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

Percentage Accurate: 69.7% → 99.3%

Time: 9.6s

Alternatives: 13

Speedup: 2.5×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

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 + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+
     (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
     0.279195317918525))
   (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))

C

double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

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 + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
}

Python

def code(x, y, z):
	return x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(6.012459259764103 + z\right) \cdot z\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+30} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right)}{37.606951580302194 + {t\_0}^{3}}, \left(\left({t\_0}^{2} + 11.224803678858207\right) - 3.350343815022304 \cdot t\_0\right) \cdot y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (+ 6.012459259764103 z) z)))
   (if (or (<= z -1.8e+30) (not (<= z 190000000.0)))
     (fma 0.0692910599291889 y x)
     (fma
      (/
       (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
       (+ 37.606951580302194 (pow t_0 3.0)))
      (* (- (+ (pow t_0 2.0) 11.224803678858207) (* 3.350343815022304 t_0)) y)
      x))))

C

double code(double x, double y, double z) {
	double t_0 = (6.012459259764103 + z) * z;
	double tmp;
	if ((z <= -1.8e+30) || !(z <= 190000000.0)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = fma((fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525) / (37.606951580302194 + pow(t_0, 3.0))), (((pow(t_0, 2.0) + 11.224803678858207) - (3.350343815022304 * t_0)) * y), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(6.012459259764103 + z) * z)
	tmp = 0.0
	if ((z <= -1.8e+30) || !(z <= 190000000.0))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = fma(Float64(fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525) / Float64(37.606951580302194 + (t_0 ^ 3.0))), Float64(Float64(Float64((t_0 ^ 2.0) + 11.224803678858207) - Float64(3.350343815022304 * t_0)) * y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(6.012459259764103 + z), $MachinePrecision] * z), $MachinePrecision]}, If[Or[LessEqual[z, -1.8e+30], N[Not[LessEqual[z, 190000000.0]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] / N[(37.606951580302194 + N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Power[t$95$0, 2.0], $MachinePrecision] + 11.224803678858207), $MachinePrecision] - N[(3.350343815022304 * t$95$0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e30 or 1.9e8 < z

   1. Initial program 37.8%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -1.8000000000000001e30 < z < 1.9e8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   4. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right)}{37.606951580302194 + {\left(\left(6.012459259764103 + z\right) \cdot z\right)}^{3}}, \left(\left({\left(\left(6.012459259764103 + z\right) \cdot z\right)}^{2} + 11.224803678858207\right) - 3.350343815022304 \cdot \left(\left(6.012459259764103 + z\right) \cdot z\right)\right) \cdot y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+30} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right)}{37.606951580302194 + {\left(\left(6.012459259764103 + z\right) \cdot z\right)}^{3}}, \left(\left({\left(\left(6.012459259764103 + z\right) \cdot z\right)}^{2} + 11.224803678858207\right) - 3.350343815022304 \cdot \left(\left(6.012459259764103 + z\right) \cdot z\right)\right) \cdot y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45} \lor \neg \left(z \leq 5 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\frac{0.004801250986110448 \cdot \left(z \cdot z\right) - 0.24180012482592123}{0.0692910599291889 \cdot z - 0.4917317610505968} \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e+45) (not (<= z 5e+27)))
   (fma 0.0692910599291889 y x)
   (+
    x
    (/
     (*
      y
      (+
       (*
        (/
         (- (* 0.004801250986110448 (* z z)) 0.24180012482592123)
         (- (* 0.0692910599291889 z) 0.4917317610505968))
        z)
       0.279195317918525))
     (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+45) || !(z <= 5e+27)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = x + ((y * (((((0.004801250986110448 * (z * z)) - 0.24180012482592123) / ((0.0692910599291889 * z) - 0.4917317610505968)) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e+45) || !(z <= 5e+27))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(0.004801250986110448 * Float64(z * z)) - 0.24180012482592123) / Float64(Float64(0.0692910599291889 * z) - 0.4917317610505968)) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e+45], N[Not[LessEqual[z, 5e+27]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(N[(0.004801250986110448 * N[(z * z), $MachinePrecision]), $MachinePrecision] - 0.24180012482592123), $MachinePrecision] / N[(N[(0.0692910599291889 * z), $MachinePrecision] - 0.4917317610505968), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e45 or 4.99999999999999979e27 < z

