) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = Float64(Float64(Float64(z / fma((x ^ 3.0), x, 47.066876606)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -16500000000.0], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 340000000000.0], N[(N[(-2.0 * z + N[(x * N[(z + N[(-2.0 * y + N[(x * N[(y - 275.038832832), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(N[Power[x, 3.0], $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e10

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -1.65e10 < x < 3.4e11

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 53.9

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

   4. Applied rewrites 53.9%

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

   if 3.4e11 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(\frac{z}{\mathsf{fma}\left(\color{blue}{{x}^{3}}, x, \frac{23533438303}{500000000}\right)} + \frac{104109730557}{25000000000}\right) \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lower-pow.f64 68.1

          \[\leadsto \left(\frac{z}{\mathsf{fma}\left({x}^{\color{blue}{3}}, x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right) \]

   11. Applied rewrites 68.1%

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

Alternative 4: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16500000000:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 340000000000:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, \mathsf{fma}\left(-2, y, z\right)\right), x, -2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\mathsf{fma}\left({x}^{3}, x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -16500000000.0)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 340000000000.0)
     (*
      (/
       1.0
       (fma
        (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
        x
        47.066876606))
      (fma (fma (- y 275.038832832) x (fma -2.0 y z)) x (* -2.0 z)))
     (* (+ (/ z (fma (pow x 3.0) x 47.066876606)) 4.16438922228) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -16500000000.0) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 340000000000.0) {
		tmp = (1.0 / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * fma(fma((y - 275.038832832), x, fma(-2.0, y, z)), x, (-2.0 * z));
	} else {
		tmp = ((z / fma(pow(x, 3.0), x, 47.066876606)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -16500000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 340000000000.0)
		tmp = Float64(Float64(1.0 / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) * fma(fma(Float64(y - 275.038832832), x, fma(-2.0, y, z)), x, Float64(-2.0 * z)));
	else
		tmp = Float64(Float64(Float64(z / fma((x ^ 3.0), x, 47.066876606)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -16500000000.0], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 340000000000.0], N[(N[(1.0 / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(y - 275.038832832), $MachinePrecision] * x + N[(-2.0 * y + z), $MachinePrecision]), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(N[Power[x, 3.0], $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e10

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -1.65e10 < x < 3.4e11

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 53.9

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

   4. Applied rewrites 53.9%

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

   6. Applied rewrites 53.7%

      \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, \mathsf{fma}\left(-2, y, z\right)\right), x, -2 \cdot z\right)} \]

   if 3.4e11 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(\frac{z}{\mathsf{fma}\left(\color{blue}{{x}^{3}}, x, \frac{23533438303}{500000000}\right)} + \frac{104109730557}{25000000000}\right) \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lower-pow.f64 68.1

          \[\leadsto \left(\frac{z}{\mathsf{fma}\left({x}^{\color{blue}{3}}, x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right) \]

   11. Applied rewrites 68.1%

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

Alternative 5: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -37:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 11800:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -37.0)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 11800.0)
     (*
      (/
       (fma
        (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
        x
        z)
       (fma
        (fma (fma 43.3400022514 x 263.505074721) x 313.399215894)
        x
        47.066876606))
      (- x 2.0))
     (*
      (+
       (/
        z
        (fma
         (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
         x
         47.066876606))
       4.16438922228)
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -37.0) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 11800.0) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(43.3400022514, x, 263.505074721), x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = ((z / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -37.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 11800.0)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(43.3400022514, x, 263.505074721), x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(z / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -37.0], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 11800.0], 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[(43.3400022514 * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -37

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -37 < x < 11800

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 50.4%

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

   if 11800 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

Alternative 6: 95.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -110:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -110.0)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 7e-5)
     (*
      (/
       (fma
        (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
        x
        z)
       (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
      (- x 2.0))
     (*
      (+
       (/
        z
        (fma
         (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
         x
         47.066876606))
       4.16438922228)
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -110.0) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 7e-5) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = ((z / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -110.0)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 7e-5)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(z / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -110.0], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-5], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -110

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -110 < x < 6.9999999999999994e-5

