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

Percentage Accurate: 58.4% → 98.8%

Time: 5.9s

Alternatives: 17

Speedup: 4.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(72.2194108904232, {x}^{3}, 487433.97159584565\right)}{{\left(4.16438922228 \cdot x\right)}^{2} + \left(6193.6101064416025 - \left(4.16438922228 \cdot x\right) \cdot 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right)\\ \end{array} \end{array} \]

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+304)
   (*
    (- x 2.0)
    (/
     (fma
      (fma
       (fma
        (/
         (fma 72.2194108904232 (pow x 3.0) 487433.97159584565)
         (+
          (pow (* 4.16438922228 x) 2.0)
          (- 6193.6101064416025 (* (* 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 (fma (/ (- (/ y (* x x))) x) -1.0 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+304) {
		tmp = (x - 2.0) * (fma(fma(fma((fma(72.2194108904232, pow(x, 3.0), 487433.97159584565) / (pow((4.16438922228 * x), 2.0) + (6193.6101064416025 - ((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 * fma((-(y / (x * x)) / x), -1.0, 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+304)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(Float64(fma(72.2194108904232, (x ^ 3.0), 487433.97159584565) / Float64((Float64(4.16438922228 * x) ^ 2.0) + Float64(6193.6101064416025 - Float64(Float64(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(x * fma(Float64(Float64(-Float64(y / Float64(x * x))) / x), -1.0, 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+304], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(72.2194108904232 * N[Power[x, 3.0], $MachinePrecision] + 487433.97159584565), $MachinePrecision] / N[(N[Power[N[(4.16438922228 * x), $MachinePrecision], 2.0], $MachinePrecision] + N[(6193.6101064416025 - N[(N[(4.16438922228 * x), $MachinePrecision] * 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]) / x), $MachinePrecision] * -1.0 + 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))) < 1.9999999999999999e304

   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%

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

      1. lift-fma.f64 N/A

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

      2. flip3-+ N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{\left(\frac{104109730557}{25000000000} \cdot x\right)}^{3} + {\frac{393497462077}{5000000000}}^{3}}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{{\left(\frac{104109730557}{25000000000} \cdot x\right)}^{3} + {\frac{393497462077}{5000000000}}^{3}}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      4. unpow-prod-down N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{{\frac{104109730557}{25000000000}}^{3} \cdot {x}^{3}} + {\frac{393497462077}{5000000000}}^{3}}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\color{blue}{\mathsf{fma}\left({\frac{104109730557}{25000000000}}^{3}, {x}^{3}, {\frac{393497462077}{5000000000}}^{3}\right)}}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      6. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\color{blue}{\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}}, {x}^{3}, {\frac{393497462077}{5000000000}}^{3}\right)}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      7. lower-pow.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, \color{blue}{{x}^{3}}, {\frac{393497462077}{5000000000}}^{3}\right)}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      8. metadata-eval N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \color{blue}{\frac{60929246449480706651316240921050533}{125000000000000000000000000000}}\right)}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      9. lower-+.f64 N/A

         \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \frac{60929246449480706651316240921050533}{125000000000000000000000000000}\right)}{\color{blue}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \left(\frac{104109730557}{25000000000} \cdot x\right) + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      10. pow2 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \frac{60929246449480706651316240921050533}{125000000000000000000000000000}\right)}{\color{blue}{{\left(\frac{104109730557}{25000000000} \cdot x\right)}^{2}} + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      11. lower-pow.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \frac{60929246449480706651316240921050533}{125000000000000000000000000000}\right)}{\color{blue}{{\left(\frac{104109730557}{25000000000} \cdot x\right)}^{2}} + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      12. lower-*.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \frac{60929246449480706651316240921050533}{125000000000000000000000000000}\right)}{{\color{blue}{\left(\frac{104109730557}{25000000000} \cdot x\right)}}^{2} + \left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      13. lower--.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \frac{60929246449480706651316240921050533}{125000000000000000000000000000}\right)}{{\left(\frac{104109730557}{25000000000} \cdot x\right)}^{2} + \color{blue}{\left(\frac{393497462077}{5000000000} \cdot \frac{393497462077}{5000000000} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      14. metadata-eval N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \frac{60929246449480706651316240921050533}{125000000000000000000000000000}\right)}{{\left(\frac{104109730557}{25000000000} \cdot x\right)}^{2} + \left(\color{blue}{\frac{154840252661040053153929}{25000000000000000000}} - \left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      15. lower-*.f64 N/A

