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

Percentage Accurate: 58.0% → 98.7%

Time: 8.7s

Alternatives: 23

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \end{array} \end{array} \]

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))
      2e+305)
   (*
    (- 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) (- (/ (- 130977.50649958357 y) (* (* x x) x)) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+305) {
		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 * (((130977.50649958357 - y) / ((x * x) * x)) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)) <= 2e+305)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / fma(fma(fma(Float64(43.3400022514 + x), x, 263.505074721), x, 313.399215894), x, 47.066876606)));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / Float64(Float64(x * x) * x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], 2e+305], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(4.16438922228 * x + 78.6994924154), $MachinePrecision] * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x + z), $MachinePrecision] / N[(N[(N[(N[(43.3400022514 + x), $MachinePrecision] * x + 263.505074721), $MachinePrecision] * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $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))) < 1.9999999999999999e305

   1. Initial program 96.5%

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

   3. Applied rewrites 99.0%

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

   if 1.9999999999999999e305 < (/.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 0.3%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 98.2

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

   7. Applied rewrites 98.2%

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

Alternative 2: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right)\\ \mathbf{elif}\;x \leq 41:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(263.505074721, x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* (- x) (- (/ (- 130977.50649958357 y) (pow x 3.0)) 4.16438922228))
   (if (<= x 41.0)
     (/
      (*
       (- x 2.0)
       (+
        (*
         (+
          (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
          y)
         x)
        z))
      (fma (fma 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 <= -270000000000.0) {
		tmp = -x * (((130977.50649958357 - y) / pow(x, 3.0)) - 4.16438922228);
	} else if (x <= 41.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(fma(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 (x <= -270000000000.0)
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / (x ^ 3.0)) - 4.16438922228));
	elseif (x <= 41.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(fma(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[x, -270000000000.0], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 41.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(263.505074721 * x + 313.399215894), $MachinePrecision] * x + 47.066876606), $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 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 94.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 94.5

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

   7. Applied rewrites 94.5%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      4. lower-pow.f64 94.5

         \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   9. Applied rewrites 94.5%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   if -2.7e11 < x < 41

   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 96.7

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

   4. Applied rewrites 96.7%

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

   if 41 < 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

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around -inf

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

   9. Applied rewrites 93.6%

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

Alternative 3: 95.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right)\\ \mathbf{elif}\;x \leq 41:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.35)
   (* (- x) (- (/ (- 130977.50649958357 y) (pow x 3.0)) 4.16438922228))
   (if (<= x 41.0)
     (/
      (*
       (- x 2.0)
       (+
        (*
         (+
          (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
          y)
         x)
        z))
      (fma 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 <= -1.35) {
		tmp = -x * (((130977.50649958357 - y) / pow(x, 3.0)) - 4.16438922228);
	} else if (x <= 41.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(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 (x <= -1.35)
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / (x ^ 3.0)) - 4.16438922228));
	elseif (x <= 41.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(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[x, -1.35], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 41.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $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 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 18.4%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 91.6

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

   7. Applied rewrites 91.6%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      4. lower-pow.f64 91.6

         \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   9. Applied rewrites 91.6%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   if -1.3500000000000001 < x < 41

   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

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

      1. +-commutative N/A

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

      2. lower-fma.f64 98.0

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

   4. Applied rewrites 98.0%

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

   if 41 < 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

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around -inf

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

   9. Applied rewrites 93.6%

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

Alternative 4: 94.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -920000000000:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right)\\ \mathbf{elif}\;x \leq 17000000000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(y, x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -920000000000.0)
   (* (- x) (- (/ (- 130977.50649958357 y) (pow x 3.0)) 4.16438922228))
   (if (<= x 17000000000.0)
     (/
      (* (- x 2.0) (fma y x z))
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (* (- x) (- (/ (- 130977.50649958357 y) (* (* x x) x)) 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -920000000000.0) {
		tmp = -x * (((130977.50649958357 - y) / pow(x, 3.0)) - 4.16438922228);
	} else if (x <= 17000000000.0) {
		tmp = ((x - 2.0) * fma(y, x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = -x * (((130977.50649958357 - y) / ((x * x) * x)) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -920000000000.0)
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / (x ^ 3.0)) - 4.16438922228));
	elseif (x <= 17000000000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(y, x, z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / Float64(Float64(x * x) * x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -920000000000.0], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 17000000000.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(y * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.2e11