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 50.9%

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

   if 6.9999999999999994e-5 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

Alternative 7: 95.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 7e-5)
     (*
      (/
       (fma
        (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
        x
        z)
       (fma 313.399215894 x 47.066876606))
      (- x 2.0))
     (*
      (+
       (/
        z
        (fma
         (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
         x
         47.066876606))
       4.16438922228)
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 7e-5) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * (x - 2.0);
	} else {
		tmp = ((z / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 7e-5)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(313.399215894, x, 47.066876606)) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(z / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-5], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -1.3500000000000001 < x < 6.9999999999999994e-5

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 50.9%

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

   if 6.9999999999999994e-5 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

Alternative 8: 95.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + \mathsf{fma}\left(-2, y, x \cdot \left(y - 275.038832832\right)\right)\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 7e-5)
     (/
      (fma -2.0 z (* x (+ z (fma -2.0 y (* x (- y 275.038832832))))))
      (+ (* 313.399215894 x) 47.066876606))
     (*
      (+
       (/
        z
        (fma
         (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
         x
         47.066876606))
       4.16438922228)
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 7e-5) {
		tmp = fma(-2.0, z, (x * (z + fma(-2.0, y, (x * (y - 275.038832832)))))) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = ((z / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 7e-5)
		tmp = Float64(fma(-2.0, z, Float64(x * Float64(z + fma(-2.0, y, Float64(x * Float64(y - 275.038832832)))))) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = Float64(Float64(Float64(z / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-5], N[(N[(-2.0 * z + N[(x * N[(z + N[(-2.0 * y + N[(x * N[(y - 275.038832832), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -1.3500000000000001 < x < 6.9999999999999994e-5

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 53.9

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

   4. Applied rewrites 53.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + \mathsf{fma}\left(-2, y, x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right)\right)}{\color{blue}{\frac{156699607947}{500000000} \cdot x} + \frac{23533438303}{500000000}} \]
   6. Step-by-step derivation

      1. lower-*.f64 50.3

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

   7. Applied rewrites 50.3%

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

   if 6.9999999999999994e-5 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

Alternative 9: 94.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x - -43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 8.5e-7)
     (*
      (/
       (fma
        (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
        x
        z)
       47.066876606)
      (- x 2.0))
     (*
      (+
       (/
        z
        (fma
         (fma (fma (- x -43.3400022514) x 263.505074721) x 313.399215894)
         x
         47.066876606))
       4.16438922228)
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 8.5e-7) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * (x - 2.0);
	} else {
		tmp = ((z / fma(fma(fma((x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 8.5e-7)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(z / fma(fma(fma(Float64(x - -43.3400022514), x, 263.505074721), x, 313.399215894), x, 47.066876606)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-7], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(N[(N[(N[(x - -43.3400022514), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -5.5 < x < 8.50000000000000014e-7

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 51.7%

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

   if 8.50000000000000014e-7 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

Alternative 10: 94.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 11800:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606} \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{{x}^{4}} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 11800.0)
     (*
      (/
       (fma
        (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
        x
        z)
       47.066876606)
      (- x 2.0))
     (* (+ (/ z (pow x 4.0)) 4.16438922228) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 11800.0) {
		tmp = (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * (x - 2.0);
	} else {
		tmp = ((z / pow(x, 4.0)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 11800.0)
		tmp = Float64(Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606) * Float64(x - 2.0));
	else
		tmp = Float64(Float64(Float64(z / (x ^ 4.0)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 11800.0], N[(N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -5.5 < x < 11800

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 51.7%

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

   if 11800 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(\frac{z}{\color{blue}{{x}^{4}}} + \frac{104109730557}{25000000000}\right) \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lower-pow.f64 47.2

          \[\leadsto \left(\frac{z}{{x}^{\color{blue}{4}}} + 4.16438922228\right) \cdot \left(x - 2\right) \]

