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

Percentage Accurate: 58.4% → 98.1%

Time: 6.0s

Alternatives: 20

Speedup: 4.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{y - 130977.50649958357}{x}\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
           y)
          x)
         z))
       (+
        (*
         (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
         x)
        47.066876606))
      5e+294)
   (*
    (- x 2.0)
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma
      (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
      x
      47.066876606)))
   (*
    (- x)
    (-
     (-
      (/
       (-
        (- (/ (- (- (/ (- y 130977.50649958357) x)) 3655.1204654076414) x))
        110.1139242984811)
       x))
     4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 5e+294) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = -x * (-((-((-((y - 130977.50649958357) / x) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 5e+294)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 5e+294], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[((-N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]) - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 4.9999999999999999e294

   1. Initial program 96.8%

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

   3. Applied rewrites 98.9%

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

   if 4.9999999999999999e294 < (/.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 1.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 0.3%

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

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 97.0%

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

Alternative 2: 96.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot x, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{y - 130977.50649958357}{x}\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          (+
           (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
           y)
          x)
         z))
       (+
        (*
         (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
         x)
        47.066876606))
      5e+294)
   (*
    (- x 2.0)
    (/
     (fma
      (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
      x
      z)
     (fma (fma (* x x) x 313.399215894) x 47.066876606)))
   (*
    (- x)
    (-
     (-
      (/
       (-
        (- (/ (- (- (/ (- y 130977.50649958357) x)) 3655.1204654076414) x))
        110.1139242984811)
       x))
     4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 5e+294) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma((x * x), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = -x * (-((-((-((y - 130977.50649958357) / x) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 5e+294)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(Float64(x * x), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 5e+294], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[((-N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]) - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 4.9999999999999999e294

   1. Initial program 96.8%

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

   3. Applied rewrites 98.9%

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

   4. Taylor expanded in x around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 96.0

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

   6. Applied rewrites 96.0%

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

   if 4.9999999999999999e294 < (/.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 1.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 0.3%

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

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 97.0%

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

Alternative 3: 96.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{y - 130977.50649958357}{x}\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 60:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x)
          (-
           (-
            (/
             (-
              (-
               (/ (- (- (/ (- y 130977.50649958357) x)) 3655.1204654076414) x))
              110.1139242984811)
             x))
           4.16438922228))))
   (if (<= x -5.5)
     t_0
     (if (<= x 60.0)
       (*
        (- x 2.0)
        (/
         (fma
          (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
          x
          z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x * (-((-((-((y - 130977.50649958357) / x) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	double tmp;
	if (x <= -5.5) {
		tmp = t_0;
	} else if (x <= 60.0) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(y - 130977.50649958357) / x)) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228))
	tmp = 0.0
	if (x <= -5.5)
		tmp = t_0;
	elseif (x <= 60.0)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[((-N[(N[((-N[(N[((-N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]) - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5], t$95$0, If[LessEqual[x, 60.0], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5 or 60 < x

   1. Initial program 17.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 13.8%

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

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 93.4%

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

   if -5.5 < x < 60

   1. Initial program 99.7%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.7%

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

Alternative 4: 94.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}, z, 4.16438922228 \cdot x\right)\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.02:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (/
           (- x 2.0)
           (fma
            (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
            x
            47.066876606))
          z
          (* 4.16438922228 x))))
   (if (<= x -2600.0)
     t_0
     (if (<= x 0.02)
       (*
        (- x 2.0)
        (/
         (fma
          (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
          x
          z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(((x - 2.0) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)), z, (4.16438922228 * x));
	double tmp;
	if (x <= -2600.0) {
		tmp = t_0;
	} else if (x <= 0.02) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(Float64(x - 2.0) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)), z, Float64(4.16438922228 * x))
	tmp = 0.0
	if (x <= -2600.0)
		tmp = t_0;
	elseif (x <= 0.02)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * z + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2600.0], t$95$0, If[LessEqual[x, 0.02], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2600 or 0.0200000000000000004 < x

   1. Initial program 17.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 18.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 91.2