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{1128428295162862690821234941118693}{15625000000000000000000000000000}, {x}^{3}, \frac{60929246449480706651316240921050533}{125000000000000000000000000000}\right)}{{\left(\frac{104109730557}{25000000000} \cdot x\right)}^{2} + \left(\frac{154840252661040053153929}{25000000000000000000} - \color{blue}{\left(\frac{104109730557}{25000000000} \cdot x\right) \cdot \frac{393497462077}{5000000000}}\right)}, x, \frac{4297481763}{31250000}\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{216700011257}{5000000000} + x, x, \frac{263505074721}{1000000000}\right), x, \frac{156699607947}{500000000}\right), x, \frac{23533438303}{500000000}\right)} \]

      16. lower-*.f64 99.0

          \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(72.2194108904232, {x}^{3}, 487433.97159584565\right)}{{\left(4.16438922228 \cdot x\right)}^{2} + \left(6193.6101064416025 - \color{blue}{\left(4.16438922228 \cdot x\right)} \cdot 78.6994924154\right)}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   5. Applied rewrites 99.0%

      \[\leadsto \left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\frac{\mathsf{fma}\left(72.2194108904232, {x}^{3}, 487433.97159584565\right)}{{\left(4.16438922228 \cdot x\right)}^{2} + \left(6193.6101064416025 - \left(4.16438922228 \cdot x\right) \cdot 78.6994924154\right)}}, x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)} \]

   if 1.9999999999999999e304 < (/.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 0.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 0.2%

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

   6. Applied rewrites 3.6%

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

   7. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   9. Applied rewrites 98.4%

      \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, \color{blue}{-1}, 4.16438922228\right) \]

   10. Taylor expanded in y around inf

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-1 \cdot \frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{neg}\left(\frac{y}{{x}^{2}}\right)}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       2. lower-neg.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       3. lower-/.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       4. unpow2 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       5. lower-*.f64 98.4

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   12. Applied rewrites 98.4%

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right)\\ \end{array} \end{array} \]

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+304)
   (*
    (- 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 (fma (/ (- (/ y (* x x))) x) -1.0 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+304) {
		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 * fma((-(y / (x * x)) / x), -1.0, 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+304)
		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(x * fma(Float64(Float64(-Float64(y / Float64(x * x))) / x), -1.0, 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+304], 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[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]) / x), $MachinePrecision] * -1.0 + 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))) < 1.9999999999999999e304

   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 1.9999999999999999e304 < (/.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 0.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 0.2%

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

   6. Applied rewrites 3.6%

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

   7. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   9. Applied rewrites 98.4%

      \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, \color{blue}{-1}, 4.16438922228\right) \]

   10. Taylor expanded in y around inf

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-1 \cdot \frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{neg}\left(\frac{y}{{x}^{2}}\right)}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       2. lower-neg.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       3. lower-/.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       4. unpow2 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       5. lower-*.f64 98.4

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   12. Applied rewrites 98.4%

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, -1, 4.16438922228\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 31.5:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          x
          (fma
           (/
            (fma
             (/ (+ 3655.1204654076414 (/ (- y 130977.50649958357) x)) x)
             -1.0
             110.1139242984811)
            x)
           -1.0
           4.16438922228))))
   (if (<= x -36.0)
     t_0
     (if (<= x 31.5)
       (/
        (*
         (- x 2.0)
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z))
        (fma 313.399215894 x 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * fma((fma(((3655.1204654076414 + ((y - 130977.50649958357) / x)) / x), -1.0, 110.1139242984811) / x), -1.0, 4.16438922228);
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 31.5) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * fma(Float64(fma(Float64(Float64(3655.1204654076414 + Float64(Float64(y - 130977.50649958357) / x)) / x), -1.0, 110.1139242984811) / x), -1.0, 4.16438922228))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 31.5)
		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 = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[(N[(N[(3655.1204654076414 + N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] * -1.0 + 110.1139242984811), $MachinePrecision] / x), $MachinePrecision] * -1.0 + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 31.5], 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], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 31.5 < 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 z around 0

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

   4. Applied rewrites 13.2%

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

   6. Applied rewrites 18.4%

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

   7. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   9. Applied rewrites 93.4%