   11. Applied rewrites 47.2%

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

Alternative 11: 93.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 11800:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{\left(263.505074721 \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{{x}^{4}} + 4.16438922228\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5)
   (*
    (-
     (/
      (-
       (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
       101.7851458539211)
      x)
     -4.16438922228)
    (- x 2.0))
   (if (<= x 11800.0)
     (/
      (* (- x 2.0) (+ (* y x) z))
      (+ (* (+ (* 263.505074721 x) 313.399215894) x) 47.066876606))
     (* (+ (/ z (pow x 4.0)) 4.16438922228) (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 11800.0) {
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = ((z / pow(x, 4.0)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.5d0)) then
        tmp = (((((3451.550173699799d0 - ((124074.40615218398d0 - y) / x)) / x) - 101.7851458539211d0) / x) - (-4.16438922228d0)) * (x - 2.0d0)
    else if (x <= 11800.0d0) then
        tmp = ((x - 2.0d0) * ((y * x) + z)) / ((((263.505074721d0 * x) + 313.399215894d0) * x) + 47.066876606d0)
    else
        tmp = ((z / (x ** 4.0d0)) + 4.16438922228d0) * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5) {
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	} else if (x <= 11800.0) {
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = ((z / Math.pow(x, 4.0)) + 4.16438922228) * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5:
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0)
	elif x <= 11800.0:
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606)
	else:
		tmp = ((z / math.pow(x, 4.0)) + 4.16438922228) * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0));
	elseif (x <= 11800.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(y * x) + z)) / Float64(Float64(Float64(Float64(263.505074721 * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = Float64(Float64(Float64(z / (x ^ 4.0)) + 4.16438922228) * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	elseif (x <= 11800.0)
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606);
	else
		tmp = ((z / (x ^ 4.0)) + 4.16438922228) * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5], N[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 11800.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] + 4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -5.5 < x < 11800

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 48.0

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

   7. Applied rewrites 48.0%

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

   if 11800 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(\frac{z}{\color{blue}{{x}^{4}}} + \frac{104109730557}{25000000000}\right) \cdot \left(x - 2\right) \]
   10. Step-by-step derivation

       1. lower-pow.f64 47.2

          \[\leadsto \left(\frac{z}{{x}^{\color{blue}{4}}} + 4.16438922228\right) \cdot \left(x - 2\right) \]

   11. Applied rewrites 47.2%

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

Alternative 12: 92.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{\frac{3451.550173699799 - \frac{124074.40615218398 - y}{x}}{x} - 101.7851458539211}{x} - -4.16438922228\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 32:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{\left(263.505074721 \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (-
           (/
            (-
             (/ (- 3451.550173699799 (/ (- 124074.40615218398 y) x)) x)
             101.7851458539211)
            x)
           -4.16438922228)
          (- x 2.0))))
   (if (<= x -5.5)
     t_0
     (if (<= x 32.0)
       (/
        (* (- x 2.0) (+ (* 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 = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	double tmp;
	if (x <= -5.5) {
		tmp = t_0;
	} else if (x <= 32.0) {
		tmp = ((x - 2.0) * ((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 = (((((3451.550173699799d0 - ((124074.40615218398d0 - y) / x)) / x) - 101.7851458539211d0) / x) - (-4.16438922228d0)) * (x - 2.0d0)
    if (x <= (-5.5d0)) then
        tmp = t_0
    else if (x <= 32.0d0) then
        tmp = ((x - 2.0d0) * ((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 = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	double tmp;
	if (x <= -5.5) {
		tmp = t_0;
	} else if (x <= 32.0) {
		tmp = ((x - 2.0) * ((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 = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0)
	tmp = 0
	if x <= -5.5:
		tmp = t_0
	elif x <= 32.0:
		tmp = ((x - 2.0) * ((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(Float64(Float64(Float64(Float64(Float64(3451.550173699799 - Float64(Float64(124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -5.5)
		tmp = t_0;
	elseif (x <= 32.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(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 = (((((3451.550173699799 - ((124074.40615218398 - y) / x)) / x) - 101.7851458539211) / x) - -4.16438922228) * (x - 2.0);
	tmp = 0.0;
	if (x <= -5.5)
		tmp = t_0;
	elseif (x <= 32.0)
		tmp = ((x - 2.0) * ((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[(N[(N[(N[(N[(N[(3451.550173699799 - N[(N[(124074.40615218398 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision] - -4.16438922228), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5], t$95$0, If[LessEqual[x, 32.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * 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 < -5.5 or 32 < x

   1. Initial program 58.7%

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]
   2. 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 61.7%