   1. Initial program 31.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -2.2e45 < z < 4.99999999999999979e27

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right)} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      2. flip-+ N/A

         \[\leadsto x + \frac{y \cdot \left(\color{blue}{\frac{\left(z \cdot \frac{692910599291889}{10000000000000000}\right) \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right) - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      3. lower-/.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(\color{blue}{\frac{\left(z \cdot \frac{692910599291889}{10000000000000000}\right) \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right) - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      4. lower--.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(\frac{\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000}\right) \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right) - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      5. lift-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(\frac{\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000}\right)} \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right) - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      6. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\frac{\color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot z\right)} \cdot \left(z \cdot \frac{692910599291889}{10000000000000000}\right) - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      7. lift-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(\frac{\left(\frac{692910599291889}{10000000000000000} \cdot z\right) \cdot \color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000}\right)} - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      8. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\frac{\left(\frac{692910599291889}{10000000000000000} \cdot z\right) \cdot \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot z\right)} - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      9. swap-sqr N/A

         \[\leadsto x + \frac{y \cdot \left(\frac{\color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot \frac{692910599291889}{10000000000000000}\right) \cdot \left(z \cdot z\right)} - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      10. lower-*.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\frac{\color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot \frac{692910599291889}{10000000000000000}\right) \cdot \left(z \cdot z\right)} - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      11. metadata-eval N/A

          \[\leadsto x + \frac{y \cdot \left(\frac{\color{blue}{\frac{480125098611044764748221188321}{100000000000000000000000000000000}} \cdot \left(z \cdot z\right) - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      12. lower-*.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\frac{\frac{480125098611044764748221188321}{100000000000000000000000000000000} \cdot \color{blue}{\left(z \cdot z\right)} - \frac{307332350656623}{625000000000000} \cdot \frac{307332350656623}{625000000000000}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      13. metadata-eval N/A

          \[\leadsto x + \frac{y \cdot \left(\frac{\frac{480125098611044764748221188321}{100000000000000000000000000000000} \cdot \left(z \cdot z\right) - \color{blue}{\frac{94453173760125479739253764129}{390625000000000000000000000000}}}{z \cdot \frac{692910599291889}{10000000000000000} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      14. lower--.f64 99.6

          \[\leadsto x + \frac{y \cdot \left(\frac{0.004801250986110448 \cdot \left(z \cdot z\right) - 0.24180012482592123}{\color{blue}{z \cdot 0.0692910599291889 - 0.4917317610505968}} \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

      15. lift-*.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\frac{\frac{480125098611044764748221188321}{100000000000000000000000000000000} \cdot \left(z \cdot z\right) - \frac{94453173760125479739253764129}{390625000000000000000000000000}}{\color{blue}{z \cdot \frac{692910599291889}{10000000000000000}} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      16. *-commutative N/A

          \[\leadsto x + \frac{y \cdot \left(\frac{\frac{480125098611044764748221188321}{100000000000000000000000000000000} \cdot \left(z \cdot z\right) - \frac{94453173760125479739253764129}{390625000000000000000000000000}}{\color{blue}{\frac{692910599291889}{10000000000000000} \cdot z} - \frac{307332350656623}{625000000000000}} \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      17. lower-*.f64 99.6

          \[\leadsto x + \frac{y \cdot \left(\frac{0.004801250986110448 \cdot \left(z \cdot z\right) - 0.24180012482592123}{\color{blue}{0.0692910599291889 \cdot z} - 0.4917317610505968} \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   4. Applied rewrites 99.6%

      \[\leadsto x + \frac{y \cdot \left(\color{blue}{\frac{0.004801250986110448 \cdot \left(z \cdot z\right) - 0.24180012482592123}{0.0692910599291889 \cdot z - 0.4917317610505968}} \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45} \lor \neg \left(z \leq 5 \cdot 10^{+27}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\frac{0.004801250986110448 \cdot \left(z \cdot z\right) - 0.24180012482592123}{0.0692910599291889 \cdot z - 0.4917317610505968} \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e+45) (not (<= z 190000000.0)))
   (fma 0.0692910599291889 y x)
   (+
    x
    (/
     (fma
      (fma 0.0692910599291889 z 0.4917317610505968)
      (* z y)
      (* 0.279195317918525 y))
     (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+45) || !(z <= 190000000.0)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = x + (fma(fma(0.0692910599291889, z, 0.4917317610505968), (z * y), (0.279195317918525 * y)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e+45) || !(z <= 190000000.0))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = Float64(x + Float64(fma(fma(0.0692910599291889, z, 0.4917317610505968), Float64(z * y), Float64(0.279195317918525 * y)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e+45], N[Not[LessEqual[z, 190000000.0]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(x + N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(0.279195317918525 * y), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e45 or 1.9e8 < z

   1. Initial program 34.8%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -2.2e45 < z < 1.9e8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      2. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      3. distribute-rgt-in N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right) \cdot y + \frac{11167812716741}{40000000000000} \cdot y}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      4. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right)} \cdot y + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      5. associate-*l* N/A

         \[\leadsto x + \frac{\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot \left(z \cdot y\right)} + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      7. lift-+.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      8. lift-*.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000}} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      9. *-commutative N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000} \cdot z} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right)}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      11. lower-*.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), \color{blue}{z \cdot y}, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      12. lower-*.f64 99.6