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

   7. Applied rewrites 91.2%

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

   if -2600 < x < 0.0200000000000000004

   1. Initial program 99.6%

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.6%

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

Alternative 5: 94.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}, z, 4.16438922228 \cdot x\right)\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.02:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (/
           (- x 2.0)
           (fma
            (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
            x
            47.066876606))
          z
          (* 4.16438922228 x))))
   (if (<= x -2600.0)
     t_0
     (if (<= x 0.02)
       (*
        (- x 2.0)
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(((x - 2.0) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)), z, (4.16438922228 * x));
	double tmp;
	if (x <= -2600.0) {
		tmp = t_0;
	} else if (x <= 0.02) {
		tmp = (x - 2.0) * (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(Float64(x - 2.0) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)), z, Float64(4.16438922228 * x))
	tmp = 0.0
	if (x <= -2600.0)
		tmp = t_0;
	elseif (x <= 0.02)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * z + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2600.0], t$95$0, If[LessEqual[x, 0.02], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2600 or 0.0200000000000000004 < x

   1. Initial program 17.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 18.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 91.2

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

   7. Applied rewrites 91.2%

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

   if -2600 < x < 0.0200000000000000004

   1. Initial program 99.6%

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.6%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 98.6%

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

Alternative 6: 94.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}, z, 4.16438922228 \cdot x\right)\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.019:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (/
           (- x 2.0)
           (fma
            (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
            x
            47.066876606))
          z
          (* 4.16438922228 x))))
   (if (<= x -2600.0)
     t_0
     (if (<= x 0.019)
       (*
        (- x 2.0)
        (/
         (fma (fma 137.519416416 x y) x z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(((x - 2.0) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)), z, (4.16438922228 * x));
	double tmp;
	if (x <= -2600.0) {
		tmp = t_0;
	} else if (x <= 0.019) {
		tmp = (x - 2.0) * (fma(fma(137.519416416, x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(Float64(x - 2.0) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)), z, Float64(4.16438922228 * x))
	tmp = 0.0
	if (x <= -2600.0)
		tmp = t_0;
	elseif (x <= 0.019)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(137.519416416, x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * z + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2600.0], t$95$0, If[LessEqual[x, 0.019], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2600 or 0.0189999999999999995 < x

   1. Initial program 17.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 18.0%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 91.1

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

   7. Applied rewrites 91.1%

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

   if -2600 < x < 0.0189999999999999995

   1. Initial program 99.6%

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 98.6%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 98.4%

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

Alternative 7: 94.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot x, x, 313.399215894\right), x, 47.066876606\right)}, z, 4.16438922228 \cdot x\right)\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+17}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (/ (- x 2.0) (fma (fma (* x x) x 313.399215894) x 47.066876606))
          z
          (* 4.16438922228 x))))
   (if (<= x -2600.0)
     t_0
     (if (<= x 9.8e+17)
       (*
        (- x 2.0)
        (/
         (fma (fma 137.519416416 x y) x z)
         (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(((x - 2.0) / fma(fma((x * x), x, 313.399215894), x, 47.066876606)), z, (4.16438922228 * x));
	double tmp;
	if (x <= -2600.0) {
		tmp = t_0;
	} else if (x <= 9.8e+17) {
		tmp = (x - 2.0) * (fma(fma(137.519416416, x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(Float64(x - 2.0) / fma(fma(Float64(x * x), x, 313.399215894), x, 47.066876606)), z, Float64(4.16438922228 * x))
	tmp = 0.0
	if (x <= -2600.0)
		tmp = t_0;
	elseif (x <= 9.8e+17)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(137.519416416, x, y), x, z) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * z + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2600.0], t$95$0, If[LessEqual[x, 9.8e+17], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2600 or 9.8e17 < x

   1. Initial program 14.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 15.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.6

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

   7. Applied rewrites 92.6%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left({x}^{2}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)}, z, \frac{104109730557}{25000000000} \cdot x\right) \]
   9. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot x, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)}, z, \frac{104109730557}{25000000000} \cdot x\right) \]

      2. lower-*.f64 92.3

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

   10. Applied rewrites 92.3%

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

   if -2600 < x < 9.8e17

   1. Initial program 99.5%

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 95.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 95.5%