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

   4. Taylor expanded in x around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   6. Applied rewrites 48.1%

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

   8. Applied rewrites 48.1%

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

   if -5.5 < x < 32

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 48.0

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

   7. Applied rewrites 48.0%

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

Alternative 13: 90.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -160:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718 - \frac{\frac{42.87307123793778}{x} - 6.349501247902845}{x}}{x}}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{\left(263.505074721 \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -160.0)
   (/
    1.0
    (/
     (-
      0.24013125253755718
      (/ (- (/ 42.87307123793778 x) 6.349501247902845) x))
     x))
   (if (<= x 3e+17)
     (/
      (* (- x 2.0) (+ (* y x) z))
      (+ (* (+ (* 263.505074721 x) 313.399215894) x) 47.066876606))
     (/ 1.0 (/ 0.24013125253755718 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -160.0) {
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	} else if (x <= 3e+17) {
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = 1.0 / (0.24013125253755718 / 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 <= (-160.0d0)) then
        tmp = 1.0d0 / ((0.24013125253755718d0 - (((42.87307123793778d0 / x) - 6.349501247902845d0) / x)) / x)
    else if (x <= 3d+17) then
        tmp = ((x - 2.0d0) * ((y * x) + z)) / ((((263.505074721d0 * x) + 313.399215894d0) * x) + 47.066876606d0)
    else
        tmp = 1.0d0 / (0.24013125253755718d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -160.0) {
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	} else if (x <= 3e+17) {
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = 1.0 / (0.24013125253755718 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -160.0:
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x)
	elif x <= 3e+17:
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606)
	else:
		tmp = 1.0 / (0.24013125253755718 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -160.0)
		tmp = Float64(1.0 / Float64(Float64(0.24013125253755718 - Float64(Float64(Float64(42.87307123793778 / x) - 6.349501247902845) / x)) / x));
	elseif (x <= 3e+17)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(y * x) + z)) / Float64(Float64(Float64(Float64(263.505074721 * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = Float64(1.0 / Float64(0.24013125253755718 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -160.0)
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	elseif (x <= 3e+17)
		tmp = ((x - 2.0) * ((y * x) + z)) / ((((263.505074721 * x) + 313.399215894) * x) + 47.066876606);
	else
		tmp = 1.0 / (0.24013125253755718 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -160.0], N[(1.0 / N[(N[(0.24013125253755718 - N[(N[(N[(42.87307123793778 / x), $MachinePrecision] - 6.349501247902845), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+17], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.24013125253755718 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -160

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around -inf

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{\color{blue}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      8. lower-/.f64 45.3

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}} \]

   6. Applied rewrites 45.3%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}}} \]

   8. Applied rewrites 45.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{0.24013125253755718 - \frac{\frac{42.87307123793778}{x} - 6.349501247902845}{x}}{x}}} \]

   if -160 < x < 3e17

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 48.0

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

   7. Applied rewrites 48.0%

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

   if 3e17 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 45.2

         \[\leadsto \frac{1}{\frac{0.24013125253755718}{\color{blue}{x}}} \]

   6. Applied rewrites 45.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.24013125253755718}{x}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 90.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718 - \frac{\frac{42.87307123793778}{x} - 6.349501247902845}{x}}{x}}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+17}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35)
   (/
    1.0
    (/
     (-
      0.24013125253755718
      (/ (- (/ 42.87307123793778 x) 6.349501247902845) x))
     x))
   (if (<= x 3e+17)
     (/ (* (- x 2.0) (+ (* y x) z)) (+ (* 313.399215894 x) 47.066876606))
     (/ 1.0 (/ 0.24013125253755718 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	} else if (x <= 3e+17) {
		tmp = ((x - 2.0) * ((y * x) + z)) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = 1.0 / (0.24013125253755718 / 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 <= (-1.35d0)) then
        tmp = 1.0d0 / ((0.24013125253755718d0 - (((42.87307123793778d0 / x) - 6.349501247902845d0) / x)) / x)
    else if (x <= 3d+17) then
        tmp = ((x - 2.0d0) * ((y * x) + z)) / ((313.399215894d0 * x) + 47.066876606d0)
    else
        tmp = 1.0d0 / (0.24013125253755718d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.35) {
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	} else if (x <= 3e+17) {
		tmp = ((x - 2.0) * ((y * x) + z)) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = 1.0 / (0.24013125253755718 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.35:
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x)
	elif x <= 3e+17:
		tmp = ((x - 2.0) * ((y * x) + z)) / ((313.399215894 * x) + 47.066876606)
	else:
		tmp = 1.0 / (0.24013125253755718 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.35)
		tmp = Float64(1.0 / Float64(Float64(0.24013125253755718 - Float64(Float64(Float64(42.87307123793778 / x) - 6.349501247902845) / x)) / x));
	elseif (x <= 3e+17)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(y * x) + z)) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = Float64(1.0 / Float64(0.24013125253755718 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.35)
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	elseif (x <= 3e+17)
		tmp = ((x - 2.0) * ((y * x) + z)) / ((313.399215894 * x) + 47.066876606);
	else
		tmp = 1.0 / (0.24013125253755718 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.35], N[(1.0 / N[(N[(0.24013125253755718 - N[(N[(N[(42.87307123793778 / x), $MachinePrecision] - 6.349501247902845), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+17], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.24013125253755718 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around -inf