      \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, \color{blue}{-1}, 4.16438922228\right) \]

   if -36 < x < 31.5

   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

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

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

Alternative 4: 95.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, -1, 4.16438922228\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 30.5:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + \mathsf{fma}\left(-2, y, x \cdot \left(y - 275.038832832\right)\right)\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          x
          (fma
           (/
            (fma
             (/ (+ 3655.1204654076414 (/ (- y 130977.50649958357) x)) x)
             -1.0
             110.1139242984811)
            x)
           -1.0
           4.16438922228))))
   (if (<= x -36.0)
     t_0
     (if (<= x 30.5)
       (/
        (fma -2.0 z (* x (+ z (fma -2.0 y (* x (- y 275.038832832))))))
        (+ (* 313.399215894 x) 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * fma((fma(((3655.1204654076414 + ((y - 130977.50649958357) / x)) / x), -1.0, 110.1139242984811) / x), -1.0, 4.16438922228);
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 30.5) {
		tmp = fma(-2.0, z, (x * (z + fma(-2.0, y, (x * (y - 275.038832832)))))) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * fma(Float64(fma(Float64(Float64(3655.1204654076414 + Float64(Float64(y - 130977.50649958357) / x)) / x), -1.0, 110.1139242984811) / x), -1.0, 4.16438922228))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 30.5)
		tmp = Float64(fma(-2.0, z, Float64(x * Float64(z + fma(-2.0, y, Float64(x * Float64(y - 275.038832832)))))) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[(N[(N[(3655.1204654076414 + N[(N[(y - 130977.50649958357), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] * -1.0 + 110.1139242984811), $MachinePrecision] / x), $MachinePrecision] * -1.0 + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 30.5], N[(N[(-2.0 * z + N[(x * N[(z + N[(-2.0 * y + N[(x * N[(y - 275.038832832), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 30.5 < 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 z around 0

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

   4. Applied rewrites 13.2%

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

   6. Applied rewrites 18.4%

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

   7. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   9. Applied rewrites 93.4%

      \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, \color{blue}{-1}, 4.16438922228\right) \]

   if -36 < x < 30.5

   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

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

      1. lower-*.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 66.4

         \[\leadsto \frac{-2 \cdot z}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 66.4%

      \[\leadsto \frac{-2 \cdot z}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 97.7

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

   10. Applied rewrites 97.7%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-2, z, x \cdot \left(z + \mathsf{fma}\left(-2, y, x \cdot \left(y - 275.038832832\right)\right)\right)\right)}}{313.399215894 \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 95.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right)\\ \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 24:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + \mathsf{fma}\left(-2, y, x \cdot \left(y - 275.038832832\right)\right)\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (fma (/ (- (/ y (* x x))) x) -1.0 4.16438922228))))
   (if (<= x -1.35)
     t_0
     (if (<= x 24.0)
       (/
        (fma -2.0 z (* x (+ z (fma -2.0 y (* x (- y 275.038832832))))))
        (+ (* 313.399215894 x) 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * fma((-(y / (x * x)) / x), -1.0, 4.16438922228);
	double tmp;
	if (x <= -1.35) {
		tmp = t_0;
	} else if (x <= 24.0) {
		tmp = fma(-2.0, z, (x * (z + fma(-2.0, y, (x * (y - 275.038832832)))))) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * fma(Float64(Float64(-Float64(y / Float64(x * x))) / x), -1.0, 4.16438922228))
	tmp = 0.0
	if (x <= -1.35)
		tmp = t_0;
	elseif (x <= 24.0)
		tmp = Float64(fma(-2.0, z, Float64(x * Float64(z + fma(-2.0, y, Float64(x * Float64(y - 275.038832832)))))) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[((-N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]) / x), $MachinePrecision] * -1.0 + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35], t$95$0, If[LessEqual[x, 24.0], N[(N[(-2.0 * z + N[(x * N[(z + N[(-2.0 * y + N[(x * N[(y - 275.038832832), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001 or 24 < x

   1. Initial program 17.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 13.4%

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

   6. Applied rewrites 18.6%

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

   7. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   9. Applied rewrites 93.2%

      \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, \color{blue}{-1}, 4.16438922228\right) \]

   10. Taylor expanded in y around inf

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-1 \cdot \frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{neg}\left(\frac{y}{{x}^{2}}\right)}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       2. lower-neg.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       3. lower-/.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       4. unpow2 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       5. lower-*.f64 92.8

