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

Percentage Accurate: 68.7% → 99.5%

Time: 7.1s

Alternatives: 12

Speedup: 6.7×

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: 68.7% 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: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+15}:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{elif}\;z \leq 200000000:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(0.004801250986110448, z \cdot z, -0.24180012482592123\right)}{0.0692910599291889 \cdot z - 0.4917317610505968}, z, 0.279195317918525\right) \cdot y}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.3e+15)
   (+ x (* 0.0692910599291889 y))
   (if (<= z 200000000.0)
     (+
      x
      (/
       (*
        (fma
         (/
          (fma 0.004801250986110448 (* z z) -0.24180012482592123)
          (- (* 0.0692910599291889 z) 0.4917317610505968))
         z
         0.279195317918525)
        y)
       (fma (+ 6.012459259764103 z) z 3.350343815022304)))
     (fma y 0.0692910599291889 (+ x (* (/ y z) 0.07512208616047561))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.3e+15) {
		tmp = x + (0.0692910599291889 * y);
	} else if (z <= 200000000.0) {
		tmp = x + ((fma((fma(0.004801250986110448, (z * z), -0.24180012482592123) / ((0.0692910599291889 * z) - 0.4917317610505968)), z, 0.279195317918525) * y) / fma((6.012459259764103 + z), z, 3.350343815022304));
	} else {
		tmp = fma(y, 0.0692910599291889, (x + ((y / z) * 0.07512208616047561)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.3e+15)
		tmp = Float64(x + Float64(0.0692910599291889 * y));
	elseif (z <= 200000000.0)
		tmp = Float64(x + Float64(Float64(fma(Float64(fma(0.004801250986110448, Float64(z * z), -0.24180012482592123) / Float64(Float64(0.0692910599291889 * z) - 0.4917317610505968)), z, 0.279195317918525) * y) / fma(Float64(6.012459259764103 + z), z, 3.350343815022304)));
	else
		tmp = fma(y, 0.0692910599291889, Float64(x + Float64(Float64(y / z) * 0.07512208616047561)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.3e+15], N[(x + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 200000000.0], N[(x + N[(N[(N[(N[(N[(0.004801250986110448 * N[(z * z), $MachinePrecision] + -0.24180012482592123), $MachinePrecision] / N[(N[(0.0692910599291889 * z), $MachinePrecision] - 0.4917317610505968), $MachinePrecision]), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] * y), $MachinePrecision] / N[(N[(6.012459259764103 + z), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 0.0692910599291889 + N[(x + N[(N[(y / z), $MachinePrecision] * 0.07512208616047561), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e15

   1. Initial program 43.2%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.7%

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

   if -4.3e15 < z < 2e8

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. 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. *-commutative N/A

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

      3. lower-*.f64 99.7

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 99.7

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 99.7

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

      11. lift-+.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 99.7

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 99.7

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

   4. Applied rewrites 99.7%

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

      1. lift-fma.f64 N/A

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

      2. flip-+ N/A

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

      3. lower-/.f64 N/A

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

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

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

      5. swap-sqr N/A

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

      6. metadata-eval N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. metadata-eval N/A

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

      12. metadata-eval N/A

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

      13. lower--.f64 N/A

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

      14. lower-*.f64 99.8

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

   6. Applied rewrites 99.8%

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

   if 2e8 < z

   1. Initial program 40.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.07512208616047561, \frac{y}{z}, \mathsf{fma}\left(0.0692910599291889, y, x\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.6%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{0.0692910599291889}, x + \frac{y}{z} \cdot 0.07512208616047561\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+15}:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{elif}\;z \leq 200000000:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(0.004801250986110448, z \cdot z, -0.24180012482592123\right)}{0.0692910599291889 \cdot z - 0.4917317610505968}, z, 0.279195317918525\right) \cdot y}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1900000000 \lor \neg \left(z \leq 200000000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right) \cdot y}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1900000000.0) (not (<= z 200000000.0)))
   (fma y 0.0692910599291889 (+ x (* (/ y z) 0.07512208616047561)))
   (+
    x
    (/
     (*
      (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
      y)
     (fma (+ 6.012459259764103 z) z 3.350343815022304)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1900000000.0) || !(z <= 200000000.0)) {
		tmp = fma(y, 0.0692910599291889, (x + ((y / z) * 0.07512208616047561)));
	} else {
		tmp = x + ((fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525) * y) / fma((6.012459259764103 + z), z, 3.350343815022304));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1900000000.0) || !(z <= 200000000.0))
		tmp = fma(y, 0.0692910599291889, Float64(x + Float64(Float64(y / z) * 0.07512208616047561)));
	else
		tmp = Float64(x + Float64(Float64(fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525) * y) / fma(Float64(6.012459259764103 + z), z, 3.350343815022304)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1900000000.0], N[Not[LessEqual[z, 200000000.0]], $MachinePrecision]], N[(y * 0.0692910599291889 + N[(x + N[(N[(y / z), $MachinePrecision] * 0.07512208616047561), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] * y), $MachinePrecision] / N[(N[(6.012459259764103 + z), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e9 or 2e8 < z

   1. Initial program 42.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.07512208616047561, \frac{y}{z}, \mathsf{fma}\left(0.0692910599291889, y, x\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.6%

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

   if -1.9e9 < z < 2e8

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \]
   2. Add Preprocessing
   3. 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. *-commutative N/A