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, \color{blue}{0.279195317918525 \cdot y}\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   4. Applied rewrites 99.6%

      \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e+45) (not (<= z 190000000.0)))
   (fma 0.0692910599291889 y x)
   (+
    x
    (/
     (fma
      (fma 0.0692910599291889 z 0.4917317610505968)
      (* z y)
      (* 0.279195317918525 y))
     (fma (+ 6.012459259764103 z) z 3.350343815022304)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+45) || !(z <= 190000000.0)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = x + (fma(fma(0.0692910599291889, z, 0.4917317610505968), (z * y), (0.279195317918525 * y)) / fma((6.012459259764103 + z), z, 3.350343815022304));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e+45) || !(z <= 190000000.0))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = Float64(x + Float64(fma(fma(0.0692910599291889, z, 0.4917317610505968), Float64(z * y), Float64(0.279195317918525 * y)) / fma(Float64(6.012459259764103 + z), z, 3.350343815022304)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e+45], N[Not[LessEqual[z, 190000000.0]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(x + N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(0.279195317918525 * y), $MachinePrecision]), $MachinePrecision] / N[(N[(6.012459259764103 + z), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e45 or 1.9e8 < z

   1. Initial program 34.8%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -2.2e45 < z < 1.9e8

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      2. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      3. distribute-rgt-in N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right) \cdot y + \frac{11167812716741}{40000000000000} \cdot y}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      4. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right)} \cdot y + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      5. associate-*l* N/A

         \[\leadsto x + \frac{\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot \left(z \cdot y\right)} + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      7. lift-+.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      8. lift-*.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000}} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      9. *-commutative N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000} \cdot z} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right)}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      11. lower-*.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), \color{blue}{z \cdot y}, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      12. lower-*.f64 99.6

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, \color{blue}{0.279195317918525 \cdot y}\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   4. Applied rewrites 99.6%

      \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\color{blue}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\color{blue}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z} + \frac{104698244219447}{31250000000000}} \]

      3. lift-+.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\color{blue}{\left(z + \frac{6012459259764103}{1000000000000000}\right)} \cdot z + \frac{104698244219447}{31250000000000}} \]

      4. +-commutative N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\color{blue}{\left(\frac{6012459259764103}{1000000000000000} + z\right)} \cdot z + \frac{104698244219447}{31250000000000}} \]

      5. lift-+.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\color{blue}{\left(\frac{6012459259764103}{1000000000000000} + z\right)} \cdot z + \frac{104698244219447}{31250000000000}} \]

      6. lift-fma.f64 99.6

         \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}{\color{blue}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}} \]

   6. Applied rewrites 99.6%

      \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}{\color{blue}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+45} \lor \neg \left(z \leq 190000000\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889 - \frac{-0.07512208616047561}{z}, x\right)\\ \mathbf{elif}\;z \leq 4.2:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-0.00277777777751721, y, \left(y \cdot 0.0007936505811533442\right) \cdot z\right), z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (fma y (- 0.0692910599291889 (/ -0.07512208616047561 z)) x)
   (if (<= z 4.2)
     (fma
      (fma -0.00277777777751721 y (* (* y 0.0007936505811533442) z))
      z
      (fma 0.08333333333333323 y x))
     (fma 0.0692910599291889 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = fma(y, (0.0692910599291889 - (-0.07512208616047561 / z)), x);
	} else if (z <= 4.2) {
		tmp = fma(fma(-0.00277777777751721, y, ((y * 0.0007936505811533442) * z)), z, fma(0.08333333333333323, y, x));
	} else {
		tmp = fma(0.0692910599291889, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = fma(y, Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z)), x);
	elseif (z <= 4.2)
		tmp = fma(fma(-0.00277777777751721, y, Float64(Float64(y * 0.0007936505811533442) * z)), z, fma(0.08333333333333323, y, x));
	else
		tmp = fma(0.0692910599291889, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 4.2], N[(N[(-0.00277777777751721 * y + N[(N[(y * 0.0007936505811533442), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z + N[(0.08333333333333323 * y + x), $MachinePrecision]), $MachinePrecision], N[(0.0692910599291889 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 40.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right) + x} \]

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

         \[\leadsto \color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) + \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)} + x \]

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

         \[\leadsto \left(\color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y - \left(\mathsf{neg}\left(\frac{307332350656623}{625000000000000}\right)\right) \cdot \frac{y}{z}\right)} + \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right) + x \]

