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

Percentage Accurate: 58.1% → 98.3%

Time: 7.9s

Alternatives: 18

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.1% 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: 98.3% accurate, 0.5× speedup

Math

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

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))
      INFINITY)
   (*
    (- 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)))
   (* 4.16438922228 x)))

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)) <= ((double) INFINITY)) {
		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 = 4.16438922228 * x;
	}
	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)) <= Inf)
		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(4.16438922228 * x);
	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], Infinity], 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[(4.16438922228 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

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

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 45.2

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

   9. Applied rewrites 45.2%

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

Alternative 2: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -2.12 \cdot 10^{+24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228))))
   (if (<= x -2.12e+24)
     t_0
     (if (<= x 2.7e+15)
       (*
        (- x 2.0)
        (/
         (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
         (fma
          (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	double tmp;
	if (x <= -2.12e+24) {
		tmp = t_0;
	} else if (x <= 2.7e+15) {
		tmp = (x - 2.0) * (fma(fma(fma(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 = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228))
	tmp = 0.0
	if (x <= -2.12e+24)
		tmp = t_0;
	elseif (x <= 2.7e+15)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(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 = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.12e+24], t$95$0, If[LessEqual[x, 2.7e+15], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(78.6994924154 * 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], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1200000000000001e24 or 2.7e15 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 48.3%

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

   if -2.1200000000000001e24 < x < 2.7e15

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

Alternative 3: 96.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 23500000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228))))
   (if (<= x -3.5e+23)
     t_0
     (if (<= x 23500000000000.0)
       (/
        (* (- x 2.0) (fma (fma 137.519416416 x y) x z))
        (+
         (*
          (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
          x)
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	double tmp;
	if (x <= -3.5e+23) {
		tmp = t_0;
	} else if (x <= 23500000000000.0) {
		tmp = ((x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228))
	tmp = 0.0
	if (x <= -3.5e+23)
		tmp = t_0;
	elseif (x <= 23500000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+23], t$95$0, If[LessEqual[x, 23500000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000002e23 or 2.35e13 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 48.3%

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

   if -3.5000000000000002e23 < x < 2.35e13

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\left(x - 2\right) \cdot \color{blue}{\left(z + x \cdot \left(y + \frac{4297481763}{31250000} \cdot x\right)\right)}}{\left(\left(\left(x + \frac{216700011257}{5000000000}\right) \cdot x + \frac{263505074721}{1000000000}\right) \cdot x + \frac{156699607947}{500000000}\right) \cdot x + \frac{23533438303}{500000000}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 53.6

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

   4. Applied rewrites 53.6%

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

Alternative 4: 95.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -2.12 \cdot 10^{+24}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228))))
   (if (<= x -2.12e+24)
     t_0
     (if (<= x 2.7e+15)
       (*
        (- x 2.0)
        (/
         (fma y x z)
         (fma
          (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
          x
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	double tmp;
	if (x <= -2.12e+24) {
		tmp = t_0;
	} else if (x <= 2.7e+15) {
		tmp = (x - 2.0) * (fma(y, x, z) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228))
	tmp = 0.0
	if (x <= -2.12e+24)
		tmp = t_0;
	elseif (x <= 2.7e+15)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(y, x, z) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.12e+24], t$95$0, If[LessEqual[x, 2.7e+15], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * 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], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1200000000000001e24 or 2.7e15 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 48.3%

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

   if -2.1200000000000001e24 < x < 2.7e15

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 52.6%

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

Alternative 5: 94.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 12200000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228))))
   (if (<= x -3.5e+23)
     t_0
     (if (<= x 12200000000000.0)
       (/
        (* (- x 2.0) (fma y x z))
        (fma
         (fma (fma (+ 43.3400022514 x) x 263.505074721) x 313.399215894)
         x
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	double tmp;
	if (x <= -3.5e+23) {
		tmp = t_0;
	} else if (x <= 12200000000000.0) {
		tmp = ((x - 2.0) * fma(y, x, z)) / fma(fma(fma((43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228))
	tmp = 0.0
	if (x <= -3.5e+23)
		tmp = t_0;
	elseif (x <= 12200000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(y, x, z)) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+23], t$95$0, If[LessEqual[x, 12200000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000002e23 or 1.22e13 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 48.3%

