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

Percentage Accurate: 59.1% → 98.5%

Time: 12.6s

Alternatives: 16

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.4%

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

   3. Applied rewrites 98.1%

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

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

   1. Initial program 0.0%

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

   3. Applied rewrites 0.0%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 99.1%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 99.1

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

   9. Applied rewrites 99.1%

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

Alternative 2: 96.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+30}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(137.519416416, x, y\right), x, z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{\frac{y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+23)
   (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))
   (if (<= x 1.05e+30)
     (/
      (* (- x 2.0) (fma (fma 137.519416416 x y) x z))
      (+
       (*
        (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894)
        x)
       47.066876606))
     (*
      (- 4.16438922228 (/ (- 101.7851458539211 (/ (/ y x) x)) x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+23) {
		tmp = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	} else if (x <= 1.05e+30) {
		tmp = ((x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 - ((y / x) / x)) / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+23)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0));
	elseif (x <= 1.05e+30)
		tmp = Float64(Float64(Float64(x - 2.0) * fma(fma(137.519416416, x, y), x, z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(y / x) / x)) / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+23], N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+30], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(137.519416416 * x + y), $MachinePrecision] * x + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.9999999999999992e22

   1. Initial program 11.7%

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

   3. Applied rewrites 17.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 96.3%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 96.3

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

   9. Applied rewrites 96.3%

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

   if -9.9999999999999992e22 < x < 1.05e30

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 96.4

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

   4. Applied rewrites 96.4%

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

   if 1.05e30 < x

   1. Initial program 10.6%

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

   3. Applied rewrites 17.4%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 97.3%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 97.3

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

   9. Applied rewrites 97.3%

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

Alternative 3: 95.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 55:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{\frac{y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))
   (if (<= x 55.0)
     (/
      (*
       (- x 2.0)
       (+
        (*
         (+
          (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
          y)
         x)
        z))
      (fma 313.399215894 x 47.066876606))
     (*
      (- 4.16438922228 (/ (- 101.7851458539211 (/ (/ y x) x)) x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	} else if (x <= 55.0) {
		tmp = ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 - ((y / x) / x)) / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0));
	elseif (x <= 55.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(y / x) / x)) / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 55.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 16.9%

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

   3. Applied rewrites 22.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 93.4%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.1

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

   9. Applied rewrites 93.1%

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

   if -36 < x < 55

   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 98.1

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

   4. Applied rewrites 98.1%

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

   if 55 < x

   1. Initial program 17.8%

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

   3. Applied rewrites 24.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 94.2%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 94.1

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

   9. Applied rewrites 94.1%

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

Alternative 4: 95.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 55:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(\mathsf{fma}\left(78.6994924154, x, 137.519416416\right), x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{\frac{y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))
   (if (<= x 55.0)
     (/
      (* (- x 2.0) (+ (* (fma (fma 78.6994924154 x 137.519416416) x y) x) z))
      (fma 313.399215894 x 47.066876606))
     (*
      (- 4.16438922228 (/ (- 101.7851458539211 (/ (/ y x) x)) x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	} else if (x <= 55.0) {
		tmp = ((x - 2.0) * ((fma(fma(78.6994924154, x, 137.519416416), x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 - ((y / x) / x)) / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0));
	elseif (x <= 55.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(fma(78.6994924154, x, 137.519416416), x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(y / x) / x)) / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 55.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(78.6994924154 * x + 137.519416416), $MachinePrecision] * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 16.9%

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

   3. Applied rewrites 22.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 93.4%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.1

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

   9. Applied rewrites 93.1%

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

   if -36 < x < 55

   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 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 98.1

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

   7. Applied rewrites 98.1%

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

   if 55 < x

   1. Initial program 17.8%

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

   3. Applied rewrites 24.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 94.2%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 94.1

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

   9. Applied rewrites 94.1%

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

Alternative 5: 95.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 110:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(137.519416416 \cdot x + y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{\frac{y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))
   (if (<= x 110.0)
     (/
      (* (- x 2.0) (+ (* (+ (* 137.519416416 x) y) x) z))
      (fma 313.399215894 x 47.066876606))
     (*
      (- 4.16438922228 (/ (- 101.7851458539211 (/ (/ y x) x)) x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	} else if (x <= 110.0) {
		tmp = ((x - 2.0) * ((((137.519416416 * x) + y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 - ((y / x) / x)) / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0));
	elseif (x <= 110.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(137.519416416 * x) + y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(y / x) / x)) / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 110.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(137.519416416 * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 16.9%