      5. associate-+l- N/A

         \[\leadsto \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y - \left(\left(\mathsf{neg}\left(\frac{307332350656623}{625000000000000}\right)\right) \cdot \frac{y}{z} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\color{blue}{y \cdot \frac{692910599291889}{10000000000000000}} - \left(\left(\mathsf{neg}\left(\frac{307332350656623}{625000000000000}\right)\right) \cdot \frac{y}{z} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right) + x \]

      7. metadata-eval N/A

         \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\color{blue}{\frac{-307332350656623}{625000000000000}} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right) + x \]

      8. associate-*r/ N/A

         \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y}{z}} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right) + x \]

      9. metadata-eval N/A

         \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y}{z} - \color{blue}{\frac{-4166096748901211929300981260567}{10000000000000000000000000000000}} \cdot \frac{y}{z}\right)\right) + x \]

      10. associate-*r/ N/A

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y}{z} - \color{blue}{\frac{\frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) + x \]

      11. div-sub N/A

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right) + x \]

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

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \frac{\color{blue}{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}}{z}\right) + x \]

      13. associate-/l* N/A

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \color{blue}{y \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{z}}\right) + x \]

      14. distribute-lft-out-- N/A

          \[\leadsto \color{blue}{y \cdot \left(\frac{692910599291889}{10000000000000000} - \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{z}\right)} + x \]

      15. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{692910599291889}{10000000000000000} - \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{z}, x\right)} \]

   5. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 0.0692910599291889 - \frac{-0.07512208616047561}{z}, x\right)} \]

   if -5.4000000000000004 < z < 4.20000000000000018

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + z \cdot \left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot \left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot z} + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{307332350656623}{2093964884388940} \cdot y + z \cdot \left(\frac{692910599291889}{33503438150223040} \cdot y - \left(\frac{272651677654809570312500000}{10961722342634967150292985809} \cdot y + \frac{6012459259764103}{3350343815022304} \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)\right)\right) - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y, z, x + \frac{279195317918525}{3350343815022304} \cdot y\right)} \]

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-0.00277777777751721, y, \left(y \cdot 0.0007936505811533442\right) \cdot z\right), z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)} \]

   if 4.20000000000000018 < z

   1. Initial program 40.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.0)))
   (fma 0.0692910599291889 y x)
   (fma (* -0.00277777777751721 y) z (fma 0.08333333333333323 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.0)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = fma((-0.00277777777751721 * y), z, fma(0.08333333333333323, y, x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4) || !(z <= 5.0))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = fma(Float64(-0.00277777777751721 * y), z, fma(0.08333333333333323, y, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.0]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(N[(-0.00277777777751721 * y), $MachinePrecision] * z + N[(0.08333333333333323 * y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5 < z

   1. Initial program 40.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -5.4000000000000004 < z < 5

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      2. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      3. distribute-rgt-in N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right) \cdot y + \frac{11167812716741}{40000000000000} \cdot y}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      4. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right)} \cdot y + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      5. associate-*l* N/A

         \[\leadsto x + \frac{\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot \left(z \cdot y\right)} + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      7. lift-+.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      8. lift-*.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000}} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      9. *-commutative N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000} \cdot z} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right)}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      11. lower-*.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), \color{blue}{z \cdot y}, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      12. lower-*.f64 99.6

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, \color{blue}{0.279195317918525 \cdot y}\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   4. Applied rewrites 99.6%

      \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{-1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y + \frac{307332350656623}{2093964884388940} \cdot y\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto x + \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \left(\frac{-1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y + \frac{307332350656623}{2093964884388940} \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto x + \left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y + \frac{-1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)}\right) \]

      3. metadata-eval N/A

         \[\leadsto x + \left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right)} \cdot y\right)\right) \]

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

         \[\leadsto x + \left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)}\right) \]

      5. associate-+r- N/A

         \[\leadsto \color{blue}{\left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) - \left(\mathsf{neg}\left(z\right)\right) \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \]

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

         \[\leadsto \color{blue}{\left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \]

      7. *-commutative N/A

         \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot z} \]

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

         \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right)} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \left(y \cdot \color{blue}{\frac{-155900051080628738716045985239}{56124018394291031809500087342080}}\right) \cdot z \]

      10. *-commutative N/A

          \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\left(\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot y\right)} \cdot z \]

      11. associate-*r* N/A

          \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot \left(y \cdot z\right)} \]

      12. +-commutative N/A

          \[\leadsto \color{blue}{\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot \left(y \cdot z\right) + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right)} \]

      13. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot y\right) \cdot z} + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

      14. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot \frac{-155900051080628738716045985239}{56124018394291031809500087342080}\right)} \cdot z + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

      15. metadata-eval N/A

          \[\leadsto \left(y \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right) \cdot z + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

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

          \[\leadsto \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \cdot z + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y, z, x + \frac{279195317918525}{3350343815022304} \cdot y\right)} \]