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

   if -3.5000000000000002e23 < x < 1.22e13

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 52.6%

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

   8. Applied rewrites 51.3%

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

Alternative 6: 94.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 147000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228))))
   (if (<= x -36.0)
     t_0
     (if (<= x 147000.0)
       (/
        (* (- x 2.0) (+ (* (fma (fma 78.6994924154 x 137.519416416) x y) x) z))
        (fma 313.399215894 x 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 147000.0) {
		tmp = ((x - 2.0) * ((fma(fma(78.6994924154, x, 137.519416416), x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-y) + 124074.40615218398) / x)) + 3451.550173699799) / x)) + 101.7851458539211) / x)) + 4.16438922228))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 147000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(fma(78.6994924154, x, 137.519416416), x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[((-N[(N[((-N[(N[((-N[(N[((-y) + 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]) + 3451.550173699799), $MachinePrecision] / x), $MachinePrecision]) + 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]) + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 147000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 147000 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 48.3%

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

   if -36 < x < 147000

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 50.5

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 51.8

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

   7. Applied rewrites 51.8%

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

Alternative 7: 92.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+28}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+16}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6e+28)
   (* 4.16438922228 x)
   (if (<= x 1.8e+16)
     (* (- x 2.0) (/ (fma y x z) (fma (* (* x x) x) x 47.066876606)))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e+28) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.8e+16) {
		tmp = (x - 2.0) * (fma(y, x, z) / fma(((x * x) * x), x, 47.066876606));
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6e+28)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.8e+16)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(y, x, z) / fma(Float64(Float64(x * x) * x), x, 47.066876606)));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6e+28], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.8e+16], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x + z), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0000000000000002e28

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 45.2

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

   9. Applied rewrites 45.2%

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

   if -6.0000000000000002e28 < x < 1.8e16

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 52.6%

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

   7. Taylor expanded in x around inf

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

      1. unpow3 N/A

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

      2. pow2 N/A

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

      3. lower-*.f64 N/A

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

      4. pow2 N/A

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

      5. lift-*.f64 51.0

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

   9. Applied rewrites 51.0%

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

   if 1.8e16 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

Alternative 8: 91.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 138000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -36.0)
     t_0
     (if (<= x 138000000000.0)
       (/
        (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z))
        (fma 313.399215894 x 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 138000000000.0) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 138000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 138000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 1.38e11 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

   if -36 < x < 1.38e11

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 50.5

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 50.6

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

   7. Applied rewrites 50.6%

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

Alternative 9: 90.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+17}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 138000000000:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e+17)
   (* 4.16438922228 x)
   (if (<= x 138000000000.0)
     (*
      (- x 2.0)
      (/ (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+17) {
		tmp = 4.16438922228 * x;
	} else if (x <= 138000000000.0) {
		tmp = (x - 2.0) * (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e+17)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 138000000000.0)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) / 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e+17], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 138000000000.0], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e17

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 45.2

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

   9. Applied rewrites 45.2%

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

   if -4.2e17 < x < 1.38e11

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative 50.2

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

      2. *-commutative 50.2

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

      3. +-commutative 50.2

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

      4. *-commutative 50.2

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

      5. *-commutative 50.2

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

   9. Applied rewrites 50.2%

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

   if 1.38e11 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

Alternative 10: 90.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 138000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -36.0)
     t_0
     (if (<= x 138000000000.0)
       (/ (* (- x 2.0) (+ (* y x) z)) (fma 313.399215894 x 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 138000000000.0) {
		tmp = ((x - 2.0) * ((y * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 138000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(y * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 138000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 1.38e11 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

   if -36 < x < 1.38e11

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 50.5

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

   4. Applied rewrites 50.5%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 48.3

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

   7. Applied rewrites 48.3%

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

Alternative 11: 89.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+17}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 138000000000:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(y, x, z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e+17)
   (* 4.16438922228 x)
   (if (<= x 138000000000.0)
     (* (- x 2.0) (/ (fma y x z) 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+17) {
		tmp = 4.16438922228 * x;
	} else if (x <= 138000000000.0) {
		tmp = (x - 2.0) * (fma(y, x, z) / 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e+17)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 138000000000.0)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(y, x, z) / 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e+17], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 138000000000.0], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x + z), $MachinePrecision] / 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e17

