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

Percentage Accurate: 58.3% → 98.7%

Time: 9.9s

Alternatives: 20

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.3% 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: 98.7% accurate, 0.5× speedup

Math

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

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

C

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

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 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(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));
	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[(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]]

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 93.4%

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

   3. Applied rewrites 98.5%

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

   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 0.0%

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

   3. Applied rewrites 0.0%

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

   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 99.1%

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

Alternative 2: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot x\right) \cdot 4.16438922228, x, y\right), x, z\right)}{\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, x, 47.066876606\right)}\\ t_1 := \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 4000000000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (/
           (fma (fma (* (* x x) 4.16438922228) x y) x z)
           (fma (* (* x x) x) x 47.066876606))))
        (t_1
         (/
          (*
           (- 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))))
   (if (<= t_1 -1000000.0)
     t_0
     (if (<= t_1 4000000000000.0)
       (*
        (fma
         (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
         x
         z)
        (/ (- x 2.0) (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       (if (<= t_1 INFINITY)
         t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (fma(fma(((x * x) * 4.16438922228), x, y), x, z) / fma(((x * x) * x), x, 47.066876606));
	double t_1 = ((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 tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_0;
	} else if (t_1 <= 4000000000000.0) {
		tmp = fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * ((x - 2.0) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(fma(fma(Float64(Float64(x * x) * 4.16438922228), x, y), x, z) / fma(Float64(Float64(x * x) * x), x, 47.066876606)))
	t_1 = 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))
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_0;
	elseif (t_1 <= 4000000000000.0)
		tmp = Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) * Float64(Float64(x - 2.0) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	elseif (t_1 <= Inf)
		tmp = t_0;
	else
		tmp = 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));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(x * x), $MachinePrecision] * 4.16438922228), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -1000000.0], t$95$0, If[LessEqual[t$95$1, 4000000000000.0], N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], 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]]]]]]

Derivation

1. Split input into 3 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))) < -1e6 or 4e12 < (/.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 90.5%

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

   3. Applied rewrites 97.9%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      4. unpow3 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 93.5

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

   6. Applied rewrites 93.5%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. pow2 N/A

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

      4. lift-*.f64 93.5

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

   9. Applied rewrites 93.5%

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

   if -1e6 < (/.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))) < 4e12

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

   6. Applied rewrites 98.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

   8. Applied rewrites 97.7%

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

   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 90.5%

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

   3. Applied rewrites 97.9%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 25.0%

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

Alternative 3: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot x\right) \cdot 4.16438922228, x, y\right), x, z\right)}{\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, x, 47.066876606\right)}\\ t_1 := \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 4000000000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x 2.0)
          (/
           (fma (fma (* (* x x) 4.16438922228) x y) x z)
           (fma (* (* x x) x) x 47.066876606))))
        (t_1
         (/
          (*
           (- 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))))
   (if (<= t_1 -1000000.0)
     t_0
     (if (<= t_1 4000000000000.0)
       (*
        (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
        (/ (- x 2.0) (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
       (if (<= t_1 INFINITY)
         t_0
         (*
          (- x 2.0)
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799)
                x))
              101.7851458539211)
             x))
           4.16438922228)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x - 2.0) * (fma(fma(((x * x) * 4.16438922228), x, y), x, z) / fma(((x * x) * x), x, 47.066876606));
	double t_1 = ((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 tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_0;
	} else if (t_1 <= 4000000000000.0) {
		tmp = fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * ((x - 2.0) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - 2.0) * Float64(fma(fma(Float64(Float64(x * x) * 4.16438922228), x, y), x, z) / fma(Float64(Float64(x * x) * x), x, 47.066876606)))
	t_1 = 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))
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_0;
	elseif (t_1 <= 4000000000000.0)
		tmp = Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(Float64(x - 2.0) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	elseif (t_1 <= Inf)
		tmp = t_0;
	else
		tmp = 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));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(x * x), $MachinePrecision] * 4.16438922228), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -1000000.0], t$95$0, If[LessEqual[t$95$1, 4000000000000.0], N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], 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]]]]]]

Derivation

1. Split input into 3 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))) < -1e6 or 4e12 < (/.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 90.5%

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

   3. Applied rewrites 97.9%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      4. unpow3 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 93.5

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

   6. Applied rewrites 93.5%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. pow2 N/A

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

      4. lift-*.f64 93.5

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

   9. Applied rewrites 93.5%

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

   if -1e6 < (/.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))) < 4e12

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

   6. Applied rewrites 98.0%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 97.9%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift--.f64 N/A