   7. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889 - \frac{-0.07512208616047561}{z}, x\right)\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (fma y (- 0.0692910599291889 (/ -0.07512208616047561 z)) x)
   (if (<= z 5.0)
     (fma (* -0.00277777777751721 y) z (fma 0.08333333333333323 y x))
     (fma 0.0692910599291889 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = fma(y, (0.0692910599291889 - (-0.07512208616047561 / z)), x);
	} else if (z <= 5.0) {
		tmp = fma((-0.00277777777751721 * y), z, fma(0.08333333333333323, y, x));
	} else {
		tmp = fma(0.0692910599291889, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = fma(y, Float64(0.0692910599291889 - Float64(-0.07512208616047561 / z)), x);
	elseif (z <= 5.0)
		tmp = fma(Float64(-0.00277777777751721 * y), z, fma(0.08333333333333323, y, x));
	else
		tmp = fma(0.0692910599291889, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(y * N[(0.0692910599291889 - N[(-0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 5.0], N[(N[(-0.00277777777751721 * y), $MachinePrecision] * z + N[(0.08333333333333323 * y + x), $MachinePrecision]), $MachinePrecision], N[(0.0692910599291889 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 40.4%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right)\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) - \frac{4166096748901211929300981260567}{10000000000000000000000000000000} \cdot \frac{y}{z}\right) + x} \]

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

         \[\leadsto \color{blue}{\left(\left(\frac{692910599291889}{10000000000000000} \cdot y + \frac{307332350656623}{625000000000000} \cdot \frac{y}{z}\right) + \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)} + x \]

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

         \[\leadsto \left(\color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y - \left(\mathsf{neg}\left(\frac{307332350656623}{625000000000000}\right)\right) \cdot \frac{y}{z}\right)} + \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right) + x \]

      5. associate-+l- N/A

         \[\leadsto \color{blue}{\left(\frac{692910599291889}{10000000000000000} \cdot y - \left(\left(\mathsf{neg}\left(\frac{307332350656623}{625000000000000}\right)\right) \cdot \frac{y}{z} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right)} + x \]

      6. *-commutative N/A

         \[\leadsto \left(\color{blue}{y \cdot \frac{692910599291889}{10000000000000000}} - \left(\left(\mathsf{neg}\left(\frac{307332350656623}{625000000000000}\right)\right) \cdot \frac{y}{z} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right) + x \]

      7. metadata-eval N/A

         \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\color{blue}{\frac{-307332350656623}{625000000000000}} \cdot \frac{y}{z} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right) + x \]

      8. associate-*r/ N/A

         \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y}{z}} - \left(\mathsf{neg}\left(\frac{4166096748901211929300981260567}{10000000000000000000000000000000}\right)\right) \cdot \frac{y}{z}\right)\right) + x \]

      9. metadata-eval N/A

         \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y}{z} - \color{blue}{\frac{-4166096748901211929300981260567}{10000000000000000000000000000000}} \cdot \frac{y}{z}\right)\right) + x \]

      10. associate-*r/ N/A

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \left(\frac{\frac{-307332350656623}{625000000000000} \cdot y}{z} - \color{blue}{\frac{\frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right)\right) + x \]

      11. div-sub N/A

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}\right) + x \]

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

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \frac{\color{blue}{y \cdot \left(\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}\right)}}{z}\right) + x \]

      13. associate-/l* N/A

          \[\leadsto \left(y \cdot \frac{692910599291889}{10000000000000000} - \color{blue}{y \cdot \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{z}}\right) + x \]

      14. distribute-lft-out-- N/A

          \[\leadsto \color{blue}{y \cdot \left(\frac{692910599291889}{10000000000000000} - \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{z}\right)} + x \]

      15. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{692910599291889}{10000000000000000} - \frac{\frac{-307332350656623}{625000000000000} - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000}}{z}, x\right)} \]

   5. Applied rewrites 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 0.0692910599291889 - \frac{-0.07512208616047561}{z}, x\right)} \]

   if -5.4000000000000004 < z < 5

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      2. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      3. distribute-rgt-in N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right) \cdot y + \frac{11167812716741}{40000000000000} \cdot y}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      4. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z\right)} \cdot y + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      5. associate-*l* N/A

         \[\leadsto x + \frac{\color{blue}{\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot \left(z \cdot y\right)} + \frac{11167812716741}{40000000000000} \cdot y}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      6. lower-fma.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      7. lift-+.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      8. lift-*.f64 N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{z \cdot \frac{692910599291889}{10000000000000000}} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      9. *-commutative N/A

         \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000} \cdot z} + \frac{307332350656623}{625000000000000}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      10. lower-fma.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right)}, z \cdot y, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      11. lower-*.f64 N/A