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   12. Applied rewrites 92.8%

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   if -1.3500000000000001 < x < 24

   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 66.6

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

   4. Applied rewrites 66.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 66.6

         \[\leadsto \frac{-2 \cdot z}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 66.6%

      \[\leadsto \frac{-2 \cdot z}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 98.0

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

   10. Applied rewrites 98.0%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(-2, z, x \cdot \left(z + \mathsf{fma}\left(-2, y, x \cdot \left(y - 275.038832832\right)\right)\right)\right)}}{313.399215894 \cdot x + 47.066876606} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 94.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right)\\ \mathbf{if}\;x \leq -0.17:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 25.5:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(4.16438922228, x, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (fma (/ (- (/ y (* x x))) x) -1.0 4.16438922228))))
   (if (<= x -0.17)
     t_0
     (if (<= x 25.5)
       (*
        (- x 2.0)
        (/
         (fma
          (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
          x
          z)
         47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * fma((-(y / (x * x)) / x), -1.0, 4.16438922228);
	double tmp;
	if (x <= -0.17) {
		tmp = t_0;
	} else if (x <= 25.5) {
		tmp = (x - 2.0) * (fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, z) / 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * fma(Float64(Float64(-Float64(y / Float64(x * x))) / x), -1.0, 4.16438922228))
	tmp = 0.0
	if (x <= -0.17)
		tmp = t_0;
	elseif (x <= 25.5)
		tmp = Float64(Float64(x - 2.0) * Float64(fma(fma(fma(fma(4.16438922228, x, 78.6994924154), x, 137.519416416), x, y), x, 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[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]) / x), $MachinePrecision] * -1.0 + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.17], t$95$0, If[LessEqual[x, 25.5], 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] / 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.170000000000000012 or 25.5 < x

   1. Initial program 17.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 13.5%

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

   6. Applied rewrites 18.7%

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

   7. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   9. Applied rewrites 93.0%

      \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, \color{blue}{-1}, 4.16438922228\right) \]

   10. Taylor expanded in y around inf

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-1 \cdot \frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{neg}\left(\frac{y}{{x}^{2}}\right)}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       2. lower-neg.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       3. lower-/.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       4. unpow2 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       5. lower-*.f64 92.7

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   12. Applied rewrites 92.7%

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   if -0.170000000000000012 < x < 25.5

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

      1. *-commutative 97.1

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

      2. +-commutative 97.1

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

      3. *-commutative 97.1

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

   6. Applied rewrites 97.1%

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

Alternative 7: 92.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right)\\ \mathbf{if}\;x \leq -0.019:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 24:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + -2 \cdot y\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (fma (/ (- (/ y (* x x))) x) -1.0 4.16438922228))))
   (if (<= x -0.019)
     t_0
     (if (<= x 24.0)
       (/
        (fma -2.0 z (* x (+ z (* -2.0 y))))
        (+ (* 313.399215894 x) 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * fma((-(y / (x * x)) / x), -1.0, 4.16438922228);
	double tmp;
	if (x <= -0.019) {
		tmp = t_0;
	} else if (x <= 24.0) {
		tmp = fma(-2.0, z, (x * (z + (-2.0 * y)))) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * fma(Float64(Float64(-Float64(y / Float64(x * x))) / x), -1.0, 4.16438922228))
	tmp = 0.0
	if (x <= -0.019)
		tmp = t_0;
	elseif (x <= 24.0)
		tmp = Float64(fma(-2.0, z, Float64(x * Float64(z + Float64(-2.0 * y)))) / Float64(Float64(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[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]) / x), $MachinePrecision] * -1.0 + 4.16438922228), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.019], t$95$0, If[LessEqual[x, 24.0], N[(N[(-2.0 * z + N[(x * N[(z + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0189999999999999995 or 24 < x

   1. Initial program 17.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 13.6%

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

   6. Applied rewrites 18.7%

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

   7. Taylor expanded in x around -inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   9. Applied rewrites 92.9%

      \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{3655.1204654076414 + \frac{y - 130977.50649958357}{x}}{x}, -1, 110.1139242984811\right)}{x}, \color{blue}{-1}, 4.16438922228\right) \]