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

Alternative 8: 90.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot x, x, 313.399215894\right), x, 47.066876606\right)}, z, 4.16438922228 \cdot x\right)\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+17}:\\ \;\;\;\;\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma
          (/ (- x 2.0) (fma (fma (* x x) x 313.399215894) x 47.066876606))
          z
          (* 4.16438922228 x))))
   (if (<= x -2600.0)
     t_0
     (if (<= x 9.8e+17)
       (*
        (- x 2.0)
        (fma
         (fma 0.0212463641547976 y (* -0.14147091005106402 z))
         x
         (* 0.0212463641547976 z)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(((x - 2.0) / fma(fma((x * x), x, 313.399215894), x, 47.066876606)), z, (4.16438922228 * x));
	double tmp;
	if (x <= -2600.0) {
		tmp = t_0;
	} else if (x <= 9.8e+17) {
		tmp = (x - 2.0) * fma(fma(0.0212463641547976, y, (-0.14147091005106402 * z)), x, (0.0212463641547976 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(Float64(x - 2.0) / fma(fma(Float64(x * x), x, 313.399215894), x, 47.066876606)), z, Float64(4.16438922228 * x))
	tmp = 0.0
	if (x <= -2600.0)
		tmp = t_0;
	elseif (x <= 9.8e+17)
		tmp = Float64(Float64(x - 2.0) * fma(fma(0.0212463641547976, y, Float64(-0.14147091005106402 * z)), x, Float64(0.0212463641547976 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x - 2.0), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision] * z + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2600.0], t$95$0, If[LessEqual[x, 9.8e+17], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * y + N[(-0.14147091005106402 * z), $MachinePrecision]), $MachinePrecision] * x + N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2600 or 9.8e17 < x

   1. Initial program 14.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 15.2%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 92.6

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

   7. Applied rewrites 92.6%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left({x}^{2}, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)}, z, \frac{104109730557}{25000000000} \cdot x\right) \]
   9. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(x \cdot x, x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)}, z, \frac{104109730557}{25000000000} \cdot x\right) \]

      2. lower-*.f64 92.3

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

   10. Applied rewrites 92.3%

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

   if -2600 < x < 9.8e17

   1. Initial program 99.5%

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{500000000}{23533438303} \cdot z}\right) \]

      2. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{500000000}{23533438303}} \cdot z\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{500000000}{23533438303} \cdot z\right) \]

      4. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot y + \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{500000000}{23533438303} \cdot z\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-78349803973500000000}{553822718361107519809} \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      8. lower-*.f64 89.5

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right) \]

   6. Applied rewrites 89.5%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2600:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\frac{3655.1204654076414}{x} - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+17}:\\ \;\;\;\;\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2600.0)
   (*
    (- x)
    (- (- (/ (- (/ 3655.1204654076414 x) 110.1139242984811) x)) 4.16438922228))
   (if (<= x 9.8e+17)
     (*
      (- x 2.0)
      (fma
       (fma 0.0212463641547976 y (* -0.14147091005106402 z))
       x
       (* 0.0212463641547976 z)))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2600.0) {
		tmp = -x * (-(((3655.1204654076414 / x) - 110.1139242984811) / x) - 4.16438922228);
	} else if (x <= 9.8e+17) {
		tmp = (x - 2.0) * fma(fma(0.0212463641547976, y, (-0.14147091005106402 * z)), x, (0.0212463641547976 * z));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2600.0)
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(3655.1204654076414 / x) - 110.1139242984811) / x)) - 4.16438922228));
	elseif (x <= 9.8e+17)
		tmp = Float64(Float64(x - 2.0) * fma(fma(0.0212463641547976, y, Float64(-0.14147091005106402 * z)), x, Float64(0.0212463641547976 * z)));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2600.0], N[((-x) * N[((-N[(N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+17], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * y + N[(-0.14147091005106402 * z), $MachinePrecision]), $MachinePrecision] * x + N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2600

   1. Initial program 16.4%

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

   2. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 87.4

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

   4. Applied rewrites 87.4%

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

   if -2600 < x < 9.8e17

   1. Initial program 99.5%

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{500000000}{23533438303} \cdot z}\right) \]

      2. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{500000000}{23533438303}} \cdot z\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{500000000}{23533438303} \cdot z\right) \]

      4. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot y + \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{500000000}{23533438303} \cdot z\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-78349803973500000000}{553822718361107519809} \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      8. lower-*.f64 89.5

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right) \]