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

       4. associate-/l* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. lift--.f64 97.6

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

   11. Applied rewrites 97.6%

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

   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 90.5%

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

   3. Applied rewrites 97.9%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 25.0%

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

Alternative 4: 96.4% accurate, 0.5× speedup

Math

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

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 (* (* x x) x) x 47.066876606)))
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))))

C

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

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 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(Float64(Float64(x * x) * x), x, 47.066876606)));
	else
		tmp = 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));
	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[(x * x), $MachinePrecision] * x), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

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 93.4%

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

   3. Applied rewrites 98.5%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      4. unpow3 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 94.8

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

   6. Applied rewrites 94.8%

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

   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 0.0%

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

   3. Applied rewrites 0.0%

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

   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 99.1%

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

Alternative 5: 96.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+75}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq -35:\\ \;\;\;\;x \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\left(x \cdot x\right) \cdot 4.16438922228, x, y\right), x, z\right)}{\mathsf{fma}\left(\left(x \cdot x\right) \cdot x, x, 47.066876606\right)}\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(\frac{130977.50649958357}{x} + \left(-\frac{y}{x}\right)\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+75)
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))
   (if (<= x -35.0)
     (*
      x
      (/
       (fma (fma (* (* x x) 4.16438922228) x y) x z)
       (fma (* (* x x) x) x 47.066876606)))
     (if (<= x 6800000.0)
       (/
        (* (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) (- x 2.0))
        (fma 313.399215894 x 47.066876606))
       (*
        (- x)
        (-
         (-
          (/
           (-
            (-
             (/
              (- (+ (/ 130977.50649958357 x) (- (/ y x))) 3655.1204654076414)
              x))
            110.1139242984811)
           x))
         4.16438922228))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+75) {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	} else if (x <= -35.0) {
		tmp = x * (fma(fma(((x * x) * 4.16438922228), x, y), x, z) / fma(((x * x) * x), x, 47.066876606));
	} else if (x <= 6800000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * (x - 2.0)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = -x * (-((-((((130977.50649958357 / x) + -(y / x)) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+75)
		tmp = 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));
	elseif (x <= -35.0)
		tmp = Float64(x * Float64(fma(fma(Float64(Float64(x * x) * 4.16438922228), x, y), x, z) / fma(Float64(Float64(x * x) * x), x, 47.066876606)));
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(130977.50649958357 / x) + Float64(-Float64(y / x))) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+75], 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, -35.0], N[(x * N[(N[(N[(N[(N[(x * x), $MachinePrecision] * 4.16438922228), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[(N[(N[(130977.50649958357 / x), $MachinePrecision] + (-N[(y / x), $MachinePrecision])), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.5999999999999997e75

   1. Initial program 0.0%

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

   3. Applied rewrites 0.1%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 99.1%

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

   if -4.5999999999999997e75 < x < -35

   1. Initial program 69.7%

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

   3. Applied rewrites 93.6%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{104109730557}{25000000000}, x, \frac{393497462077}{5000000000}\right), x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left({x}^{3}, x, \frac{23533438303}{500000000}\right)} \]

      4. unpow3 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 84.9

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

   6. Applied rewrites 84.9%

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

   7. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. pow2 N/A

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

      4. lift-*.f64 85.0

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

   9. Applied rewrites 85.0%

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

   10. Taylor expanded in x around inf

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

   12. Applied rewrites 85.0%

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

   if -35 < x < 6.8e6

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

   6. Applied rewrites 97.9%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 97.8%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 97.4%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 94.6%

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

Alternative 6: 95.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(\frac{130977.50649958357}{x} + \left(-\frac{y}{x}\right)\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))
   (if (<= x 6800000.0)
     (/
      (* (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) (- x 2.0))
      (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
     (*
      (- x)
      (-
       (-
        (/
         (-
          (-
           (/
            (- (+ (/ 130977.50649958357 x) (- (/ y x))) 3655.1204654076414)
            x))
          110.1139242984811)
         x))
       4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	} else if (x <= 6800000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * (x - 2.0)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606);
	} else {
		tmp = -x * (-((-((((130977.50649958357 / x) + -(y / x)) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = 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));
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(130977.50649958357 / x) + Float64(-Float64(y / x))) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], 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, 6800000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[(N[(N[(130977.50649958357 / x), $MachinePrecision] + (-N[(y / x), $MachinePrecision])), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   3. Applied rewrites 18.4%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 96.0%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

   6. Applied rewrites 95.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 95.6%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 94.6%