   10. Taylor expanded in y around inf

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-1 \cdot \frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]
   11. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{\mathsf{neg}\left(\frac{y}{{x}^{2}}\right)}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       2. lower-neg.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       3. lower-/.f64 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{{x}^{2}}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       4. unpow2 N/A

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, \frac{104109730557}{25000000000}\right) \]

       5. lower-*.f64 92.5

          \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   12. Applied rewrites 92.5%

       \[\leadsto x \cdot \mathsf{fma}\left(\frac{-\frac{y}{x \cdot x}}{x}, -1, 4.16438922228\right) \]

   if -0.0189999999999999995 < x < 24

   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 66.7

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

   4. Applied rewrites 66.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 66.7

         \[\leadsto \frac{-2 \cdot z}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 66.7%

      \[\leadsto \frac{-2 \cdot z}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 93.1

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

   10. Applied rewrites 93.1%

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

Alternative 8: 89.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -0.019:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 60:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2, z, x \cdot \left(z + -2 \cdot y\right)\right)}{313.399215894 \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -0.019)
     t_0
     (if (<= x 60.0)
       (/
        (fma -2.0 z (* x (+ z (* -2.0 y))))
        (+ (* 313.399215894 x) 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -0.019) {
		tmp = t_0;
	} else if (x <= 60.0) {
		tmp = fma(-2.0, z, (x * (z + (-2.0 * y)))) / ((313.399215894 * x) + 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -0.019)
		tmp = t_0;
	elseif (x <= 60.0)
		tmp = Float64(fma(-2.0, z, Float64(x * Float64(z + Float64(-2.0 * y)))) / Float64(Float64(313.399215894 * x) + 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -0.019], t$95$0, If[LessEqual[x, 60.0], N[(N[(-2.0 * z + N[(x * N[(z + N[(-2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(313.399215894 * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0189999999999999995 or 60 < x

   1. Initial program 17.7%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 86.8

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

   4. Applied rewrites 86.8%

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

   if -0.0189999999999999995 < x < 60

   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 66.7

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

   4. Applied rewrites 66.7%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 66.7

         \[\leadsto \frac{-2 \cdot z}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 66.7%

      \[\leadsto \frac{-2 \cdot z}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 93.1

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

   10. Applied rewrites 93.1%

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

Alternative 9: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -2800000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3000000000:\\ \;\;\;\;\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(0.0212463641547976, y, -0.14147091005106402 \cdot z\right), x, 0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -2800000000000.0)
     t_0
     (if (<= x 3000000000.0)
       (*
        (- x 2.0)
        (fma
         (fma 0.0212463641547976 y (* -0.14147091005106402 z))
         x
         (* 0.0212463641547976 z)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -2800000000000.0) {
		tmp = t_0;
	} else if (x <= 3000000000.0) {
		tmp = (x - 2.0) * fma(fma(0.0212463641547976, y, (-0.14147091005106402 * z)), x, (0.0212463641547976 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -2800000000000.0)
		tmp = t_0;
	elseif (x <= 3000000000.0)
		tmp = Float64(Float64(x - 2.0) * fma(fma(0.0212463641547976, y, Float64(-0.14147091005106402 * z)), x, Float64(0.0212463641547976 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2800000000000.0], t$95$0, If[LessEqual[x, 3000000000.0], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * y + N[(-0.14147091005106402 * z), $MachinePrecision]), $MachinePrecision] * x + N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e12 or 3e9 < x

   1. Initial program 15.0%

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

   2. Taylor expanded in x around 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 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.8e12 < x < 3e9

   1. Initial program 99.5%

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. metadata-eval N/A

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

      8. lower-*.f64 90.1

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

   6. Applied rewrites 90.1%

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

Alternative 10: 89.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -2800000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 26.5:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-2, y, z\right), 0.0212463641547976, 0.28294182010212804 \cdot z\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -2800000000000.0)
     t_0
     (if (<= x 26.5)
       (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 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -2800000000000.0) {
		tmp = t_0;
	} else if (x <= 26.5) {
		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(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -2800000000000.0)
		tmp = t_0;
	elseif (x <= 26.5)
		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[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2800000000000.0], t$95$0, If[LessEqual[x, 26.5], 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 < -2.8e12 or 26.5 < 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 88.3

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

   4. Applied rewrites 88.3%

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

   if -2.8e12 < x < 26.5

   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

      \[\leadsto \color{blue}{\frac{-1000000000}{23533438303} \cdot z + x \cdot \left(\frac{500000000}{23533438303} \cdot \left(z + -2 \cdot y\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   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 90.9