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

   3. Applied rewrites 22.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 93.4%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.1

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

   9. Applied rewrites 93.1%

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

   if -36 < x < 110

   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 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 97.9

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

   7. Applied rewrites 97.9%

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

   if 110 < x

   1. Initial program 17.8%

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

   3. Applied rewrites 24.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 94.2%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 94.1

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

   9. Applied rewrites 94.1%

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

Alternative 6: 95.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 110:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\mathsf{fma}\left(137.519416416, x, y\right) \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{\frac{y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))
   (if (<= x 110.0)
     (/
      (* (- x 2.0) (+ (* (fma 137.519416416 x y) x) z))
      (fma 313.399215894 x 47.066876606))
     (*
      (- 4.16438922228 (/ (- 101.7851458539211 (/ (/ y x) x)) x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	} else if (x <= 110.0) {
		tmp = ((x - 2.0) * ((fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 - ((y / x) / x)) / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0));
	elseif (x <= 110.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(fma(137.519416416, x, y) * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(y / x) / x)) / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 110.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(137.519416416 * x + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 16.9%

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

   3. Applied rewrites 22.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 93.4%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.1

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

   9. Applied rewrites 93.1%

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

   if -36 < x < 110

   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 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 97.9

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

   7. Applied rewrites 97.9%

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

   if 110 < x

   1. Initial program 17.8%

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

   3. Applied rewrites 24.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 94.2%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 94.1

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

   9. Applied rewrites 94.1%

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

Alternative 7: 93.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;\left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{elif}\;x \leq 45:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{101.7851458539211 - \frac{\frac{y}{x}}{x}}{x}\right) \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))
   (if (<= x 45.0)
     (/ (* (- x 2.0) (+ (* y x) z)) (fma 313.399215894 x 47.066876606))
     (*
      (- 4.16438922228 (/ (- 101.7851458539211 (/ (/ y x) x)) x))
      (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	} else if (x <= 45.0) {
		tmp = ((x - 2.0) * ((y * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - ((101.7851458539211 - ((y / x) / x)) / x)) * (x - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0));
	elseif (x <= 45.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(y * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(Float64(101.7851458539211 - Float64(Float64(y / x) / x)) / x)) * Float64(x - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 45.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(N[(101.7851458539211 - N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 16.9%

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

   3. Applied rewrites 22.3%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 93.4%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.1

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

   9. Applied rewrites 93.1%

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

   if -36 < x < 45

   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 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 93.3

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

   7. Applied rewrites 93.3%

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

   if 45 < x

   1. Initial program 17.8%

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

   3. Applied rewrites 24.4%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 94.1%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 94.1

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

   9. Applied rewrites 94.1%

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

Alternative 8: 93.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -36:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 45:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(y \cdot x + z\right)}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))))
   (if (<= x -36.0)
     t_0
     (if (<= x 45.0)
       (/ (* (- x 2.0) (+ (* y x) z)) (fma 313.399215894 x 47.066876606))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	double tmp;
	if (x <= -36.0) {
		tmp = t_0;
	} else if (x <= 45.0) {
		tmp = ((x - 2.0) * ((y * x) + z)) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -36.0)
		tmp = t_0;
	elseif (x <= 45.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(y * x) + z)) / fma(313.399215894, x, 47.066876606));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -36.0], t$95$0, If[LessEqual[x, 45.0], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(y * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -36 or 45 < x

   1. Initial program 17.3%

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

   3. Applied rewrites 23.4%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 93.8%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.5

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

   9. Applied rewrites 93.5%

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

   if -36 < x < 45

   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 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 93.3