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), \color{blue}{z \cdot y}, \frac{11167812716741}{40000000000000} \cdot y\right)}{\left(z + \frac{6012459259764103}{1000000000000000}\right) \cdot z + \frac{104698244219447}{31250000000000}} \]

      12. lower-*.f64 99.6

          \[\leadsto x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, \color{blue}{0.279195317918525 \cdot y}\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   4. Applied rewrites 99.6%

      \[\leadsto x + \frac{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{-1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y + \frac{307332350656623}{2093964884388940} \cdot y\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto x + \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \left(\frac{-1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y + \frac{307332350656623}{2093964884388940} \cdot y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto x + \left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y + \frac{-1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)}\right) \]

      3. metadata-eval N/A

         \[\leadsto x + \left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right)} \cdot y\right)\right) \]

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

         \[\leadsto x + \left(\frac{279195317918525}{3350343815022304} \cdot y - \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)}\right) \]

      5. associate-+r- N/A

         \[\leadsto \color{blue}{\left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) - \left(\mathsf{neg}\left(z\right)\right) \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \]

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

         \[\leadsto \color{blue}{\left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \]

      7. *-commutative N/A

         \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot z} \]

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

         \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right)} \cdot z \]

      9. metadata-eval N/A

         \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \left(y \cdot \color{blue}{\frac{-155900051080628738716045985239}{56124018394291031809500087342080}}\right) \cdot z \]

      10. *-commutative N/A

          \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\left(\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot y\right)} \cdot z \]

      11. associate-*r* N/A

          \[\leadsto \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) + \color{blue}{\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot \left(y \cdot z\right)} \]

      12. +-commutative N/A

          \[\leadsto \color{blue}{\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot \left(y \cdot z\right) + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right)} \]

      13. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot y\right) \cdot z} + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

      14. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot \frac{-155900051080628738716045985239}{56124018394291031809500087342080}\right)} \cdot z + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

      15. metadata-eval N/A

          \[\leadsto \left(y \cdot \color{blue}{\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)}\right) \cdot z + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

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

          \[\leadsto \color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)} \cdot z + \left(x + \frac{279195317918525}{3350343815022304} \cdot y\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y, z, x + \frac{279195317918525}{3350343815022304} \cdot y\right)} \]

   7. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)} \]

   if 5 < z

   1. Initial program 40.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889 - \frac{-0.07512208616047561}{z}, x\right)\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(-0.00277777777751721, z, 0.08333333333333323\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 5.0)))
   (fma 0.0692910599291889 y x)
   (fma y (fma -0.00277777777751721 z 0.08333333333333323) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 5.0)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = fma(y, fma(-0.00277777777751721, z, 0.08333333333333323), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4) || !(z <= 5.0))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = fma(y, fma(-0.00277777777751721, z, 0.08333333333333323), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 5.0]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(y * N[(-0.00277777777751721 * z + 0.08333333333333323), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 5 < z

   1. Initial program 40.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -5.4000000000000004 < z < 5

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{279195317918525}{3350343815022304} \cdot y + z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right)\right) + x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot \left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) + \frac{279195317918525}{3350343815022304} \cdot y\right)} + x \]

      3. *-commutative N/A

         \[\leadsto \left(\color{blue}{\left(\frac{307332350656623}{2093964884388940} \cdot y - \frac{1678650474502018223880473708075}{11224803678858206361900017468416} \cdot y\right) \cdot z} + \frac{279195317918525}{3350343815022304} \cdot y\right) + x \]

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

         \[\leadsto \left(\color{blue}{\left(y \cdot \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right)\right)} \cdot z + \frac{279195317918525}{3350343815022304} \cdot y\right) + x \]

      5. associate-*l* N/A

         \[\leadsto \left(\color{blue}{y \cdot \left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right)} + \frac{279195317918525}{3350343815022304} \cdot y\right) + x \]

      6. *-commutative N/A

         \[\leadsto \left(y \cdot \left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z\right) + \color{blue}{y \cdot \frac{279195317918525}{3350343815022304}}\right) + x \]

      7. distribute-lft-out N/A

         \[\leadsto \color{blue}{y \cdot \left(\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z + \frac{279195317918525}{3350343815022304}\right)} + x \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}\right) \cdot z + \frac{279195317918525}{3350343815022304}, x\right)} \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(\frac{307332350656623}{2093964884388940} - \frac{1678650474502018223880473708075}{11224803678858206361900017468416}, z, \frac{279195317918525}{3350343815022304}\right)}, x\right) \]

      10. metadata-eval 99.1

          \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\color{blue}{-0.00277777777751721}, z, 0.08333333333333323\right), x\right) \]