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 45.2

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

   9. Applied rewrites 45.2%

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

   if -4.2e17 < x < 1.38e11

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 52.6%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative 48.2

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

      2. *-commutative 48.2

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

      3. +-commutative 48.2

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

      4. *-commutative 48.2

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

      5. *-commutative 48.2

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

   9. Applied rewrites 48.2%

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

   if 1.38e11 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

Alternative 12: 76.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -0.1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;\left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -0.1)
     t_0
     (if (<= x 0.92)
       (*
        (-
         (* (fma -1.787568985856513 x 0.3041881842569256) x)
         0.0424927283095952)
        z)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -0.1) {
		tmp = t_0;
	} else if (x <= 0.92) {
		tmp = ((fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -0.1)
		tmp = t_0;
	elseif (x <= 0.92)
		tmp = Float64(Float64(Float64(fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952) * z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -0.1], t$95$0, If[LessEqual[x, 0.92], N[(N[(N[(N[(-1.787568985856513 * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.10000000000000001 or 0.92000000000000004 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

   if -0.10000000000000001 < x < 0.92000000000000004

   1. Initial program 58.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

   4. Applied rewrites 37.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(x \cdot \left(\frac{168466327098500000000}{553822718361107519809} + \frac{-23298017199368982832548000000000}{13033352773350869092174451844127} \cdot x\right) - \frac{1000000000}{23533438303}\right) \cdot z \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 35.1

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

   7. Applied rewrites 35.1%

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

Alternative 13: 76.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -0.082:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 138000000000:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 0.3041881842569256, x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -0.082)
     t_0
     (if (<= x 138000000000.0)
       (fma (* z 0.3041881842569256) x (* -0.0424927283095952 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -0.082) {
		tmp = t_0;
	} else if (x <= 138000000000.0) {
		tmp = fma((z * 0.3041881842569256), x, (-0.0424927283095952 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -0.082)
		tmp = t_0;
	elseif (x <= 138000000000.0)
		tmp = fma(Float64(z * 0.3041881842569256), x, Float64(-0.0424927283095952 * z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -0.082], t$95$0, If[LessEqual[x, 138000000000.0], N[(N[(z * 0.3041881842569256), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0820000000000000034 or 1.38e11 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

   if -0.0820000000000000034 < x < 1.38e11

   1. Initial program 58.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

   4. Applied rewrites 37.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. metadata-eval N/A

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

      6. lower-*.f64 N/A

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

      7. lift-*.f64 35.0

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

   7. Applied rewrites 35.0%

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

Alternative 14: 76.7% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -0.082:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 138000000000:\\ \;\;\;\;\left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -0.082)
     t_0
     (if (<= x 138000000000.0)
       (* (- (* 0.3041881842569256 x) 0.0424927283095952) z)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -0.082) {
		tmp = t_0;
	} else if (x <= 138000000000.0) {
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    if (x <= (-0.082d0)) then
        tmp = t_0
    else if (x <= 138000000000.0d0) then
        tmp = ((0.3041881842569256d0 * x) - 0.0424927283095952d0) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -0.082) {
		tmp = t_0;
	} else if (x <= 138000000000.0) {
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 - (110.1139242984811 / x)) * x
	tmp = 0
	if x <= -0.082:
		tmp = t_0
	elif x <= 138000000000.0:
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -0.082)
		tmp = t_0;
	elseif (x <= 138000000000.0)
		tmp = Float64(Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952) * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	tmp = 0.0;
	if (x <= -0.082)
		tmp = t_0;
	elseif (x <= 138000000000.0)
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -0.082], t$95$0, If[LessEqual[x, 138000000000.0], N[(N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0820000000000000034 or 1.38e11 < x