   1. Initial program 14.9%

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

   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 94.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 94.6

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

   7. Applied rewrites 94.6%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      4. lower-pow.f64 94.6

         \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   9. Applied rewrites 94.6%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   if -9.2e11 < x < 1.7e10

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 93.3

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

   4. Applied rewrites 93.3%

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

   if 1.7e10 < x

   1. Initial program 13.6%

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

   2. Taylor expanded in x around -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 95.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 95.1

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

   7. Applied rewrites 95.1%

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

Alternative 5: 94.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right)\\ \mathbf{elif}\;x \leq 24.5:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(-\frac{\left(-\frac{\left(-\frac{\left(-y\right) + 124074.40615218398}{x}\right) + 3451.550173699799}{x}\right) + 101.7851458539211}{x}\right) + 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* (- x) (- (/ (- 130977.50649958357 y) (pow x 3.0)) 4.16438922228))
   (if (<= x 24.5)
     (/
      (fma (+ (fma (- y 275.038832832) x (* -2.0 y)) z) x (* -2.0 z))
      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 <= -270000000000.0) {
		tmp = -x * (((130977.50649958357 - y) / pow(x, 3.0)) - 4.16438922228);
	} else if (x <= 24.5) {
		tmp = fma((fma((y - 275.038832832), x, (-2.0 * y)) + z), x, (-2.0 * z)) / 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 (x <= -270000000000.0)
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / (x ^ 3.0)) - 4.16438922228));
	elseif (x <= 24.5)
		tmp = Float64(fma(Float64(fma(Float64(y - 275.038832832), x, Float64(-2.0 * y)) + z), x, Float64(-2.0 * z)) / 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[x, -270000000000.0], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 24.5], N[(N[(N[(N[(N[(y - 275.038832832), $MachinePrecision] * x + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $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 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 94.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 94.5

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

   7. Applied rewrites 94.5%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      4. lower-pow.f64 94.5

         \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   9. Applied rewrites 94.5%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   if -2.7e11 < x < 24.5

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 89.9%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{x \cdot \left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) + \color{blue}{-2 \cdot z}}{\frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) \cdot x + \color{blue}{-2} \cdot z}{\frac{23533438303}{500000000}} \]

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 94.6

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

   10. Applied rewrites 94.6%

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

   if 24.5 < x

   1. Initial program 15.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around -inf

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

   9. Applied rewrites 93.6%

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

Alternative 6: 94.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right)\\ \mathbf{elif}\;x \leq 32:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* (- x) (- (/ (- 130977.50649958357 y) (pow x 3.0)) 4.16438922228))
   (if (<= x 32.0)
     (/
      (fma (+ (fma (- y 275.038832832) x (* -2.0 y)) z) x (* -2.0 z))
      47.066876606)
     (* (- x) (- (/ (- 130977.50649958357 y) (* (* x x) x)) 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = -x * (((130977.50649958357 - y) / pow(x, 3.0)) - 4.16438922228);
	} else if (x <= 32.0) {
		tmp = fma((fma((y - 275.038832832), x, (-2.0 * y)) + z), x, (-2.0 * z)) / 47.066876606;
	} else {
		tmp = -x * (((130977.50649958357 - y) / ((x * x) * x)) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / (x ^ 3.0)) - 4.16438922228));
	elseif (x <= 32.0)
		tmp = Float64(fma(Float64(fma(Float64(y - 275.038832832), x, Float64(-2.0 * y)) + z), x, Float64(-2.0 * z)) / 47.066876606);
	else
		tmp = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / Float64(Float64(x * x) * x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 32.0], N[(N[(N[(N[(N[(y - 275.038832832), $MachinePrecision] * x + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 94.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 94.5

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

   7. Applied rewrites 94.5%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      4. lower-pow.f64 94.5

         \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   9. Applied rewrites 94.5%

      \[\leadsto \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{{x}^{3}} - 4.16438922228\right) \]

   if -2.7e11 < x < 32

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 89.9%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{x \cdot \left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) + \color{blue}{-2 \cdot z}}{\frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) \cdot x + \color{blue}{-2} \cdot z}{\frac{23533438303}{500000000}} \]

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 94.6

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

   10. Applied rewrites 94.6%

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

   if 32 < x

   1. Initial program 15.8%

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

   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 93.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 93.2