   5. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(-0.00277777777751721, z, 0.08333333333333323\right), x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 5\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(-0.00277777777751721, z, 0.08333333333333323\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 6\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4) (not (<= z 6.0)))
   (fma 0.0692910599291889 y x)
   (fma 0.08333333333333323 y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4) || !(z <= 6.0)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = fma(0.08333333333333323, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4) || !(z <= 6.0))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = fma(0.08333333333333323, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4], N[Not[LessEqual[z, 6.0]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(0.08333333333333323 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 6 < z

   1. Initial program 40.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 99.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -5.4000000000000004 < z < 6

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{279195317918525}{3350343815022304} \cdot y + x} \]

      2. lower-fma.f64 98.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   5. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \lor \neg \left(z \leq 6\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-44} \lor \neg \left(z \leq -9.8 \cdot 10^{-176}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.6e-44) (not (<= z -9.8e-176)))
   (fma 0.0692910599291889 y x)
   (* 0.08333333333333323 y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e-44) || !(z <= -9.8e-176)) {
		tmp = fma(0.0692910599291889, y, x);
	} else {
		tmp = 0.08333333333333323 * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.6e-44) || !(z <= -9.8e-176))
		tmp = fma(0.0692910599291889, y, x);
	else
		tmp = Float64(0.08333333333333323 * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.6e-44], N[Not[LessEqual[z, -9.8e-176]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(0.08333333333333323 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000027e-44 or -9.7999999999999994e-176 < z

   1. Initial program 69.6%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 81.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   if -8.60000000000000027e-44 < z < -9.7999999999999994e-176

   1. Initial program 99.5%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{279195317918525}{3350343815022304} \cdot y + x} \]

      2. lower-fma.f64 99.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{279195317918525}{3350343815022304} \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 74.8%

      \[\leadsto 0.08333333333333323 \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-44} \lor \neg \left(z \leq -9.8 \cdot 10^{-176}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;0.08333333333333323 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.054 \lor \neg \left(y \leq 4.6 \cdot 10^{+113}\right):\\ \;\;\;\;0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.054) (not (<= y 4.6e+113)))
   (* 0.08333333333333323 y)
   (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.054) || !(y <= 4.6e+113)) {
		tmp = 0.08333333333333323 * y;
	} else {
		tmp = 1.0 * 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 ((y <= (-0.054d0)) .or. (.not. (y <= 4.6d+113))) then
        tmp = 0.08333333333333323d0 * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.054) || !(y <= 4.6e+113)) {
		tmp = 0.08333333333333323 * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.054) or not (y <= 4.6e+113):
		tmp = 0.08333333333333323 * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.054) || !(y <= 4.6e+113))
		tmp = Float64(0.08333333333333323 * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.054) || ~((y <= 4.6e+113)))
		tmp = 0.08333333333333323 * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.054], N[Not[LessEqual[y, 4.6e+113]], $MachinePrecision]], N[(0.08333333333333323 * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0539999999999999994 or 4.59999999999999993e113 < y

   1. Initial program 68.8%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{279195317918525}{3350343815022304} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{279195317918525}{3350343815022304} \cdot y + x} \]

      2. lower-fma.f64 69.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   5. Applied rewrites 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, x\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{279195317918525}{3350343815022304} \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto 0.08333333333333323 \cdot \color{blue}{y} \]

   if -0.0539999999999999994 < y < 4.59999999999999993e113

   1. Initial program 77.2%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 84.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(1 + \frac{692910599291889}{10000000000000000} \cdot \frac{y}{x}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 83.5%

      \[\leadsto \mathsf{fma}\left(\frac{y}{x}, 0.0692910599291889, 1\right) \cdot \color{blue}{x} \]

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 74.1%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.054 \lor \neg \left(y \leq 4.6 \cdot 10^{+113}\right):\\ \;\;\;\;0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -60000000000000 \lor \neg \left(y \leq 2.3 \cdot 10^{+103}\right):\\ \;\;\;\;0.0692910599291889 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -60000000000000.0) (not (<= y 2.3e+103)))
   (* 0.0692910599291889 y)
   (* 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -60000000000000.0) || !(y <= 2.3e+103)) {
		tmp = 0.0692910599291889 * y;
	} else {
		tmp = 1.0 * 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 ((y <= (-60000000000000.0d0)) .or. (.not. (y <= 2.3d+103))) then
        tmp = 0.0692910599291889d0 * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -60000000000000.0) || !(y <= 2.3e+103)) {
		tmp = 0.0692910599291889 * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -60000000000000.0) or not (y <= 2.3e+103):
		tmp = 0.0692910599291889 * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -60000000000000.0) || !(y <= 2.3e+103))
		tmp = Float64(0.0692910599291889 * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -60000000000000.0) || ~((y <= 2.3e+103)))
		tmp = 0.0692910599291889 * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -60000000000000.0], N[Not[LessEqual[y, 2.3e+103]], $MachinePrecision]], N[(0.0692910599291889 * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e13 or 2.30000000000000008e103 < y