   6. Applied rewrites 89.5%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right)} \]

   if 9.8e17 < x

   1. Initial program 12.3%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 10: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2600:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+17}:\\ \;\;\;\;\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2600.0)
   (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x)))
   (if (<= x 9.8e+17)
     (*
      (- x 2.0)
      (fma
       (fma 0.0212463641547976 y (* -0.14147091005106402 z))
       x
       (* 0.0212463641547976 z)))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2600.0) {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else if (x <= 9.8e+17) {
		tmp = (x - 2.0) * fma(fma(0.0212463641547976, y, (-0.14147091005106402 * z)), x, (0.0212463641547976 * z));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2600.0)
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	elseif (x <= 9.8e+17)
		tmp = Float64(Float64(x - 2.0) * fma(fma(0.0212463641547976, y, Float64(-0.14147091005106402 * z)), x, Float64(0.0212463641547976 * z)));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2600.0], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+17], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * y + N[(-0.14147091005106402 * z), $MachinePrecision]), $MachinePrecision] * x + N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2600

   1. Initial program 16.4%

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

   3. Applied rewrites 21.7%

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

   4. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 87.4

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

   6. Applied rewrites 87.4%

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

   if -2600 < x < 9.8e17

   1. Initial program 99.5%

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in x around 0

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\frac{500000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(x \cdot \left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{500000000}{23533438303} \cdot z}\right) \]

      2. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \left(\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{500000000}{23533438303}} \cdot z\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot y - \frac{78349803973500000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{500000000}{23533438303} \cdot z\right) \]

      4. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot y + \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{500000000}{23533438303} \cdot z\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \left(\mathsf{neg}\left(\frac{78349803973500000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\frac{500000000}{23533438303}, y, \frac{-78349803973500000000}{553822718361107519809} \cdot z\right), x, \frac{500000000}{23533438303} \cdot z\right) \]

      8. lower-*.f64 89.5

         \[\leadsto \left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right) \]

   6. Applied rewrites 89.5%

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right)} \]

   if 9.8e17 < x

   1. Initial program 12.3%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 11: 77.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-5.843575199059173, x, -0.0424927283095952 \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-64}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot z}{47.066876606}\\ \mathbf{elif}\;x \leq 0.032:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (fma -5.843575199059173 x (* -0.0424927283095952 y)) x)))
   (if (<= x -2600.0)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
     (if (<= x -3.15e-49)
       t_0
       (if (<= x 8e-64)
         (/ (* (- x 2.0) z) 47.066876606)
         (if (<= x 0.032) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(-5.843575199059173, x, (-0.0424927283095952 * y)) * x;
	double tmp;
	if (x <= -2600.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= -3.15e-49) {
		tmp = t_0;
	} else if (x <= 8e-64) {
		tmp = ((x - 2.0) * z) / 47.066876606;
	} else if (x <= 0.032) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(-5.843575199059173, x, Float64(-0.0424927283095952 * y)) * x)
	tmp = 0.0
	if (x <= -2600.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= -3.15e-49)
		tmp = t_0;
	elseif (x <= 8e-64)
		tmp = Float64(Float64(Float64(x - 2.0) * z) / 47.066876606);
	elseif (x <= 0.032)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-5.843575199059173 * x + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2600.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -3.15e-49], t$95$0, If[LessEqual[x, 8e-64], N[(N[(N[(x - 2.0), $MachinePrecision] * z), $MachinePrecision] / 47.066876606), $MachinePrecision], If[LessEqual[x, 0.032], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2600

   1. Initial program 16.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 87.4

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

   4. Applied rewrites 87.4%

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

   if -2600 < x < -3.1499999999999998e-49 or 7.99999999999999972e-64 < x < 0.032000000000000001

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 58.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) \cdot x + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      6. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y - \frac{4297481763}{15625000}\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      12. lower-*.f64 51.3

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot x \]

   7. Applied rewrites 51.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot \color{blue}{x} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{-137519416416}{23533438303}, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 49.7%

       \[\leadsto \mathsf{fma}\left(-5.843575199059173, x, -0.0424927283095952 \cdot y\right) \cdot x \]

   if -3.1499999999999998e-49 < x < 7.99999999999999972e-64

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. +-commutative N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 73.2%