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

   7. Applied rewrites 93.2%

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

Alternative 7: 94.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 32:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x)
          (- (/ (- 130977.50649958357 y) (* (* x x) x)) 4.16438922228))))
   (if (<= x -270000000000.0)
     t_0
     (if (<= x 32.0)
       (/
        (fma (+ (fma (- y 275.038832832) x (* -2.0 y)) z) x (* -2.0 z))
        47.066876606)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x * (((130977.50649958357 - y) / ((x * x) * x)) - 4.16438922228);
	double tmp;
	if (x <= -270000000000.0) {
		tmp = t_0;
	} else if (x <= 32.0) {
		tmp = fma((fma((y - 275.038832832), x, (-2.0 * y)) + z), x, (-2.0 * z)) / 47.066876606;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / Float64(Float64(x * x) * x)) - 4.16438922228))
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = t_0;
	elseif (x <= 32.0)
		tmp = Float64(fma(Float64(fma(Float64(y - 275.038832832), x, Float64(-2.0 * y)) + z), x, Float64(-2.0 * z)) / 47.066876606);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -270000000000.0], t$95$0, If[LessEqual[x, 32.0], N[(N[(N[(N[(N[(y - 275.038832832), $MachinePrecision] * x + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e11 or 32 < x

   1. Initial program 15.4%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 93.9

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

   7. Applied rewrites 93.9%

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

   if -2.7e11 < x < 32

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 89.9%

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

   8. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{x \cdot \left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) + \color{blue}{-2 \cdot z}}{\frac{23533438303}{500000000}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\left(z + \left(-2 \cdot y + x \cdot \left(y - \frac{4297481763}{15625000}\right)\right)\right) \cdot x + \color{blue}{-2} \cdot z}{\frac{23533438303}{500000000}} \]

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 94.6

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

   10. Applied rewrites 94.6%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y - 275.038832832, x, -2 \cdot y\right) + z, x, -2 \cdot z\right)}}{47.066876606} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 92.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 11.5:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), x, -2 \cdot z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x)
          (- (/ (- 130977.50649958357 y) (* (* x x) x)) 4.16438922228))))
   (if (<= x -1.35)
     t_0
     (if (<= x 11.5)
       (/ (fma (fma -2.0 y z) x (* -2.0 z)) (fma 313.399215894 x 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x * (((130977.50649958357 - y) / ((x * x) * x)) - 4.16438922228);
	double tmp;
	if (x <= -1.35) {
		tmp = t_0;
	} else if (x <= 11.5) {
		tmp = fma(fma(-2.0, y, z), x, (-2.0 * z)) / 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(130977.50649958357 - y) / Float64(Float64(x * x) * x)) - 4.16438922228))
	tmp = 0.0
	if (x <= -1.35)
		tmp = t_0;
	elseif (x <= 11.5)
		tmp = Float64(fma(fma(-2.0, y, z), x, Float64(-2.0 * z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35], t$95$0, If[LessEqual[x, 11.5], N[(N[(N[(-2.0 * y + z), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001 or 11.5 < x

   1. Initial program 17.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 92.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 92.4

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

   7. Applied rewrites 92.4%

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

   if -1.3500000000000001 < x < 11.5

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 92.9

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

   4. Applied rewrites 92.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.4

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

   7. Applied rewrites 92.4%

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

Alternative 9: 92.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00365:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x)
          (- (/ (- 130977.50649958357 y) (* (* x x) x)) 4.16438922228))))
   (if (<= x -270000000000.0)
     t_0
     (if (<= x 0.00365)
       (fma
        (fma (fma -2.0 y z) 0.0212463641547976 (* 0.28294182010212804 z))
        x
        (* -0.0424927283095952 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x * (((130977.50649958357 - y) / ((x * x) * x)) - 4.16438922228);
	double tmp;
	if (x <= -270000000000.0) {
		tmp = t_0;
	} else if (x <= 0.00365) {
		tmp = fma(fma(fma(-2.0, y, z), 0.0212463641547976, (0.28294182010212804 * z)), x, (-0.0424927283095952 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / Float64(Float64(x * x) * x)) - 4.16438922228))
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = t_0;
	elseif (x <= 0.00365)
		tmp = fma(fma(fma(-2.0, y, z), 0.0212463641547976, Float64(0.28294182010212804 * z)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -270000000000.0], t$95$0, If[LessEqual[x, 0.00365], N[(N[(N[(-2.0 * y + z), $MachinePrecision] * 0.0212463641547976 + N[(0.28294182010212804 * z), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e11 or 0.00365000000000000003 < x