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

   7. Applied rewrites 93.3%

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

Alternative 9: 93.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -85000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.16:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-2 \cdot y, 0.0212463641547976, z \cdot 0.3041881842569256\right), x, -0.0424927283095952 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))))
   (if (<= x -85000000.0)
     t_0
     (if (<= x 0.16)
       (fma
        (fma (* -2.0 y) 0.0212463641547976 (* z 0.3041881842569256))
        x
        (* -0.0424927283095952 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	double tmp;
	if (x <= -85000000.0) {
		tmp = t_0;
	} else if (x <= 0.16) {
		tmp = fma(fma((-2.0 * y), 0.0212463641547976, (z * 0.3041881842569256)), x, (-0.0424927283095952 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -85000000.0)
		tmp = t_0;
	elseif (x <= 0.16)
		tmp = fma(fma(Float64(-2.0 * y), 0.0212463641547976, Float64(z * 0.3041881842569256)), x, Float64(-0.0424927283095952 * z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -85000000.0], t$95$0, If[LessEqual[x, 0.16], N[(N[(N[(-2.0 * y), $MachinePrecision] * 0.0212463641547976 + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision] * x + N[(-0.0424927283095952 * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5e7 or 0.160000000000000003 < x

   1. Initial program 17.1%

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

   3. Applied rewrites 23.1%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 93.9%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.7

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

   9. Applied rewrites 93.7%

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

   if -8.5e7 < x < 0.160000000000000003

   1. Initial program 99.6%

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

   3. Applied rewrites 99.6%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-2 \cdot y, 0.0212463641547976, z \cdot 0.3041881842569256\right), x, -0.0424927283095952 \cdot z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 82.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(4.16438922228 - \frac{-y}{\left(x \cdot x\right) \cdot x}\right) \cdot \left(x - 2\right)\\ \mathbf{if}\;x \leq -85000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;-0.0424927283095952 \cdot z - \left(5.843575199059173 \cdot x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 4.16438922228 (/ (- y) (* (* x x) x))) (- x 2.0))))
   (if (<= x -85000000.0)
     t_0
     (if (<= x 1.4)
       (- (* -0.0424927283095952 z) (* (* 5.843575199059173 x) x))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	double tmp;
	if (x <= -85000000.0) {
		tmp = t_0;
	} else if (x <= 1.4) {
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (4.16438922228d0 - (-y / ((x * x) * x))) * (x - 2.0d0)
    if (x <= (-85000000.0d0)) then
        tmp = t_0
    else if (x <= 1.4d0) then
        tmp = ((-0.0424927283095952d0) * z) - ((5.843575199059173d0 * x) * x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	double tmp;
	if (x <= -85000000.0) {
		tmp = t_0;
	} else if (x <= 1.4) {
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0)
	tmp = 0
	if x <= -85000000.0:
		tmp = t_0
	elif x <= 1.4:
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(4.16438922228 - Float64(Float64(-y) / Float64(Float64(x * x) * x))) * Float64(x - 2.0))
	tmp = 0.0
	if (x <= -85000000.0)
		tmp = t_0;
	elseif (x <= 1.4)
		tmp = Float64(Float64(-0.0424927283095952 * z) - Float64(Float64(5.843575199059173 * x) * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (4.16438922228 - (-y / ((x * x) * x))) * (x - 2.0);
	tmp = 0.0;
	if (x <= -85000000.0)
		tmp = t_0;
	elseif (x <= 1.4)
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(4.16438922228 - N[((-y) / N[(N[(x * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -85000000.0], t$95$0, If[LessEqual[x, 1.4], N[(N[(-0.0424927283095952 * z), $MachinePrecision] - N[(N[(5.843575199059173 * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5e7 or 1.3999999999999999 < x

   1. Initial program 16.9%

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

   3. Applied rewrites 23.0%

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

   4. Taylor expanded in x around -inf

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   6. Applied rewrites 94.1%

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

   7. Taylor expanded in y around inf

      \[\leadsto \left(\frac{104109730557}{25000000000} - -1 \cdot \color{blue}{\frac{y}{{x}^{3}}}\right) \cdot \left(x - 2\right) \]
   8. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-1 \cdot y}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      2. mul-1-neg N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      3. lower-/.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{\mathsf{neg}\left(y\right)}{{x}^{\color{blue}{3}}}\right) \cdot \left(x - 2\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto \left(\frac{104109730557}{25000000000} - \frac{-y}{{x}^{3}}\right) \cdot \left(x - 2\right) \]