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

   if 0.032000000000000001 < x

   1. Initial program 17.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 85.9

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

   4. Applied rewrites 85.9%

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

Alternative 12: 77.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-5.843575199059173, x, -0.0424927283095952 \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-64}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 0.032:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (fma -5.843575199059173 x (* -0.0424927283095952 y)) x)))
   (if (<= x -2600.0)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
     (if (<= x -3.15e-49)
       t_0
       (if (<= x 8e-64)
         (* -0.0424927283095952 z)
         (if (<= x 0.032) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(-5.843575199059173, x, (-0.0424927283095952 * y)) * x;
	double tmp;
	if (x <= -2600.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= -3.15e-49) {
		tmp = t_0;
	} else if (x <= 8e-64) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 0.032) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(-5.843575199059173, x, Float64(-0.0424927283095952 * y)) * x)
	tmp = 0.0
	if (x <= -2600.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= -3.15e-49)
		tmp = t_0;
	elseif (x <= 8e-64)
		tmp = Float64(-0.0424927283095952 * z);
	elseif (x <= 0.032)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-5.843575199059173 * x + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2600.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -3.15e-49], t$95$0, If[LessEqual[x, 8e-64], N[(-0.0424927283095952 * z), $MachinePrecision], If[LessEqual[x, 0.032], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2600

   1. Initial program 16.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 87.4

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

   4. Applied rewrites 87.4%

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

   if -2600 < x < -3.1499999999999998e-49 or 7.99999999999999972e-64 < x < 0.032000000000000001

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 58.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) \cdot x + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      6. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y - \frac{4297481763}{15625000}\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      12. lower-*.f64 51.3

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot x \]

   7. Applied rewrites 51.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot \color{blue}{x} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{-137519416416}{23533438303}, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 49.7%

       \[\leadsto \mathsf{fma}\left(-5.843575199059173, x, -0.0424927283095952 \cdot y\right) \cdot x \]

   if -3.1499999999999998e-49 < x < 7.99999999999999972e-64

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   if 0.032000000000000001 < x

   1. Initial program 17.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 85.9

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

   4. Applied rewrites 85.9%

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

Alternative 13: 77.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-5.843575199059173, x, -0.0424927283095952 \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -3800:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-64}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 0.032:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (fma -5.843575199059173 x (* -0.0424927283095952 y)) x)))
   (if (<= x -3800.0)
     (* (- x 2.0) 4.16438922228)
     (if (<= x -3.15e-49)
       t_0
       (if (<= x 8e-64)
         (* -0.0424927283095952 z)
         (if (<= x 0.032) t_0 (* 4.16438922228 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = fma(-5.843575199059173, x, (-0.0424927283095952 * y)) * x;
	double tmp;
	if (x <= -3800.0) {
		tmp = (x - 2.0) * 4.16438922228;
	} else if (x <= -3.15e-49) {
		tmp = t_0;
	} else if (x <= 8e-64) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 0.032) {
		tmp = t_0;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(-5.843575199059173, x, Float64(-0.0424927283095952 * y)) * x)
	tmp = 0.0
	if (x <= -3800.0)
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	elseif (x <= -3.15e-49)
		tmp = t_0;
	elseif (x <= 8e-64)
		tmp = Float64(-0.0424927283095952 * z);
	elseif (x <= 0.032)
		tmp = t_0;
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(-5.843575199059173 * x + N[(-0.0424927283095952 * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -3800.0], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision], If[LessEqual[x, -3.15e-49], t$95$0, If[LessEqual[x, 8e-64], N[(-0.0424927283095952 * z), $MachinePrecision], If[LessEqual[x, 0.032], t$95$0, N[(4.16438922228 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3800

   1. Initial program 16.4%

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

   3. Applied rewrites 21.7%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 87.2%

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

   if -3800 < x < -3.1499999999999998e-49 or 7.99999999999999972e-64 < x < 0.032000000000000001

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 58.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) \cdot x + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      6. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y - \frac{4297481763}{15625000}\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      12. lower-*.f64 51.3

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot x \]