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{\color{blue}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      8. lower-/.f64 45.3

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}} \]

   6. Applied rewrites 45.3%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}}} \]

   8. Applied rewrites 45.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{0.24013125253755718 - \frac{\frac{42.87307123793778}{x} - 6.349501247902845}{x}}{x}}} \]

   if -1.3500000000000001 < x < 3e17

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 48.4

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

   7. Applied rewrites 48.4%

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

   if 3e17 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 45.2

         \[\leadsto \frac{1}{\frac{0.24013125253755718}{\color{blue}{x}}} \]

   6. Applied rewrites 45.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.24013125253755718}{x}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 76.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718 - \frac{\frac{42.87307123793778}{x} - 6.349501247902845}{x}}{x}}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+17}:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4)
   (/
    1.0
    (/
     (-
      0.24013125253755718
      (/ (- (/ 42.87307123793778 x) 6.349501247902845) x))
     x))
   (if (<= x -4.2e-67)
     (/ (* x (* y (- x 2.0))) (+ (* 313.399215894 x) 47.066876606))
     (if (<= x 3e+17)
       (* (* 0.0212463641547976 z) (- x 2.0))
       (/ 1.0 (/ 0.24013125253755718 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4) {
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	} else if (x <= -4.2e-67) {
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606);
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 1.0 / (0.24013125253755718 / 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 <= (-1.4d0)) then
        tmp = 1.0d0 / ((0.24013125253755718d0 - (((42.87307123793778d0 / x) - 6.349501247902845d0) / x)) / x)
    else if (x <= (-4.2d-67)) then
        tmp = (x * (y * (x - 2.0d0))) / ((313.399215894d0 * x) + 47.066876606d0)
    else if (x <= 3d+17) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = 1.0d0 / (0.24013125253755718d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4) {
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	} else if (x <= -4.2e-67) {
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606);
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 1.0 / (0.24013125253755718 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4:
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x)
	elif x <= -4.2e-67:
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606)
	elif x <= 3e+17:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = 1.0 / (0.24013125253755718 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4)
		tmp = Float64(1.0 / Float64(Float64(0.24013125253755718 - Float64(Float64(Float64(42.87307123793778 / x) - 6.349501247902845) / x)) / x));
	elseif (x <= -4.2e-67)
		tmp = Float64(Float64(x * Float64(y * Float64(x - 2.0))) / Float64(Float64(313.399215894 * x) + 47.066876606));
	elseif (x <= 3e+17)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = Float64(1.0 / Float64(0.24013125253755718 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4)
		tmp = 1.0 / ((0.24013125253755718 - (((42.87307123793778 / x) - 6.349501247902845) / x)) / x);
	elseif (x <= -4.2e-67)
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606);
	elseif (x <= 3e+17)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = 1.0 / (0.24013125253755718 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4], N[(1.0 / N[(N[(0.24013125253755718 - N[(N[(N[(42.87307123793778 / x), $MachinePrecision] - 6.349501247902845), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-67], N[(N[(x * N[(y * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+17], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.24013125253755718 / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.3999999999999999