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

Alternative 7: 95.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \frac{x - 2}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(\frac{130977.50649958357}{x} + \left(-\frac{y}{x}\right)\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (*
    (- x 2.0)
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- y) 124074.40615218398) x)) 3451.550173699799) x))
        101.7851458539211)
       x))
     4.16438922228))
   (if (<= x 6800000.0)
     (*
      (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z)
      (/ (- x 2.0) (fma (fma 263.505074721 x 313.399215894) x 47.066876606)))
     (*
      (- x)
      (-
       (-
        (/
         (-
          (-
           (/
            (- (+ (/ 130977.50649958357 x) (- (/ y x))) 3655.1204654076414)
            x))
          110.1139242984811)
         x))
       4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = (x - 2.0) * (-((-((-((-y + 124074.40615218398) / x) + 3451.550173699799) / x) + 101.7851458539211) / x) + 4.16438922228);
	} else if (x <= 6800000.0) {
		tmp = fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * ((x - 2.0) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	} else {
		tmp = -x * (-((-((((130977.50649958357 / x) + -(y / x)) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = 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));
	elseif (x <= 6800000.0)
		tmp = Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(Float64(x - 2.0) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(130977.50649958357 / x) + Float64(-Float64(y / x))) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], 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, 6800000.0], N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(N[(x - 2.0), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) * N[((-N[(N[((-N[(N[(N[(N[(130977.50649958357 / x), $MachinePrecision] + (-N[(y / x), $MachinePrecision])), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   3. Applied rewrites 18.4%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 96.0%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

   6. Applied rewrites 95.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 95.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. lift--.f64 N/A

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

       4. associate-/l* N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. lift--.f64 95.4

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

   11. Applied rewrites 95.4%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 94.6%

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

Alternative 8: 95.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot \left(\left(-\frac{\left(-\frac{\left(\frac{130977.50649958357}{x} + \left(-\frac{y}{x}\right)\right) - 3655.1204654076414}{x}\right) - 110.1139242984811}{x}\right) - 4.16438922228\right)\\ \mathbf{if}\;x \leq -35:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x)
          (-
           (-
            (/
             (-
              (-
               (/
                (- (+ (/ 130977.50649958357 x) (- (/ y x))) 3655.1204654076414)
                x))
              110.1139242984811)
             x))
           4.16438922228))))
   (if (<= x -35.0)
     t_0
     (if (<= x 6800000.0)
       (/
        (* (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) (- x 2.0))
        (fma 313.399215894 x 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x * (-((-((((130977.50649958357 / x) + -(y / x)) - 3655.1204654076414) / x) - 110.1139242984811) / x) - 4.16438922228);
	double tmp;
	if (x <= -35.0) {
		tmp = t_0;
	} else if (x <= 6800000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * (x - 2.0)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(130977.50649958357 / x) + Float64(-Float64(y / x))) - 3655.1204654076414) / x)) - 110.1139242984811) / x)) - 4.16438922228))
	tmp = 0.0
	if (x <= -35.0)
		tmp = t_0;
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[((-N[(N[((-N[(N[(N[(N[(130977.50649958357 / x), $MachinePrecision] + (-N[(y / x), $MachinePrecision])), $MachinePrecision] - 3655.1204654076414), $MachinePrecision] / x), $MachinePrecision]) - 110.1139242984811), $MachinePrecision] / x), $MachinePrecision]) - 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -35.0], t$95$0, If[LessEqual[x, 6800000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -35 or 6.8e6 < x

   1. Initial program 16.8%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 93.9%

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

   if -35 < x < 6.8e6

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

   6. Applied rewrites 97.9%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 97.8%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 97.4%

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

Alternative 9: 95.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \mathbf{if}\;x \leq -35:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -35.0)
     t_0
     (if (<= x 6800000.0)
       (/
        (* (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) (- x 2.0))
        (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 <= -35.0) {
		tmp = t_0;
	} else if (x <= 6800000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * (x - 2.0)) / 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 <= -35.0)
		tmp = t_0;
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / 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, -35.0], t$95$0, If[LessEqual[x, 6800000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -35 or 6.8e6 < x

   1. Initial program 16.8%

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

   3. Applied rewrites 23.1%

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

   4. Taylor expanded in x around -inf

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

   6. Applied rewrites 93.9%

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

   if -35 < x < 6.8e6

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

   6. Applied rewrites 97.9%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 97.8%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 97.4%