   7. Applied rewrites 51.3%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot \color{blue}{x} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{-137519416416}{23533438303}, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 49.7%

       \[\leadsto \mathsf{fma}\left(-5.843575199059173, x, -0.0424927283095952 \cdot y\right) \cdot x \]

   if -3.1499999999999998e-49 < x < 7.99999999999999972e-64

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 72.9

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

   4. Applied rewrites 72.9%

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

   if 0.032000000000000001 < x

   1. Initial program 17.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 85.9

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

   4. Applied rewrites 85.9%

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

Alternative 14: 89.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2600:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \mathbf{elif}\;x \leq 2.4:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2600.0)
   (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x)))
   (if (<= x 2.4)
     (fma
      (fma -0.0424927283095952 y (* z 0.3041881842569256))
      x
      (* -0.0424927283095952 z))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2600.0) {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	} else if (x <= 2.4) {
		tmp = fma(fma(-0.0424927283095952, y, (z * 0.3041881842569256)), x, (-0.0424927283095952 * z));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2600.0)
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	elseif (x <= 2.4)
		tmp = fma(fma(-0.0424927283095952, y, Float64(z * 0.3041881842569256)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2600.0], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4], N[(N[(-0.0424927283095952 * y + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2600

   1. Initial program 16.4%

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

   3. Applied rewrites 21.7%

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

   4. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 87.4

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

   6. Applied rewrites 87.4%

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

   if -2600 < x < 2.39999999999999991

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate--l+ N/A

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

      5. lower-fma.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 92.2

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

   7. Applied rewrites 92.2%

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

   if 2.39999999999999991 < x

   1. Initial program 17.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 86.2

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

   4. Applied rewrites 86.2%

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

Alternative 15: 89.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2600:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{elif}\;x \leq 2.4:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.0424927283095952, y, z \cdot 0.3041881842569256\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2600.0)
   (* (- 4.16438922228 (/ 110.1139242984811 x)) x)
   (if (<= x 2.4)
     (fma
      (fma -0.0424927283095952 y (* z 0.3041881842569256))
      x
      (* -0.0424927283095952 z))
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2600.0) {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	} else if (x <= 2.4) {
		tmp = fma(fma(-0.0424927283095952, y, (z * 0.3041881842569256)), x, (-0.0424927283095952 * z));
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2600.0)
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	elseif (x <= 2.4)
		tmp = fma(fma(-0.0424927283095952, y, Float64(z * 0.3041881842569256)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2600.0], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.4], N[(N[(-0.0424927283095952 * y + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2600

   1. Initial program 16.4%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 87.4

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

   4. Applied rewrites 87.4%

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

   if -2600 < x < 2.39999999999999991

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. associate--l+ N/A

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

      5. lower-fma.f64 N/A

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

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

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

      7. metadata-eval N/A

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

      8. lower-*.f64 N/A

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

      9. lift-*.f64 92.2

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

   7. Applied rewrites 92.2%

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

   if 2.39999999999999991 < x

   1. Initial program 17.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 86.2

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

   4. Applied rewrites 86.2%

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

Alternative 16: 76.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot 4.16438922228\\ \mathbf{if}\;x \leq -2600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(0.0212463641547976 \cdot z\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;\left(-0.0424927283095952 \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x 2.0) 4.16438922228)))
   (if (<= x -2600.0)
     t_0
     (if (<= x 1.4e-62)
       (* (- x 2.0) (* 0.0212463641547976 z))
       (if (<= x 1.25e-6) (* (* -0.0424927283095952 y) x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * 4.16438922228;
	double tmp;
	if (x <= -2600.0) {
		tmp = t_0;
	} else if (x <= 1.4e-62) {
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	} else if (x <= 1.25e-6) {
		tmp = (-0.0424927283095952 * y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - 2.0d0) * 4.16438922228d0
    if (x <= (-2600.0d0)) then
        tmp = t_0
    else if (x <= 1.4d-62) then
        tmp = (x - 2.0d0) * (0.0212463641547976d0 * z)
    else if (x <= 1.25d-6) then
        tmp = ((-0.0424927283095952d0) * y) * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * 4.16438922228;
	double tmp;
	if (x <= -2600.0) {
		tmp = t_0;
	} else if (x <= 1.4e-62) {
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	} else if (x <= 1.25e-6) {
		tmp = (-0.0424927283095952 * y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - 2.0) * 4.16438922228
	tmp = 0
	if x <= -2600.0:
		tmp = t_0
	elif x <= 1.4e-62:
		tmp = (x - 2.0) * (0.0212463641547976 * z)
	elif x <= 1.25e-6:
		tmp = (-0.0424927283095952 * y) * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * 4.16438922228)
	tmp = 0.0
	if (x <= -2600.0)
		tmp = t_0;
	elseif (x <= 1.4e-62)
		tmp = Float64(Float64(x - 2.0) * Float64(0.0212463641547976 * z));
	elseif (x <= 1.25e-6)
		tmp = Float64(Float64(-0.0424927283095952 * y) * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - 2.0) * 4.16438922228;
	tmp = 0.0;
	if (x <= -2600.0)
		tmp = t_0;
	elseif (x <= 1.4e-62)
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	elseif (x <= 1.25e-6)
		tmp = (-0.0424927283095952 * y) * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]}, If[LessEqual[x, -2600.0], t$95$0, If[LessEqual[x, 1.4e-62], N[(N[(x - 2.0), $MachinePrecision] * N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-6], N[(N[(-0.0424927283095952 * y), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2600 or 1.2500000000000001e-6 < x