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around -inf

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{\color{blue}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      8. lower-/.f64 45.3

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}} \]

   6. Applied rewrites 45.3%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}}} \]

   8. Applied rewrites 45.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{0.24013125253755718 - \frac{\frac{42.87307123793778}{x} - 6.349501247902845}{x}}{x}}} \]

   if -1.3999999999999999 < x < -4.2000000000000003e-67

   1. Initial program 58.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 16.7

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

   4. Applied rewrites 16.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 15.6

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

   7. Applied rewrites 15.6%

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

   if -4.2000000000000003e-67 < x < 3e17

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 35.2

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

   11. Applied rewrites 35.2%

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

   if 3e17 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 45.2

         \[\leadsto \frac{1}{\frac{0.24013125253755718}{\color{blue}{x}}} \]

   6. Applied rewrites 45.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.24013125253755718}{x}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 16: 76.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;\frac{1}{-1 \cdot \frac{\frac{-6.349501247902845}{x} - 0.24013125253755718}{x}}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \left(x - 2\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+17}:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4)
   (/ 1.0 (* -1.0 (/ (- (/ -6.349501247902845 x) 0.24013125253755718) x)))
   (if (<= x -4.2e-67)
     (/ (* x (* y (- x 2.0))) (+ (* 313.399215894 x) 47.066876606))
     (if (<= x 3e+17)
       (* (* 0.0212463641547976 z) (- x 2.0))
       (/ 1.0 (/ 0.24013125253755718 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4) {
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x));
	} else if (x <= -4.2e-67) {
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606);
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 1.0 / (0.24013125253755718 / 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 <= (-1.4d0)) then
        tmp = 1.0d0 / ((-1.0d0) * ((((-6.349501247902845d0) / x) - 0.24013125253755718d0) / x))
    else if (x <= (-4.2d-67)) then
        tmp = (x * (y * (x - 2.0d0))) / ((313.399215894d0 * x) + 47.066876606d0)
    else if (x <= 3d+17) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = 1.0d0 / (0.24013125253755718d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4) {
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x));
	} else if (x <= -4.2e-67) {
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606);
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 1.0 / (0.24013125253755718 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4:
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x))
	elif x <= -4.2e-67:
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606)
	elif x <= 3e+17:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = 1.0 / (0.24013125253755718 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4)
		tmp = Float64(1.0 / Float64(-1.0 * Float64(Float64(Float64(-6.349501247902845 / x) - 0.24013125253755718) / x)));
	elseif (x <= -4.2e-67)
		tmp = Float64(Float64(x * Float64(y * Float64(x - 2.0))) / Float64(Float64(313.399215894 * x) + 47.066876606));
	elseif (x <= 3e+17)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = Float64(1.0 / Float64(0.24013125253755718 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4)
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x));
	elseif (x <= -4.2e-67)
		tmp = (x * (y * (x - 2.0))) / ((313.399215894 * x) + 47.066876606);
	elseif (x <= 3e+17)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = 1.0 / (0.24013125253755718 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4], N[(1.0 / N[(-1.0 * N[(N[(N[(-6.349501247902845 / x), $MachinePrecision] - 0.24013125253755718), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-67], N[(N[(x * N[(y * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+17], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.24013125253755718 / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.3999999999999999

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around -inf

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{\color{blue}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      8. lower-/.f64 45.3

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}} \]

   6. Applied rewrites 45.3%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}}} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{1}{-1 \cdot \frac{\frac{\frac{-68821202686550684400745}{10838835996651139530249}}{x} - \frac{25000000000}{104109730557}}{x}} \]
   8. Step-by-step derivation

      1. lower-/.f64 45.3

         \[\leadsto \frac{1}{-1 \cdot \frac{\frac{-6.349501247902845}{x} - 0.24013125253755718}{x}} \]

   9. Applied rewrites 45.3%

      \[\leadsto \frac{1}{-1 \cdot \frac{\frac{-6.349501247902845}{x} - 0.24013125253755718}{x}} \]

   if -1.3999999999999999 < x < -4.2000000000000003e-67

   1. Initial program 58.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 16.7

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

   4. Applied rewrites 16.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 15.6

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

   7. Applied rewrites 15.6%

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

   if -4.2000000000000003e-67 < x < 3e17

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 35.2

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

   11. Applied rewrites 35.2%

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

   if 3e17 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 45.2

         \[\leadsto \frac{1}{\frac{0.24013125253755718}{\color{blue}{x}}} \]