   1. Initial program 68.9%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 62.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{692910599291889}{10000000000000000} \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 44.8%

      \[\leadsto 0.0692910599291889 \cdot \color{blue}{y} \]

   if -6e13 < y < 2.30000000000000008e103

   1. Initial program 77.0%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

      2. lower-fma.f64 83.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   5. Applied rewrites 83.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(1 + \frac{692910599291889}{10000000000000000} \cdot \frac{y}{x}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 82.8%

      \[\leadsto \mathsf{fma}\left(\frac{y}{x}, 0.0692910599291889, 1\right) \cdot \color{blue}{x} \]

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 73.4%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -60000000000000 \lor \neg \left(y \leq 2.3 \cdot 10^{+103}\right):\\ \;\;\;\;0.0692910599291889 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.1% accurate, 7.8× speedup

Math

\[\begin{array}{l} \\ 0.0692910599291889 \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* 0.0692910599291889 y))

C

double code(double x, double y, double z) {
	return 0.0692910599291889 * y;
}

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 = 0.0692910599291889d0 * y
end function

Java

public static double code(double x, double y, double z) {
	return 0.0692910599291889 * y;
}

Python

def code(x, y, z):
	return 0.0692910599291889 * y

Julia

function code(x, y, z)
	return Float64(0.0692910599291889 * y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0692910599291889 * y;
end

Wolfram

code[x_, y_, z_] := N[(0.0692910599291889 * y), $MachinePrecision]

Derivation

1. Initial program 73.8%

   \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + \frac{692910599291889}{10000000000000000} \cdot y} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{692910599291889}{10000000000000000} \cdot y + x} \]

   2. lower-fma.f64 75.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

5. Applied rewrites 75.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.0692910599291889, y, x\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{692910599291889}{10000000000000000} \cdot \color{blue}{y} \]
7. Step-by-step derivation

8. Applied rewrites 26.2%

   \[\leadsto 0.0692910599291889 \cdot \color{blue}{y} \]
9. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (-
          (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y)
          (- (/ (* 0.40462203869992125 y) (* z z)) x))))
   (if (< z -8120153.652456675)
     t_0
     (if (< z 6.576118972787377e+20)
       (+
        x
        (*
         (*
          y
          (+
           (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
           0.279195317918525))
         (/ 1.0 (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	double tmp;
	if (z < -8120153.652456675) {
		tmp = t_0;
	} else if (z < 6.576118972787377e+20) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	} 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 = (((0.07512208616047561d0 / z) + 0.0692910599291889d0) * y) - (((0.40462203869992125d0 * y) / (z * z)) - x)
    if (z < (-8120153.652456675d0)) then
        tmp = t_0
    else if (z < 6.576118972787377d+20) then
        tmp = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) * (1.0d0 / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	double tmp;
	if (z < -8120153.652456675) {
		tmp = t_0;
	} else if (z < 6.576118972787377e+20) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x)
	tmp = 0
	if z < -8120153.652456675:
		tmp = t_0
	elif z < 6.576118972787377e+20:
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(0.07512208616047561 / z) + 0.0692910599291889) * y) - Float64(Float64(Float64(0.40462203869992125 * y) / Float64(z * z)) - x))
	tmp = 0.0
	if (z < -8120153.652456675)
		tmp = t_0;
	elseif (z < 6.576118972787377e+20)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * Float64(1.0 / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((0.07512208616047561 / z) + 0.0692910599291889) * y) - (((0.40462203869992125 * y) / (z * z)) - x);
	tmp = 0.0;
	if (z < -8120153.652456675)
		tmp = t_0;
	elseif (z < 6.576118972787377e+20)
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) * (1.0 / (((z + 6.012459259764103) * z) + 3.350343815022304)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(0.07512208616047561 / z), $MachinePrecision] + 0.0692910599291889), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(0.40462203869992125 * y), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -8120153.652456675], t$95$0, If[Less[z, 6.576118972787377e+20], N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024359 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -324806146098267/40000000) (- (* (+ (/ 7512208616047561/100000000000000000 z) 692910599291889/10000000000000000) y) (- (/ (* 323697630959937/800000000000000 y) (* z z)) x)) (if (< z 657611897278737700000) (+ x (* (* y (+ (* (+ (* z 692910599291889/10000000000000000) 307332350656623/625000000000000) z) 11167812716741/40000000000000)) (/ 1 (+ (* (+ z 6012459259764103/1000000000000000) z) 104698244219447/31250000000000)))) (- (* (+ (/ 7512208616047561/100000000000000000 z) 692910599291889/10000000000000000) y) (- (/ (* 323697630959937/800000000000000 y) (* z z)) x)))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))