   1. Initial program 17.6%

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

   3. Applied rewrites 23.1%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 86.1%

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

   if -2600 < x < 1.40000000000000001e-62

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 69.4

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

   6. Applied rewrites 69.4%

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

   if 1.40000000000000001e-62 < x < 1.2500000000000001e-6

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 57.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) \cdot x + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      6. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y - \frac{4297481763}{15625000}\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      12. lower-*.f64 56.7

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot x \]

   7. Applied rewrites 56.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot \color{blue}{x} \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]
   9. Step-by-step derivation

      1. lift-*.f64 39.7

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

   10. Applied rewrites 39.7%

       \[\leadsto \left(-0.0424927283095952 \cdot y\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 76.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot 4.16438922228\\ \mathbf{if}\;x \leq -2700:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;\left(-0.0424927283095952 \cdot y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x 2.0) 4.16438922228)))
   (if (<= x -2700.0)
     t_0
     (if (<= x 1.4e-62)
       (* -0.0424927283095952 z)
       (if (<= x 1.25e-6) (* (* -0.0424927283095952 y) x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * 4.16438922228;
	double tmp;
	if (x <= -2700.0) {
		tmp = t_0;
	} else if (x <= 1.4e-62) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 1.25e-6) {
		tmp = (-0.0424927283095952 * y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x - 2.0d0) * 4.16438922228d0
    if (x <= (-2700.0d0)) then
        tmp = t_0
    else if (x <= 1.4d-62) then
        tmp = (-0.0424927283095952d0) * z
    else if (x <= 1.25d-6) then
        tmp = ((-0.0424927283095952d0) * y) * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * 4.16438922228;
	double tmp;
	if (x <= -2700.0) {
		tmp = t_0;
	} else if (x <= 1.4e-62) {
		tmp = -0.0424927283095952 * z;
	} else if (x <= 1.25e-6) {
		tmp = (-0.0424927283095952 * y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - 2.0) * 4.16438922228
	tmp = 0
	if x <= -2700.0:
		tmp = t_0
	elif x <= 1.4e-62:
		tmp = -0.0424927283095952 * z
	elif x <= 1.25e-6:
		tmp = (-0.0424927283095952 * y) * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * 4.16438922228)
	tmp = 0.0
	if (x <= -2700.0)
		tmp = t_0;
	elseif (x <= 1.4e-62)
		tmp = Float64(-0.0424927283095952 * z);
	elseif (x <= 1.25e-6)
		tmp = Float64(Float64(-0.0424927283095952 * y) * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - 2.0) * 4.16438922228;
	tmp = 0.0;
	if (x <= -2700.0)
		tmp = t_0;
	elseif (x <= 1.4e-62)
		tmp = -0.0424927283095952 * z;
	elseif (x <= 1.25e-6)
		tmp = (-0.0424927283095952 * y) * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]}, If[LessEqual[x, -2700.0], t$95$0, If[LessEqual[x, 1.4e-62], N[(-0.0424927283095952 * z), $MachinePrecision], If[LessEqual[x, 1.25e-6], N[(N[(-0.0424927283095952 * y), $MachinePrecision] * x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2700 or 1.2500000000000001e-6 < x