   6. Applied rewrites 45.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.24013125253755718}{x}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 17: 76.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10:\\ \;\;\;\;\frac{1}{-1 \cdot \frac{\frac{-6.349501247902845}{x} - 0.24013125253755718}{x}}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+17}:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.24013125253755718}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -10.0)
   (/ 1.0 (* -1.0 (/ (- (/ -6.349501247902845 x) 0.24013125253755718) x)))
   (if (<= x 3e+17)
     (* (* 0.0212463641547976 z) (- x 2.0))
     (/ 1.0 (/ 0.24013125253755718 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -10.0) {
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x));
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 1.0 / (0.24013125253755718 / 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 <= (-10.0d0)) then
        tmp = 1.0d0 / ((-1.0d0) * ((((-6.349501247902845d0) / x) - 0.24013125253755718d0) / x))
    else if (x <= 3d+17) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = 1.0d0 / (0.24013125253755718d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -10.0) {
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x));
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = 1.0 / (0.24013125253755718 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -10.0:
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x))
	elif x <= 3e+17:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = 1.0 / (0.24013125253755718 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -10.0)
		tmp = Float64(1.0 / Float64(-1.0 * Float64(Float64(Float64(-6.349501247902845 / x) - 0.24013125253755718) / x)));
	elseif (x <= 3e+17)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = Float64(1.0 / Float64(0.24013125253755718 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -10.0)
		tmp = 1.0 / (-1.0 * (((-6.349501247902845 / x) - 0.24013125253755718) / x));
	elseif (x <= 3e+17)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = 1.0 / (0.24013125253755718 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -10.0], N[(1.0 / N[(-1.0 * N[(N[(N[(-6.349501247902845 / x), $MachinePrecision] - 0.24013125253755718), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+17], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(0.24013125253755718 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -10

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around -inf

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \color{blue}{\frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{\color{blue}{x}}} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      6. lower--.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{\frac{68821202686550684400745}{10838835996651139530249} - \frac{48379186685422091754128006001718670}{1128428295162862690821234941118693} \cdot \frac{1}{x}}{x} - \frac{25000000000}{104109730557}}{x}} \]

      8. lower-/.f64 45.3

         \[\leadsto \frac{1}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}} \]

   6. Applied rewrites 45.3%

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{6.349501247902845 - 42.87307123793778 \cdot \frac{1}{x}}{x} - 0.24013125253755718}{x}}} \]

   7. Taylor expanded in x around inf

      \[\leadsto \frac{1}{-1 \cdot \frac{\frac{\frac{-68821202686550684400745}{10838835996651139530249}}{x} - \frac{25000000000}{104109730557}}{x}} \]
   8. Step-by-step derivation

      1. lower-/.f64 45.3

         \[\leadsto \frac{1}{-1 \cdot \frac{\frac{-6.349501247902845}{x} - 0.24013125253755718}{x}} \]

   9. Applied rewrites 45.3%

      \[\leadsto \frac{1}{-1 \cdot \frac{\frac{-6.349501247902845}{x} - 0.24013125253755718}{x}} \]

   if -10 < x < 3e17

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 35.2

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

   11. Applied rewrites 35.2%

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

   if 3e17 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 45.2

         \[\leadsto \frac{1}{\frac{0.24013125253755718}{\color{blue}{x}}} \]