      5. unpow3 N/A

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

      6. pow2 N/A

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

      7. lower-*.f64 N/A

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

      8. pow2 N/A

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

      9. lift-*.f64 93.8

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

   9. Applied rewrites 93.8%

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

   if -8.5e7 < x < 1.3999999999999999

   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 y around 0

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

   4. Applied rewrites 73.4%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative 72.2

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

      2. distribute-lft-in 72.2

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

      3. *-commutative 72.2

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

      4. metadata-eval 72.2

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

      5. metadata-eval 72.2

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

      6. fp-cancel-sign-sub-inv 72.2

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

      7. metadata-eval 72.2

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

      8. *-commutative 72.2

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

      9. lift-+.f64 N/A

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

      10. lift-+.f64 72.2

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

      11. +-commutative 72.2

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

      12. *-commutative 72.2

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

      13. *-commutative 72.2

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

      14. +-commutative 72.2

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

      15. lift-+.f64 N/A

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

      16. lift-+.f64 72.2

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

      17. distribute-lft-in 72.2

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

      18. *-commutative 72.2

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

   7. Applied rewrites 72.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{-1000000000}{23533438303} \cdot z + \color{blue}{x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x\right)\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x\right)\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x\right)\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right)} - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x\right)\right) \]

      6. distribute-lft-neg-out N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right) \cdot x \]

   10. Applied rewrites 71.9%

       \[\leadsto -0.0424927283095952 \cdot z - \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot 0.3041881842569256, 6.658593866711955, \mathsf{fma}\left(-0.23789659216289816, z, 5.843575199059173\right)\right), x, z \cdot -0.3041881842569256\right) \cdot x} \]

   11. Taylor expanded in z around 0

       \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\frac{137519416416}{23533438303} \cdot x\right) \cdot x \]
   12. Step-by-step derivation

       1. lower-*.f64 71.4

          \[\leadsto -0.0424927283095952 \cdot z - \left(5.843575199059173 \cdot x\right) \cdot x \]

   13. Applied rewrites 71.4%

       \[\leadsto -0.0424927283095952 \cdot z - \left(5.843575199059173 \cdot x\right) \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 79.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -85000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z - \left(5.843575199059173 \cdot x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -85000000.0)
   (* 4.16438922228 x)
   (if (<= x 2.0)
     (- (* -0.0424927283095952 z) (* (* 5.843575199059173 x) x))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-85000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.0d0) then
        tmp = ((-0.0424927283095952d0) * z) - ((5.843575199059173d0 * x) * x)
    else
        tmp = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -85000000.0:
		tmp = 4.16438922228 * x
	elif x <= 2.0:
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x)
	else:
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -85000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		tmp = Float64(Float64(-0.0424927283095952 * z) - Float64(Float64(5.843575199059173 * x) * x));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -85000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.0)
		tmp = (-0.0424927283095952 * z) - ((5.843575199059173 * x) * x);
	else
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -85000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(N[(-0.0424927283095952 * z), $MachinePrecision] - N[(N[(5.843575199059173 * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5e7

   1. Initial program 15.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 88.7

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

   4. Applied rewrites 88.7%

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

   if -8.5e7 < x < 2

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 73.4%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative 72.2

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

      2. distribute-lft-in 72.2

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

      3. *-commutative 72.2

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

      4. metadata-eval 72.2

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

      5. metadata-eval 72.2

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

      6. fp-cancel-sign-sub-inv 72.2

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

      7. metadata-eval 72.2

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

      8. *-commutative 72.2

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

      9. lift-+.f64 N/A

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

      10. lift-+.f64 72.2

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

      11. +-commutative 72.2

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

      12. *-commutative 72.2

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

      13. *-commutative 72.2

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

      14. +-commutative 72.2

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

      15. lift-+.f64 N/A

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

      16. lift-+.f64 72.2

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

      17. distribute-lft-in 72.2

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

      18. *-commutative 72.2

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

   7. Applied rewrites 72.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \frac{-1000000000}{23533438303} \cdot z + \color{blue}{x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]
   9. Step-by-step derivation

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

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x\right)\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