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

   4. Applied rewrites 90.9%

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

Alternative 11: 89.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -2800000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3000000000:\\ \;\;\;\;\left(x - 2\right) \cdot \mathsf{fma}\left(0.0212463641547976 \cdot y, x, 0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -2800000000000.0)
     t_0
     (if (<= x 3000000000.0)
       (* (- x 2.0) (fma (* 0.0212463641547976 y) x (* 0.0212463641547976 z)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -2800000000000.0) {
		tmp = t_0;
	} else if (x <= 3000000000.0) {
		tmp = (x - 2.0) * fma((0.0212463641547976 * y), x, (0.0212463641547976 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -2800000000000.0)
		tmp = t_0;
	elseif (x <= 3000000000.0)
		tmp = Float64(Float64(x - 2.0) * fma(Float64(0.0212463641547976 * y), x, Float64(0.0212463641547976 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2800000000000.0], t$95$0, If[LessEqual[x, 3000000000.0], N[(N[(x - 2.0), $MachinePrecision] * N[(N[(0.0212463641547976 * y), $MachinePrecision] * x + N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e12 or 3e9 < x

   1. Initial program 15.0%

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

   2. Taylor expanded in x around 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 89.1

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

   4. Applied rewrites 89.1%

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

   if -2.8e12 < x < 3e9

   1. Initial program 99.5%

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. metadata-eval N/A

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

      8. lower-*.f64 90.1

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

   6. Applied rewrites 90.1%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 89.7

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

   9. Applied rewrites 89.7%

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

Alternative 12: 76.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-13}:\\ \;\;\;\;\frac{-2 \cdot z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ 110.1139242984811 x)) x)))
   (if (<= x -8.5e-14)
     t_0
     (if (<= x 2.05e-13) (/ (* -2.0 z) 47.066876606) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -8.5e-14) {
		tmp = t_0;
	} else if (x <= 2.05e-13) {
		tmp = (-2.0 * z) / 47.066876606;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    if (x <= (-8.5d-14)) then
        tmp = t_0
    else if (x <= 2.05d-13) then
        tmp = ((-2.0d0) * z) / 47.066876606d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	double tmp;
	if (x <= -8.5e-14) {
		tmp = t_0;
	} else if (x <= 2.05e-13) {
		tmp = (-2.0 * z) / 47.066876606;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 - (110.1139242984811 / x)) * x
	tmp = 0
	if x <= -8.5e-14:
		tmp = t_0
	elif x <= 2.05e-13:
		tmp = (-2.0 * z) / 47.066876606
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x)
	tmp = 0.0
	if (x <= -8.5e-14)
		tmp = t_0;
	elseif (x <= 2.05e-13)
		tmp = Float64(Float64(-2.0 * z) / 47.066876606);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 - (110.1139242984811 / x)) * x;
	tmp = 0.0;
	if (x <= -8.5e-14)
		tmp = t_0;
	elseif (x <= 2.05e-13)
		tmp = (-2.0 * z) / 47.066876606;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -8.5e-14], t$95$0, If[LessEqual[x, 2.05e-13], N[(N[(-2.0 * z), $MachinePrecision] / 47.066876606), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000038e-14 or 2.0500000000000001e-13 < x

   1. Initial program 21.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 83.2

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

   4. Applied rewrites 83.2%

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

   if -8.50000000000000038e-14 < x < 2.0500000000000001e-13

   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 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 68.8

         \[\leadsto \frac{-2 \cdot z}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 68.8%

      \[\leadsto \frac{-2 \cdot z}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 68.8%

       \[\leadsto \frac{-2 \cdot z}{\color{blue}{47.066876606}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 76.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-13}:\\ \;\;\;\;\frac{-2 \cdot z}{47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e-14)
   (* 4.16438922228 x)
   (if (<= x 2.05e-13)
     (/ (* -2.0 z) 47.066876606)
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.05e-13) {
		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 <= (-8.5d-14)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.05d-13) 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 <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.05e-13) {
		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 <= -8.5e-14:
		tmp = 4.16438922228 * x
	elif x <= 2.05e-13:
		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 <= -8.5e-14)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.05e-13)
		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 <= -8.5e-14)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.05e-13)
		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, -8.5e-14], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.05e-13], 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 < -8.50000000000000038e-14