   1. Initial program 15.9%

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

   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 93.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 93.3

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

   7. Applied rewrites 93.3%

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

   if -2.7e11 < x < 0.00365000000000000003

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   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 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 10: 91.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-x\right) \cdot \left(\frac{130977.50649958357 - y}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 11.5:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), x, -2 \cdot z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          (- x)
          (- (/ (- 130977.50649958357 y) (* (* x x) x)) 4.16438922228))))
   (if (<= x -270000000000.0)
     t_0
     (if (<= x 11.5) (/ (fma (fma -2.0 y z) x (* -2.0 z)) 47.066876606) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x * (((130977.50649958357 - y) / ((x * x) * x)) - 4.16438922228);
	double tmp;
	if (x <= -270000000000.0) {
		tmp = t_0;
	} else if (x <= 11.5) {
		tmp = fma(fma(-2.0, y, z), x, (-2.0 * z)) / 47.066876606;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) * Float64(Float64(Float64(130977.50649958357 - y) / Float64(Float64(x * x) * x)) - 4.16438922228))
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = t_0;
	elseif (x <= 11.5)
		tmp = Float64(fma(fma(-2.0, y, z), x, Float64(-2.0 * z)) / 47.066876606);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) * N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -270000000000.0], t$95$0, If[LessEqual[x, 11.5], N[(N[(N[(-2.0 * y + z), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e11 or 11.5 < x

   1. Initial program 15.5%

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

   2. Taylor expanded in x around -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 94.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 93.8

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

   7. Applied rewrites 93.8%

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

   if -2.7e11 < x < 11.5

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 90.0%

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

Alternative 11: 88.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 32:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), x, -2 \cdot z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x 32.0)
     (/ (fma (fma -2.0 y z) x (* -2.0 z)) 47.066876606)
     (* (- x) (- (/ 130977.50649958357 (* (* x x) x)) 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 32.0) {
		tmp = fma(fma(-2.0, y, z), x, (-2.0 * z)) / 47.066876606;
	} else {
		tmp = -x * ((130977.50649958357 / ((x * x) * x)) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 32.0)
		tmp = Float64(fma(fma(-2.0, y, z), x, Float64(-2.0 * z)) / 47.066876606);
	else
		tmp = Float64(Float64(-x) * Float64(Float64(130977.50649958357 / Float64(Float64(x * x) * x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 32.0], N[(N[(N[(-2.0 * y + z), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], N[((-x) * N[(N[(130977.50649958357 / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < 32

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 91.9

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

   4. Applied rewrites 91.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 89.9%

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

   if 32 < x

   1. Initial program 15.8%

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

   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 93.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 93.2

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

   7. Applied rewrites 93.2%

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

   8. Taylor expanded in y around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000}}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 86.0%

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

Alternative 12: 88.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2 \cdot y, x, -2 \cdot z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{130977.50649958357}{\left(x \cdot x\right) \cdot x} - 4.16438922228\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x 2.0)
     (/ (fma (* -2.0 y) x (* -2.0 z)) 47.066876606)
     (* (- x) (- (/ 130977.50649958357 (* (* x x) x)) 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = fma((-2.0 * y), x, (-2.0 * z)) / 47.066876606;
	} else {
		tmp = -x * ((130977.50649958357 / ((x * x) * x)) - 4.16438922228);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		tmp = Float64(fma(Float64(-2.0 * y), x, Float64(-2.0 * z)) / 47.066876606);
	else
		tmp = Float64(Float64(-x) * Float64(Float64(130977.50649958357 / Float64(Float64(x * x) * x)) - 4.16438922228));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(N[(-2.0 * y), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], N[((-x) * N[(N[(130977.50649958357 / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - 4.16438922228), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < 2

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 92.0

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

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 90.1%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 90.1

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

   10. Applied rewrites 90.1%

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

   if 2 < x

   1. Initial program 16.1%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 93.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{{x}^{3}} - \frac{104109730557}{25000000000}\right) \]

      3. pow3 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      4. lift-*.f64 N/A

         \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000} - y}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]