      2. lower--.f64 N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x\right)\right) \cdot \color{blue}{\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x\right)\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right)} - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \]

      4. distribute-lft-neg-out N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(x \cdot \left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right) \cdot x\right)\right) \]

      6. distribute-lft-neg-out N/A

         \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\mathsf{neg}\left(\left(\left(-1 \cdot \left(x \cdot \left(\frac{137519416416}{23533438303} + \left(\frac{-131752537360500000000}{553822718361107519809} \cdot z + \frac{156699607947}{23533438303} \cdot \left(\frac{500000000}{23533438303} \cdot z - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right)\right) + \frac{500000000}{23533438303} \cdot z\right) - \frac{-156699607947000000000}{553822718361107519809} \cdot z\right)\right)\right) \cdot x \]

   10. Applied rewrites 71.9%

       \[\leadsto -0.0424927283095952 \cdot z - \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot 0.3041881842569256, 6.658593866711955, \mathsf{fma}\left(-0.23789659216289816, z, 5.843575199059173\right)\right), x, z \cdot -0.3041881842569256\right) \cdot x} \]

   11. Taylor expanded in z around 0

       \[\leadsto \frac{-1000000000}{23533438303} \cdot z - \left(\frac{137519416416}{23533438303} \cdot x\right) \cdot x \]
   12. Step-by-step derivation

       1. lower-*.f64 71.4

          \[\leadsto -0.0424927283095952 \cdot z - \left(5.843575199059173 \cdot x\right) \cdot x \]

   13. Applied rewrites 71.4%

       \[\leadsto -0.0424927283095952 \cdot z - \left(5.843575199059173 \cdot x\right) \cdot x \]

   if 2 < x

   1. Initial program 18.3%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 86.1

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

   4. Applied rewrites 86.1%

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

Alternative 12: 76.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-13}:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{-2 \cdot z}{\mathsf{fma}\left(313.399215894, x, 47.066876606\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.8e-13)
   (* 4.16438922228 x)
   (if (<= x 4.8e-36)
     (/ (* -2.0 z) (fma 313.399215894 x 47.066876606))
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-13) {
		tmp = 4.16438922228 * x;
	} else if (x <= 4.8e-36) {
		tmp = (-2.0 * z) / fma(313.399215894, x, 47.066876606);
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.8e-13)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 4.8e-36)
		tmp = Float64(Float64(-2.0 * z) / fma(313.399215894, x, 47.066876606));
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.8e-13], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 4.8e-36], N[(N[(-2.0 * z), $MachinePrecision] / N[(313.399215894 * x + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.80000000000000009e-13