   1. Initial program 21.2%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 82.5

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

   4. Applied rewrites 82.5%

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

   if -8.50000000000000038e-14 < x < 2.0500000000000001e-13

   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 68.8

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 68.8

         \[\leadsto \frac{-2 \cdot z}{313.399215894 \cdot \color{blue}{x} + 47.066876606} \]

   7. Applied rewrites 68.8%

      \[\leadsto \frac{-2 \cdot z}{\color{blue}{313.399215894 \cdot x} + 47.066876606} \]

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 68.8%

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

   if 2.0500000000000001e-13 < x

   1. Initial program 21.2%

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

   3. Applied rewrites 27.2%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 83.5%

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

Alternative 14: 76.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-13}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(0.0212463641547976 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e-14)
   (* 4.16438922228 x)
   (if (<= x 2.05e-13)
     (* (- x 2.0) (* 0.0212463641547976 z))
     (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.05e-13) {
		tmp = (x - 2.0) * (0.0212463641547976 * 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 <= (-8.5d-14)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.05d-13) then
        tmp = (x - 2.0d0) * (0.0212463641547976d0 * 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 <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.05e-13) {
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.5e-14:
		tmp = 4.16438922228 * x
	elif x <= 2.05e-13:
		tmp = (x - 2.0) * (0.0212463641547976 * z)
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.5e-14)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.05e-13)
		tmp = Float64(Float64(x - 2.0) * Float64(0.0212463641547976 * 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 <= -8.5e-14)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.05e-13)
		tmp = (x - 2.0) * (0.0212463641547976 * z);
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e-14], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.05e-13], N[(N[(x - 2.0), $MachinePrecision] * N[(0.0212463641547976 * z), $MachinePrecision]), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.50000000000000038e-14

   1. Initial program 21.2%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 82.5

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

   4. Applied rewrites 82.5%

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

   if -8.50000000000000038e-14 < x < 2.0500000000000001e-13

   1. Initial program 99.7%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-*.f64 68.5

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

   6. Applied rewrites 68.5%

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

   if 2.0500000000000001e-13 < x

   1. Initial program 21.2%

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

   3. Applied rewrites 27.2%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 83.5%

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

Alternative 15: 76.1% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-13}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e-14)
   (* 4.16438922228 x)
   (if (<= x 2.05e-13) (* -0.0424927283095952 z) (* (- x 2.0) 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.05e-13) {
		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 <= (-8.5d-14)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.05d-13) 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 <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.05e-13) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (x - 2.0) * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.5e-14:
		tmp = 4.16438922228 * x
	elif x <= 2.05e-13:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (x - 2.0) * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.5e-14)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.05e-13)
		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 <= -8.5e-14)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.05e-13)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (x - 2.0) * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e-14], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.05e-13], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(x - 2.0), $MachinePrecision] * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.50000000000000038e-14

   1. Initial program 21.2%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 82.5

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

   4. Applied rewrites 82.5%

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

   if -8.50000000000000038e-14 < x < 2.0500000000000001e-13

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 68.5

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

   4. Applied rewrites 68.5%

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

   if 2.0500000000000001e-13 < x

   1. Initial program 21.2%

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

   3. Applied rewrites 27.2%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 83.5%

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

Alternative 16: 76.3% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-14}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 0.08:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e-14)
   (* 4.16438922228 x)
   (if (<= x 0.08) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.08) {
		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 <= (-8.5d-14)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 0.08d0) 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 <= -8.5e-14) {
		tmp = 4.16438922228 * x;
	} else if (x <= 0.08) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.5e-14:
		tmp = 4.16438922228 * x
	elif x <= 0.08:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.5e-14)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 0.08)
		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 <= -8.5e-14)
		tmp = 4.16438922228 * x;
	elseif (x <= 0.08)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e-14], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 0.08], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000038e-14 or 0.0800000000000000017 < x

   1. Initial program 19.8%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 84.4

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

   4. Applied rewrites 84.4%

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

   if -8.50000000000000038e-14 < x < 0.0800000000000000017

   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 67.7

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

   4. Applied rewrites 67.7%

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

Alternative 17: 34.6% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.4%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 34.6

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

4. Applied rewrites 34.6%

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

Developer Target 1: 98.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2025103 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

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

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