      5. lift-*.f64 92.9

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

   7. Applied rewrites 92.9%

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

   8. Taylor expanded in y around 0

      \[\leadsto \left(-x\right) \cdot \left(\frac{\frac{409304707811198655637810418659684985388407301}{3125000000000000000000000000000000000000}}{\left(x \cdot x\right) \cdot x} - \frac{104109730557}{25000000000}\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 85.7%

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

Alternative 13: 88.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2 \cdot y, x, -2 \cdot z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x 2.0)
     (/ (fma (* -2.0 y) x (* -2.0 z)) 47.066876606)
     (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = fma((-2.0 * y), x, (-2.0 * z)) / 47.066876606;
	} else {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		tmp = Float64(fma(Float64(-2.0 * y), x, Float64(-2.0 * z)) / 47.066876606);
	else
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(N[(-2.0 * y), $MachinePrecision] * x + N[(-2.0 * z), $MachinePrecision]), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < 2

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 92.0

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

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 90.1%

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

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 90.1

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

   10. Applied rewrites 90.1%

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

   if 2 < x

   1. Initial program 16.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 85.9

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

   9. Applied rewrites 85.9%

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

Alternative 14: 76.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(y \cdot \left(x - 2\right)\right) \cdot x}{47.066876606}\\ \mathbf{elif}\;x \leq 11.5:\\ \;\;\;\;\frac{-2 \cdot z}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x -8.5e-123)
     (/ (* (* y (- x 2.0)) x) 47.066876606)
     (if (<= x 11.5)
       (/ (* -2.0 z) (fma 313.399215894 x 47.066876606))
       (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8.5e-123) {
		tmp = ((y * (x - 2.0)) * x) / 47.066876606;
	} else if (x <= 11.5) {
		tmp = (-2.0 * z) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -8.5e-123)
		tmp = Float64(Float64(Float64(y * Float64(x - 2.0)) * x) / 47.066876606);
	elseif (x <= 11.5)
		tmp = Float64(Float64(-2.0 * z) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -8.5e-123], N[(N[(N[(y * N[(x - 2.0), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / 47.066876606), $MachinePrecision], If[LessEqual[x, 11.5], N[(N[(-2.0 * z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < -8.4999999999999995e-123

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 80.7

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 32.9

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

   10. Applied rewrites 32.9%

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

   if -8.4999999999999995e-123 < x < 11.5

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{-2 \cdot z}{\frac{156699607947}{500000000} \cdot x + \color{blue}{\frac{23533438303}{500000000}}} \]

      2. lower-fma.f64 70.6

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

   7. Applied rewrites 70.6%

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

   if 11.5 < x

   1. Initial program 15.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 86.1

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

   9. Applied rewrites 86.1%

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

Alternative 15: 76.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot -2}{47.066876606}\\ \mathbf{elif}\;x \leq 11.5:\\ \;\;\;\;\frac{-2 \cdot z}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x -8.5e-123)
     (/ (* (* y x) -2.0) 47.066876606)
     (if (<= x 11.5)
       (/ (* -2.0 z) (fma 313.399215894 x 47.066876606))
       (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8.5e-123) {
		tmp = ((y * x) * -2.0) / 47.066876606;
	} else if (x <= 11.5) {
		tmp = (-2.0 * z) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -8.5e-123)
		tmp = Float64(Float64(Float64(y * x) * -2.0) / 47.066876606);
	elseif (x <= 11.5)
		tmp = Float64(Float64(-2.0 * z) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -8.5e-123], N[(N[(N[(y * x), $MachinePrecision] * -2.0), $MachinePrecision] / 47.066876606), $MachinePrecision], If[LessEqual[x, 11.5], N[(N[(-2.0 * z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < -8.4999999999999995e-123

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 80.7

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 33.1

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

   10. Applied rewrites 33.1%

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

   if -8.4999999999999995e-123 < x < 11.5

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{-2 \cdot z}{\frac{156699607947}{500000000} \cdot x + \color{blue}{\frac{23533438303}{500000000}}} \]