   1. Initial program 20.4%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 83.7

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

   4. Applied rewrites 83.7%

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

   if -7.80000000000000009e-13 < x < 4.8e-36

   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 y around 0

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

   4. Applied rewrites 74.6%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative 74.6

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

      2. distribute-lft-in 74.6

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

      3. *-commutative 74.6

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

      4. metadata-eval 74.6

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

      5. metadata-eval 74.6

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

      6. fp-cancel-sign-sub-inv 74.6

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

      7. metadata-eval 74.6

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

      8. *-commutative 74.6

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

      9. lift-+.f64 N/A

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

      10. lift-+.f64 74.6

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

      11. +-commutative 74.6

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

      12. *-commutative 74.6

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

      13. *-commutative 74.6

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

      14. +-commutative 74.6

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

      15. lift-+.f64 N/A

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

      16. lift-+.f64 74.6

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

      17. distribute-lft-in 74.6

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

      18. *-commutative 74.6

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

   7. Applied rewrites 74.6%

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

   8. Taylor expanded in x around 0

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

      1. lift-*.f64 70.9

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

   10. Applied rewrites 70.9%

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

   if 4.8e-36 < x

   1. Initial program 26.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 77.5

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

   4. Applied rewrites 77.5%

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

Alternative 13: 76.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -85000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(4.16438922228 - \frac{110.1139242984811}{x}\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -85000000.0)
   (* 4.16438922228 x)
   (if (<= x 4.8e-36)
     (* -0.0424927283095952 z)
     (* (- 4.16438922228 (/ 110.1139242984811 x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 4.8e-36) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-85000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 4.8d-36) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = (4.16438922228d0 - (110.1139242984811d0 / x)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 4.8e-36) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -85000000.0:
		tmp = 4.16438922228 * x
	elif x <= 4.8e-36:
		tmp = -0.0424927283095952 * z
	else:
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -85000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 4.8e-36)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(Float64(4.16438922228 - Float64(110.1139242984811 / x)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -85000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 4.8e-36)
		tmp = -0.0424927283095952 * z;
	else
		tmp = (4.16438922228 - (110.1139242984811 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -85000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 4.8e-36], N[(-0.0424927283095952 * z), $MachinePrecision], N[(N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5e7

   1. Initial program 15.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 88.7

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

   4. Applied rewrites 88.7%

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

   if -8.5e7 < x < 4.8e-36

   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 68.9

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

   4. Applied rewrites 68.9%

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

   if 4.8e-36 < x

   1. Initial program 26.8%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(\frac{104109730557}{25000000000} - \frac{13764240537310136880149}{125000000000000000000} \cdot \frac{1}{x}\right)} \]
   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 77.5

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

   4. Applied rewrites 77.5%

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

Alternative 14: 76.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -85000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-36}:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -85000000.0)
   (* 4.16438922228 x)
   (if (<= x 4.8e-36) (* -0.0424927283095952 z) (* 4.16438922228 (- x 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 4.8e-36) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * (x - 2.0);
	}
	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) :: tmp
    if (x <= (-85000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 4.8d-36) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = 4.16438922228d0 * (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 4.8e-36) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -85000000.0:
		tmp = 4.16438922228 * x
	elif x <= 4.8e-36:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * (x - 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -85000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 4.8e-36)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(4.16438922228 * Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -85000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 4.8e-36)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -85000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 4.8e-36], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5e7

   1. Initial program 15.5%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 88.7

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

   4. Applied rewrites 88.7%

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

   if -8.5e7 < x < 4.8e-36

   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 68.9

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

   4. Applied rewrites 68.9%

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

   if 4.8e-36 < x

   1. Initial program 26.8%

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

   3. Applied rewrites 32.7%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 77.3%

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

Alternative 15: 76.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -85000000:\\ \;\;\;\;4.16438922228 \cdot x\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;-0.0424927283095952 \cdot z\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -85000000.0)
   (* 4.16438922228 x)
   (if (<= x 2.0) (* -0.0424927283095952 z) (* 4.16438922228 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-85000000.0d0)) then
        tmp = 4.16438922228d0 * x
    else if (x <= 2.0d0) then
        tmp = (-0.0424927283095952d0) * z
    else
        tmp = 4.16438922228d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -85000000.0) {
		tmp = 4.16438922228 * x;
	} else if (x <= 2.0) {
		tmp = -0.0424927283095952 * z;
	} else {
		tmp = 4.16438922228 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -85000000.0:
		tmp = 4.16438922228 * x
	elif x <= 2.0:
		tmp = -0.0424927283095952 * z
	else:
		tmp = 4.16438922228 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -85000000.0)
		tmp = Float64(4.16438922228 * x);
	elseif (x <= 2.0)
		tmp = Float64(-0.0424927283095952 * z);
	else
		tmp = Float64(4.16438922228 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -85000000.0)
		tmp = 4.16438922228 * x;
	elseif (x <= 2.0)
		tmp = -0.0424927283095952 * z;
	else
		tmp = 4.16438922228 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -85000000.0], N[(4.16438922228 * x), $MachinePrecision], If[LessEqual[x, 2.0], N[(-0.0424927283095952 * z), $MachinePrecision], N[(4.16438922228 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5e7 or 2 < x

   1. Initial program 16.9%

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

   2. Taylor expanded in x around inf

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

      1. lower-*.f64 87.3

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

   4. Applied rewrites 87.3%

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

   if -8.5e7 < x < 2

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 67.0

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

   4. Applied rewrites 67.0%

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

Alternative 16: 35.7% accurate, 13.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.1%

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

2. Taylor expanded in x around 0

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

   1. lower-*.f64 35.7

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

4. Applied rewrites 35.7%

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

Reproduce

herbie shell --seed 2025130 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))