   1. Initial program 17.6%

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

   3. Applied rewrites 23.1%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 86.1%

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

   if -2700 < x < 1.40000000000000001e-62

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 69.4

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

   4. Applied rewrites 69.4%

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

   if 1.40000000000000001e-62 < x < 1.2500000000000001e-6

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 57.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right)\right) \cdot x \]

      3. +-commutative N/A

         \[\leadsto \left(x \cdot \left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y\right) \cdot x + \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      6. fp-cancel-sub-sign-inv N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(y - \frac{4297481763}{15625000}\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(y - \frac{4297481763}{15625000}\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y, x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      10. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - \frac{4297481763}{15625000}, \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot y\right), x, \frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]

      12. lower-*.f64 56.7

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot x \]

   7. Applied rewrites 56.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, 0.0212463641547976, 0.28294182010212804 \cdot y\right), x, -0.0424927283095952 \cdot y\right) \cdot \color{blue}{x} \]

   8. Taylor expanded in x around 0

      \[\leadsto \left(\frac{-1000000000}{23533438303} \cdot y\right) \cdot x \]
   9. Step-by-step derivation

      1. lift-*.f64 39.7

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

   10. Applied rewrites 39.7%

       \[\leadsto \left(-0.0424927283095952 \cdot y\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 75.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot 4.16438922228\\ \mathbf{if}\;x \leq -2700:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-56}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x 2.0) 4.16438922228)))
   (if (<= x -2700.0) t_0 (if (<= x 1.45e-56) (* -0.0424927283095952 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * 4.16438922228;
	double tmp;
	if (x <= -2700.0) {
		tmp = t_0;
	} else if (x <= 1.45e-56) {
		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 = (x - 2.0d0) * 4.16438922228d0
    if (x <= (-2700.0d0)) then
        tmp = t_0
    else if (x <= 1.45d-56) 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 = (x - 2.0) * 4.16438922228;
	double tmp;
	if (x <= -2700.0) {
		tmp = t_0;
	} else if (x <= 1.45e-56) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - 2.0) * 4.16438922228
	tmp = 0
	if x <= -2700.0:
		tmp = t_0
	elif x <= 1.45e-56:
		tmp = -0.0424927283095952 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * 4.16438922228)
	tmp = 0.0
	if (x <= -2700.0)
		tmp = t_0;
	elseif (x <= 1.45e-56)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - 2.0) * 4.16438922228;
	tmp = 0.0;
	if (x <= -2700.0)
		tmp = t_0;
	elseif (x <= 1.45e-56)
		tmp = -0.0424927283095952 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]}, If[LessEqual[x, -2700.0], t$95$0, If[LessEqual[x, 1.45e-56], N[(-0.0424927283095952 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2700 or 1.44999999999999996e-56 < x

   1. Initial program 23.2%

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

   3. Applied rewrites 28.4%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 80.4%

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

   if -2700 < x < 1.44999999999999996e-56

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 69.2

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

   4. Applied rewrites 69.2%

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

Alternative 19: 76.4% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2700:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 86000000000:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2700.0)
   (* 4.16438922228 x)
   (if (<= x 86000000000.0) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2700.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 86000000000.0) {
		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 <= (-2700.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 86000000000.0d0) 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 <= -2700.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 86000000000.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2700.0:
		tmp = 4.16438922228 * x
	elif x <= 86000000000.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2700.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 86000000000.0)
		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 <= -2700.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 86000000000.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2700.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 86000000000.0], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2700 or 8.6e10 < x

   1. Initial program 15.3%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 88.2

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

   4. Applied rewrites 88.2%

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

   if -2700 < x < 8.6e10

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 65.2

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

   4. Applied rewrites 65.2%

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

Alternative 20: 34.8% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.4%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 34.8

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

4. Applied rewrites 34.8%

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

Developer Target 1: 98.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * 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 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * 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 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(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(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * 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[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(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] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2025095 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -332612872587000500000000000000000000000000000000000000000000000) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000) (if (< x 94299917145546730000000000000000000000000000000000000000) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (+ (* (+ (+ (* 263505074721/1000000000 x) (+ (* 216700011257/5000000000 (* x x)) (* x (* x x)))) 156699607947/500000000) x) 23533438303/500000000))) (- (+ (/ y (* x x)) (* 104109730557/25000000000 x)) 1101139242984811/10000000000000))))

  (/ (* (- 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)))