   1. Initial program 58.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 45.5

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

   4. Applied rewrites 45.5%

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

   if -0.0820000000000000034 < x < 1.38e11

   1. Initial program 58.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

   4. Applied rewrites 37.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 35.0

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

   7. Applied rewrites 35.0%

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

Alternative 15: 76.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.08:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 138000000000:\\ \;\;\;\;\left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.08)
   (* (- x 2.0) 4.16438922228)
   (if (<= x 138000000000.0)
     (* (- (* 0.3041881842569256 x) 0.0424927283095952) z)
     (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.08) {
		tmp = (x - 2.0) * 4.16438922228;
	} else if (x <= 138000000000.0) {
		tmp = ((0.3041881842569256 * x) - 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 <= (-0.08d0)) then
        tmp = (x - 2.0d0) * 4.16438922228d0
    else if (x <= 138000000000.0d0) then
        tmp = ((0.3041881842569256d0 * x) - 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 <= -0.08) {
		tmp = (x - 2.0) * 4.16438922228;
	} else if (x <= 138000000000.0) {
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.08:
		tmp = (x - 2.0) * 4.16438922228
	elif x <= 138000000000.0:
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.08)
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	elseif (x <= 138000000000.0)
		tmp = Float64(Float64(Float64(0.3041881842569256 * x) - 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 <= -0.08)
		tmp = (x - 2.0) * 4.16438922228;
	elseif (x <= 138000000000.0)
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.08], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision], If[LessEqual[x, 138000000000.0], N[(N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0800000000000000017

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 45.3%

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

   if -0.0800000000000000017 < x < 1.38e11

   1. Initial program 58.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

   4. Applied rewrites 37.0%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 35.0

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

   7. Applied rewrites 35.0%

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

   if 1.38e11 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 45.2

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

   9. Applied rewrites 45.2%

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

Alternative 16: 76.3% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+17}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e+17)
   (* 4.16438922228 x)
   (if (<= x 0.92) (* -0.0424927283095952 z) (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+17) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.92) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.2d+17)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 0.92d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = (x - 2.0d0) * 4.16438922228d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+17) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.92) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e+17:
		tmp = 4.16438922228 * x
	elif x <= 0.92:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e+17)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 0.92)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(Float64(x - 2.0) * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e+17)
		tmp = 4.16438922228 * x;
	elseif (x <= 0.92)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e+17], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 0.92], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e17

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 45.2

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

   9. Applied rewrites 45.2%

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

   if -4.2e17 < x < 0.92000000000000004

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 34.6

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

   4. Applied rewrites 34.6%

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

   if 0.92000000000000004 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 45.3%

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

Alternative 17: 76.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+17}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 150000:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e+17)
   (* 4.16438922228 x)
   (if (<= x 150000.0) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+17) {
		tmp = 4.16438922228 * x;
	} else if (x <= 150000.0) {
		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 <= (-4.2d+17)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 150000.0d0) 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 <= -4.2e+17) {
		tmp = 4.16438922228 * x;
	} else if (x <= 150000.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e+17:
		tmp = 4.16438922228 * x
	elif x <= 150000.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e+17)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 150000.0)
		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 <= -4.2e+17)
		tmp = 4.16438922228 * x;
	elseif (x <= 150000.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e+17], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 150000.0], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e17 or 1.5e5 < x

   1. Initial program 58.1%

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

   3. Applied rewrites 61.3%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 54.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 45.2

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

   9. Applied rewrites 45.2%

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

   if -4.2e17 < x < 1.5e5

   1. Initial program 58.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 34.6

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

   4. Applied rewrites 34.6%

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

Alternative 18: 45.2% accurate, 13.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 4.16438922228d0 * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.1%

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

3. Applied rewrites 61.3%

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

4. Taylor expanded in x around 0

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

6. Applied rewrites 54.7%

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

7. Taylor expanded in x around inf

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

   1. lower-*.f64 45.2

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

9. Applied rewrites 45.2%

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

Reproduce

herbie shell --seed 2025127 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))