      2. lower-fma.f64 70.6

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

   7. Applied rewrites 70.6%

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

   if 11.5 < x

   1. Initial program 15.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 86.1

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

   9. Applied rewrites 86.1%

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

Alternative 16: 75.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot -2}{47.066876606}\\ \mathbf{elif}\;x \leq 11.5:\\ \;\;\;\;\frac{-2 \cdot z}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x -8.5e-123)
     (/ (* (* y x) -2.0) 47.066876606)
     (if (<= x 11.5)
       (/ (* -2.0 z) (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 <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8.5e-123) {
		tmp = ((y * x) * -2.0) / 47.066876606;
	} else if (x <= 11.5) {
		tmp = (-2.0 * z) / 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 <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -8.5e-123)
		tmp = Float64(Float64(Float64(y * x) * -2.0) / 47.066876606);
	elseif (x <= 11.5)
		tmp = Float64(Float64(-2.0 * z) / 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, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -8.5e-123], N[(N[(N[(y * x), $MachinePrecision] * -2.0), $MachinePrecision] / 47.066876606), $MachinePrecision], If[LessEqual[x, 11.5], N[(N[(-2.0 * z), $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 4 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < -8.4999999999999995e-123

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 80.7

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 33.1

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

   10. Applied rewrites 33.1%

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

   if -8.4999999999999995e-123 < x < 11.5

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 70.6

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

   4. Applied rewrites 70.6%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{-2 \cdot z}{\frac{156699607947}{500000000} \cdot x + \color{blue}{\frac{23533438303}{500000000}}} \]

      2. lower-fma.f64 70.6

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

   7. Applied rewrites 70.6%

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

   if 11.5 < x

   1. Initial program 15.9%

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

   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 86.1

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

   4. Applied rewrites 86.1%

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

Alternative 17: 75.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(y \cdot x\right) \cdot -2}{47.066876606}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{z \cdot \left(x - 2\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x -8.5e-123)
     (/ (* (* y x) -2.0) 47.066876606)
     (if (<= x 4.5e+24)
       (/ (* 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 <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8.5e-123) {
		tmp = ((y * x) * -2.0) / 47.066876606;
	} else if (x <= 4.5e+24) {
		tmp = (z * (x - 2.0)) / 47.066876606;
	} 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 <= (-270000000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= (-8.5d-123)) then
        tmp = ((y * x) * (-2.0d0)) / 47.066876606d0
    else if (x <= 4.5d+24) then
        tmp = (z * (x - 2.0d0)) / 47.066876606d0
    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 <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= -8.5e-123) {
		tmp = ((y * x) * -2.0) / 47.066876606;
	} else if (x <= 4.5e+24) {
		tmp = (z * (x - 2.0)) / 47.066876606;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -270000000000.0:
		tmp = 4.16438922228 * x
	elif x <= -8.5e-123:
		tmp = ((y * x) * -2.0) / 47.066876606
	elif x <= 4.5e+24:
		tmp = (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 <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= -8.5e-123)
		tmp = Float64(Float64(Float64(y * x) * -2.0) / 47.066876606);
	elseif (x <= 4.5e+24)
		tmp = Float64(Float64(z * Float64(x - 2.0)) / 47.066876606);
	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 <= -270000000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= -8.5e-123)
		tmp = ((y * x) * -2.0) / 47.066876606;
	elseif (x <= 4.5e+24)
		tmp = (z * (x - 2.0)) / 47.066876606;
	else
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, -8.5e-123], N[(N[(N[(y * x), $MachinePrecision] * -2.0), $MachinePrecision] / 47.066876606), $MachinePrecision], If[LessEqual[x, 4.5e+24], N[(N[(z * 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 4 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < -8.4999999999999995e-123

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 80.7

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 74.3%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 33.1

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

   10. Applied rewrites 33.1%

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

   if -8.4999999999999995e-123 < x < 4.50000000000000019e24

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 92.1

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

   4. Applied rewrites 92.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 90.3%

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

   8. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lift--.f64 67.6

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

   10. Applied rewrites 67.6%

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

   if 4.50000000000000019e24 < x

   1. Initial program 9.7%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 91.1

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

   4. Applied rewrites 91.1%

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

Alternative 18: 75.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 11.5:\\ \;\;\;\;\left(\mathsf{fma}\left(-1.787568985856513, x, 0.3041881842569256\right) \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x 11.5)
     (*
      (-
       (* (fma -1.787568985856513 x 0.3041881842569256) x)
       0.0424927283095952)
      z)
     (* (- x 2.0) (- 4.16438922228 (/ 101.7851458539211 x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 11.5) {
		tmp = ((fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952) * z;
	} else {
		tmp = (x - 2.0) * (4.16438922228 - (101.7851458539211 / x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 11.5)
		tmp = Float64(Float64(Float64(fma(-1.787568985856513, x, 0.3041881842569256) * x) - 0.0424927283095952) * z);
	else
		tmp = Float64(Float64(x - 2.0) * Float64(4.16438922228 - Float64(101.7851458539211 / x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 11.5], N[(N[(N[(N[(-1.787568985856513 * x + 0.3041881842569256), $MachinePrecision] * x), $MachinePrecision] - 0.0424927283095952), $MachinePrecision] * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * N[(4.16438922228 - N[(101.7851458539211 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < 11.5