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

Alternative 10: 92.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -35:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -35.0)
   (* 4.16438922228 x)
   (if (<= x 6800000.0)
     (/
      (* (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) (- x 2.0))
      (fma 313.399215894 x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -35.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * (x - 2.0)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -35.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -35.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 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 < -35

   1. Initial program 16.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 86.7

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

   4. Applied rewrites 86.7%

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

   if -35 < x < 6.8e6

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 97.9

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

   4. Applied rewrites 97.9%

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

   6. Applied rewrites 97.9%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 97.8%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 97.4%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   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 88.8

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

   4. Applied rewrites 88.8%

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

Alternative 11: 92.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right) \cdot \left(x - 2\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 6800000.0)
     (/
      (* (fma (fma 137.519416416 x y) x z) (- x 2.0))
      (fma (fma 263.505074721 x 313.399215894) x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = (fma(fma(137.519416416, x, y), x, z) * (x - 2.0)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(fma(fma(137.519416416, x, y), x, z) * Float64(x - 2.0)) / fma(fma(263.505074721, x, 313.399215894), x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 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 < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

   6. Applied rewrites 95.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 95.5%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   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 88.8

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

   4. Applied rewrites 88.8%

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

Alternative 12: 91.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right), x, z\right) \cdot \left(x - 2\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 6800000.0)
     (/
      (* (fma (fma (fma 78.6994924154 x 137.519416416) x y) x z) (- x 2.0))
      47.066876606)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = (fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * (x - 2.0)) / 47.066876606;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(fma(fma(fma(78.6994924154, x, 137.519416416), x, y), x, z) * Float64(x - 2.0)) / 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, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

   6. Applied rewrites 95.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 95.6%

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

   10. Taylor expanded in x around 0

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

   12. Applied rewrites 94.0%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   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 88.8

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

   4. Applied rewrites 88.8%

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

Alternative 13: 89.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 6800000.0)
     (fma
      (fma (fma -2.0 y z) 0.0212463641547976 (* 0.28294182010212804 z))
      x
      (* -0.0424927283095952 z))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = fma(fma(fma(-2.0, y, z), 0.0212463641547976, (0.28294182010212804 * z)), x, (-0.0424927283095952 * z));
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 6800000.0)
		tmp = fma(fma(fma(-2.0, y, z), 0.0212463641547976, Float64(0.28294182010212804 * z)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(-2.0 * y + z), $MachinePrecision] * 0.0212463641547976 + N[(0.28294182010212804 * z), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{-1000000000}{23533438303} \cdot z\right) \]

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

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z + -2 \cdot y\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z + -2 \cdot y, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-2 \cdot y + z, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      11. lower-*.f64 89.8

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right) \]

   4. Applied rewrites 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)} \]

   if 6.8e6 < x

   1. Initial program 16.9%

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

   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 88.8

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

   4. Applied rewrites 88.8%

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

Alternative 14: 89.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\mathsf{fma}\left(0.3041881842569256 \cdot x - 0.0424927283095952, z, \left(y \cdot x\right) \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 6800000.0)
     (fma
      (- (* 0.3041881842569256 x) 0.0424927283095952)
      z
      (* (* y x) -0.0424927283095952))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = fma(((0.3041881842569256 * x) - 0.0424927283095952), z, ((y * x) * -0.0424927283095952));
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 6800000.0)
		tmp = fma(Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952), z, Float64(Float64(y * x) * -0.0424927283095952));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z + N[(N[(y * x), $MachinePrecision] * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{-1000000000}{23533438303} \cdot z\right) \]

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

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z + -2 \cdot y\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z + -2 \cdot y, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-2 \cdot y + z, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      11. lower-*.f64 89.8

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right) \]

   4. Applied rewrites 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)} \]

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 89.9

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

   7. Applied rewrites 89.9%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   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 88.8

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

   4. Applied rewrites 88.8%

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

Alternative 15: 89.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(-0.0424927283095952 \cdot y, x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 1.8e-12)
     (fma (* -0.0424927283095952 y) x (* -0.0424927283095952 z))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.8e-12) {
		tmp = fma((-0.0424927283095952 * y), x, (-0.0424927283095952 * z));
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.8e-12)
		tmp = fma(Float64(-0.0424927283095952 * y), x, Float64(-0.0424927283095952 * z));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.8e-12], N[(N[(-0.0424927283095952 * y), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 1.8e-12

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{-1000000000}{23533438303} \cdot z\right) \]

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

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z + -2 \cdot y\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z + -2 \cdot y, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-2 \cdot y + z, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      11. lower-*.f64 91.5

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right) \]