   6. Applied rewrites 45.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.24013125253755718}{x}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 76.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\frac{0.24013125253755718}{x}}\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+17}:\\ \;\;\;\;\left(0.0212463641547976 \cdot z\right) \cdot \left(x - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ 1.0 (/ 0.24013125253755718 x))))
   (if (<= x -1.2e-8)
     t_0
     (if (<= x 3e+17) (* (* 0.0212463641547976 z) (- x 2.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 / (0.24013125253755718 / x);
	double tmp;
	if (x <= -1.2e-8) {
		tmp = t_0;
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / (0.24013125253755718d0 / x)
    if (x <= (-1.2d-8)) then
        tmp = t_0
    else if (x <= 3d+17) then
        tmp = (0.0212463641547976d0 * z) * (x - 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 / (0.24013125253755718 / x);
	double tmp;
	if (x <= -1.2e-8) {
		tmp = t_0;
	} else if (x <= 3e+17) {
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 / (0.24013125253755718 / x)
	tmp = 0
	if x <= -1.2e-8:
		tmp = t_0
	elif x <= 3e+17:
		tmp = (0.0212463641547976 * z) * (x - 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 / Float64(0.24013125253755718 / x))
	tmp = 0.0
	if (x <= -1.2e-8)
		tmp = t_0;
	elseif (x <= 3e+17)
		tmp = Float64(Float64(0.0212463641547976 * z) * Float64(x - 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 / (0.24013125253755718 / x);
	tmp = 0.0;
	if (x <= -1.2e-8)
		tmp = t_0;
	elseif (x <= 3e+17)
		tmp = (0.0212463641547976 * z) * (x - 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 / N[(0.24013125253755718 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e-8], t$95$0, If[LessEqual[x, 3e+17], N[(N[(0.0212463641547976 * z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999999e-8 or 3e17 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 45.2

         \[\leadsto \frac{1}{\frac{0.24013125253755718}{\color{blue}{x}}} \]

   6. Applied rewrites 45.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.24013125253755718}{x}}} \]

   if -1.19999999999999999e-8 < x < 3e17

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 69.1%

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

   8. Applied rewrites 69.1%

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

   9. Taylor expanded in x around 0

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

       1. lower-*.f64 35.2

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

   11. Applied rewrites 35.2%

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

Alternative 19: 76.6% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\frac{0.24013125253755718}{x}}\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ 1.0 (/ 0.24013125253755718 x))))
   (if (<= x -1.2e-8) t_0 (if (<= x 2.0) (* -0.0424927283095952 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 / (0.24013125253755718 / x);
	double tmp;
	if (x <= -1.2e-8) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / (0.24013125253755718d0 / x)
    if (x <= (-1.2d-8)) then
        tmp = t_0
    else if (x <= 2.0d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 / (0.24013125253755718 / x);
	double tmp;
	if (x <= -1.2e-8) {
		tmp = t_0;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 / (0.24013125253755718 / x)
	tmp = 0
	if x <= -1.2e-8:
		tmp = t_0
	elif x <= 2.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 / Float64(0.24013125253755718 / x))
	tmp = 0.0
	if (x <= -1.2e-8)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 / (0.24013125253755718 / x);
	tmp = 0.0;
	if (x <= -1.2e-8)
		tmp = t_0;
	elseif (x <= 2.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 / N[(0.24013125253755718 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e-8], t$95$0, If[LessEqual[x, 2.0], N[(-0.0424927283095952 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999999e-8 or 2 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 58.6%

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

   4. Taylor expanded in x around inf

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{25000000000}{104109730557}}{x}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 45.2

         \[\leadsto \frac{1}{\frac{0.24013125253755718}{\color{blue}{x}}} \]

   6. Applied rewrites 45.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{0.24013125253755718}{x}}} \]

   if -1.19999999999999999e-8 < x < 2

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 35.0

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

   4. Applied rewrites 35.0%

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

Alternative 20: 76.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-8}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e-8)
   (* 4.16438922228 x)
   (if (<= x 2.0) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e-8) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.2d-8)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.0d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = 4.16438922228d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e-8) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e-8:
		tmp = 4.16438922228 * x
	elif x <= 2.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e-8)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.2e-8)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e-8], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999999e-8 or 2 < x

   1. Initial program 58.7%

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 45.1

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

   6. Applied rewrites 45.1%

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

   if -1.19999999999999999e-8 < x < 2

   1. Initial program 58.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 35.0

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

   4. Applied rewrites 35.0%

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

Alternative 21: 45.1% 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 58.7%

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

3. Applied rewrites 62.4%

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

4. Taylor expanded in x around inf

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

   1. lower-*.f64 45.1

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

6. Applied rewrites 45.1%

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

Reproduce

herbie shell --seed 2025159 
(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)))