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

   4. Applied rewrites 66.2%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 65.1

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

   7. Applied rewrites 65.1%

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

   if 11.5 < x

   1. Initial program 15.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 86.1

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

   9. Applied rewrites 86.1%

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

Alternative 19: 74.8% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 0.00365:\\ \;\;\;\;\left(0.3041881842569256 \cdot x - 0.0424927283095952\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x 0.00365)
     (* (- (* 0.3041881842569256 x) 0.0424927283095952) z)
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.00365) {
		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 <= (-270000000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 0.00365d0) 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 <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.00365) {
		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 <= -270000000000.0:
		tmp = 4.16438922228 * x
	elif x <= 0.00365:
		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 <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 0.00365)
		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 <= -270000000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 0.00365)
		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, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 0.00365], 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 < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < 0.00365000000000000003

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. div-sub N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

   4. Applied rewrites 66.5%

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

   5. Taylor expanded in x around 0

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

      1. lower--.f64 N/A

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

      2. lower-*.f64 65.2

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

   7. Applied rewrites 65.2%

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

   if 0.00365000000000000003 < 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

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 19.9%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 85.0%

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

Alternative 20: 74.8% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{-2 \cdot z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x 1.7) (/ (* -2.0 z) 47.066876606) (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.7) {
		tmp = (-2.0 * z) / 47.066876606;
	} 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 <= (-270000000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 1.7d0) then
        tmp = ((-2.0d0) * z) / 47.066876606d0
    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 <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.7) {
		tmp = (-2.0 * z) / 47.066876606;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -270000000000.0:
		tmp = 4.16438922228 * x
	elif x <= 1.7:
		tmp = (-2.0 * z) / 47.066876606
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.7)
		tmp = Float64(Float64(-2.0 * z) / 47.066876606);
	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 <= -270000000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 1.7)
		tmp = (-2.0 * z) / 47.066876606;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(-2.0 * z), $MachinePrecision] / 47.066876606), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < 1.69999999999999996

   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

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

      1. lower-*.f64 64.9

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

   4. Applied rewrites 64.9%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 64.7%

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

   if 1.69999999999999996 < x

   1. Initial program 16.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 85.7%

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

Alternative 21: 74.8% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 4.16438922228 x)
   (if (<= x 1.7) (* -0.0424927283095952 z) (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.7) {
		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 <= (-270000000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 1.7d0) 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 <= -270000000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 1.7) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -270000000000.0:
		tmp = 4.16438922228 * x
	elif x <= 1.7:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -270000000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 1.7)
		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 <= -270000000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 1.7)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -270000000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 1.7], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e11

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.7e11 < x < 1.69999999999999996

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 64.5

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

   4. Applied rewrites 64.5%

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

   if 1.69999999999999996 < x

   1. Initial program 16.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot \frac{104109730557}{25000000000} + \frac{393497462077}{5000000000}\right) \cdot x + \frac{4297481763}{31250000}\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{{x}^{4}}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 N/A

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

      6. unpow2 N/A

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

      7. lower-*.f64 13.9

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

   4. Applied rewrites 13.9%

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

   6. Applied rewrites 20.0%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 85.7%

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

Alternative 22: 74.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -270000000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -270000000000.0)
   (* 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 <= -270000000000.0) {
		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 <= (-270000000000.0d0)) 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 <= -270000000000.0) {
		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 <= -270000000000.0:
		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 <= -270000000000.0)
		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 <= -270000000000.0)
		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, -270000000000.0], 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 < -2.7e11 or 2 < x

   1. Initial program 15.6%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 87.4

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

   4. Applied rewrites 87.4%

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

   if -2.7e11 < x < 2

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 64.5

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

   4. Applied rewrites 64.5%

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

Alternative 23: 34.1% 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 58.0%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 34.1

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

4. Applied rewrites 34.1%

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

Reproduce

herbie shell --seed 2025114 
(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)))