   4. Applied rewrites 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)} \]

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 91.2

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

   7. Applied rewrites 91.2%

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

   if 1.8e-12 < x

   1. Initial program 21.2%

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

   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 84.5

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

   4. Applied rewrites 84.5%

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

Alternative 16: 76.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 6800000.0)
     (* (- (* 0.3041881842569256 x) 0.0424927283095952) z)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.55d+16)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 6800000.0d0) then
        tmp = ((0.3041881842569256d0 * x) - 0.0424927283095952d0) * z
    else
        tmp = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e+16:
		tmp = 4.16438922228 * x
	elif x <= 6800000.0:
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z
	else:
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(Float64(0.3041881842569256 * x) - 0.0424927283095952) * z);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.55e+16)
		tmp = 4.16438922228 * x;
	elseif (x <= 6800000.0)
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	else
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{-1000000000}{23533438303} \cdot z\right) \]

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

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z + -2 \cdot y\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z + -2 \cdot y, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-2 \cdot y + z, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      11. lower-*.f64 89.8

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right) \]

   4. Applied rewrites 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)} \]

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 65.0

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

   7. Applied rewrites 65.0%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   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 88.8

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

   4. Applied rewrites 88.8%

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

Alternative 17: 76.9% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 6800000:\\ \;\;\;\;\left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 6800000.0)
     (* (- (* 0.3041881842569256 x) 0.0424927283095952) z)
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = ((0.3041881842569256 * x) - 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 <= (-1.55d+16)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 6800000.0d0) then
        tmp = ((0.3041881842569256d0 * x) - 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 <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 6800000.0) {
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e+16:
		tmp = 4.16438922228 * x
	elif x <= 6800000.0:
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 6800000.0)
		tmp = Float64(Float64(Float64(0.3041881842569256 * x) - 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 <= -1.55e+16)
		tmp = 4.16438922228 * x;
	elseif (x <= 6800000.0)
		tmp = ((0.3041881842569256 * x) - 0.0424927283095952) * z;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 6800000.0], N[(N[(N[(0.3041881842569256 * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 6.8e6

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) + \color{blue}{\frac{-1000000000}{23533438303} \cdot z} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x + \color{blue}{\frac{-1000000000}{23533438303}} \cdot z \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z, \color{blue}{x}, \frac{-1000000000}{23533438303} \cdot z\right) \]

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

         \[\leadsto \mathsf{fma}\left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(z + -2 \cdot y\right) \cdot \frac{500000000}{23533438303} + \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z, x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z + -2 \cdot y, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-2 \cdot y + z, \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \left(\mathsf{neg}\left(\frac{-156699607947000000000}{553822718361107519809}\right)\right) \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), \frac{500000000}{23533438303}, \frac{156699607947000000000}{553822718361107519809} \cdot z\right), x, \frac{-1000000000}{23533438303} \cdot z\right) \]

      11. lower-*.f64 89.8

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right) \]

   4. Applied rewrites 89.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)} \]

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 65.0

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

   7. Applied rewrites 65.0%

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

   if 6.8e6 < x

   1. Initial program 16.9%

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

   3. Applied rewrites 23.8%

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

   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 88.6%

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

Alternative 18: 76.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 1.8e-12) (* -0.0424927283095952 z) (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.8e-12) {
		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 <= (-1.55d+16)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 1.8d-12) 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 <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.8e-12) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e+16:
		tmp = 4.16438922228 * x
	elif x <= 1.8e-12:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.8e-12)
		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 <= -1.55e+16)
		tmp = 4.16438922228 * x;
	elseif (x <= 1.8e-12)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.8e-12], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e16

   1. Initial program 12.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   if -1.55e16 < x < 1.8e-12

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 65.9

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

   4. Applied rewrites 65.9%

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

   if 1.8e-12 < x

   1. Initial program 21.2%

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

   3. Applied rewrites 27.7%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 84.3%

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

Alternative 19: 76.5% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e+16)
   (* 4.16438922228 x)
   (if (<= x 2.0) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.55d+16)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.0d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = 4.16438922228d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e+16) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.55e+16:
		tmp = 4.16438922228 * x
	elif x <= 2.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e+16)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.55e+16)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e+16], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55e16 or 2 < x

   1. Initial program 15.7%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 88.5

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

   4. Applied rewrites 88.5%

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

   if -1.55e16 < x < 2

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 65.2

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

   4. Applied rewrites 65.2%

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

Alternative 20: 34.6% accurate, 13.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.3%

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

2. Taylor expanded in x around 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%

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

Reproduce

herbie shell --seed 2025119 
(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)))