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

      3. lower-*.f64 99.7

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 99.7

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 99.7

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

      11. lift-+.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 99.7

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 99.7

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

   4. Applied rewrites 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1900000000 \lor \neg \left(z \leq 200000000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right) \cdot y}{\mathsf{fma}\left(6.012459259764103 + z, z, 3.350343815022304\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 4.4\right):\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, -0.004191293246138338, y \cdot 0.004984943827291682\right), z, -0.00277777777751721 \cdot y\right), z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -245000.0) (not (<= z 4.4)))
   (fma y 0.0692910599291889 (+ x (* (/ y z) 0.07512208616047561)))
   (fma
    (fma
     (fma y -0.004191293246138338 (* y 0.004984943827291682))
     z
     (* -0.00277777777751721 y))
    z
    (fma 0.08333333333333323 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -245000.0) || !(z <= 4.4)) {
		tmp = fma(y, 0.0692910599291889, (x + ((y / z) * 0.07512208616047561)));
	} else {
		tmp = fma(fma(fma(y, -0.004191293246138338, (y * 0.004984943827291682)), z, (-0.00277777777751721 * y)), z, fma(0.08333333333333323, y, x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -245000.0) || !(z <= 4.4))
		tmp = fma(y, 0.0692910599291889, Float64(x + Float64(Float64(y / z) * 0.07512208616047561)));
	else
		tmp = fma(fma(fma(y, -0.004191293246138338, Float64(y * 0.004984943827291682)), z, Float64(-0.00277777777751721 * y)), z, fma(0.08333333333333323, y, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -245000.0], N[Not[LessEqual[z, 4.4]], $MachinePrecision]], N[(y * 0.0692910599291889 + N[(x + N[(N[(y / z), $MachinePrecision] * 0.07512208616047561), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -0.004191293246138338 + N[(y * 0.004984943827291682), $MachinePrecision]), $MachinePrecision] * z + N[(-0.00277777777751721 * y), $MachinePrecision]), $MachinePrecision] * z + N[(0.08333333333333323 * y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -245000 or 4.4000000000000004 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.07512208616047561, \frac{y}{z}, \mathsf{fma}\left(0.0692910599291889, y, x\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.2%

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

   if -245000 < z < 4.4000000000000004

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, -0.004191293246138338, y \cdot 0.004984943827291682\right), z, -0.00277777777751721 \cdot y\right), z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 4.4\right):\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, -0.004191293246138338, y \cdot 0.004984943827291682\right), z, -0.00277777777751721 \cdot y\right), z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 5.1\right):\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -245000.0) (not (<= z 5.1)))
   (fma y 0.0692910599291889 (+ x (* (/ y z) 0.07512208616047561)))
   (fma (* -0.00277777777751721 y) z (fma 0.08333333333333323 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -245000.0) || !(z <= 5.1)) {
		tmp = fma(y, 0.0692910599291889, (x + ((y / z) * 0.07512208616047561)));
	} 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 <= -245000.0) || !(z <= 5.1))
		tmp = fma(y, 0.0692910599291889, Float64(x + Float64(Float64(y / z) * 0.07512208616047561)));
	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, -245000.0], N[Not[LessEqual[z, 5.1]], $MachinePrecision]], N[(y * 0.0692910599291889 + N[(x + N[(N[(y / z), $MachinePrecision] * 0.07512208616047561), $MachinePrecision]), $MachinePrecision]), $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 < -245000 or 5.0999999999999996 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.07512208616047561, \frac{y}{z}, \mathsf{fma}\left(0.0692910599291889, y, x\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.2%

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

   if -245000 < z < 5.0999999999999996

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 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

   5. Applied rewrites 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 5.1\right):\\ \;\;\;\;\mathsf{fma}\left(y, 0.0692910599291889, x + \frac{y}{z} \cdot 0.07512208616047561\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245000:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.07512208616047561}{z} - -0.0692910599291889, y, x\right)\\ \mathbf{elif}\;z \leq 5.1:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.07512208616047561, \frac{y}{z}, \mathsf{fma}\left(0.0692910599291889, y, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -245000.0)
   (fma (- (/ 0.07512208616047561 z) -0.0692910599291889) y x)
   (if (<= z 5.1)
     (fma (* -0.00277777777751721 y) z (fma 0.08333333333333323 y x))
     (fma 0.07512208616047561 (/ y z) (fma 0.0692910599291889 y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -245000.0) {
		tmp = fma(((0.07512208616047561 / z) - -0.0692910599291889), y, x);
	} else if (z <= 5.1) {
		tmp = fma((-0.00277777777751721 * y), z, fma(0.08333333333333323, y, x));
	} else {
		tmp = fma(0.07512208616047561, (y / z), fma(0.0692910599291889, y, x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -245000.0)
		tmp = fma(Float64(Float64(0.07512208616047561 / z) - -0.0692910599291889), y, x);
	elseif (z <= 5.1)
		tmp = fma(Float64(-0.00277777777751721 * y), z, fma(0.08333333333333323, y, x));
	else
		tmp = fma(0.07512208616047561, Float64(y / z), fma(0.0692910599291889, y, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -245000.0], N[(N[(N[(0.07512208616047561 / z), $MachinePrecision] - -0.0692910599291889), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 5.1], N[(N[(-0.00277777777751721 * y), $MachinePrecision] * z + N[(0.08333333333333323 * y + x), $MachinePrecision]), $MachinePrecision], N[(0.07512208616047561 * N[(y / z), $MachinePrecision] + N[(0.0692910599291889 * y + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -245000

   1. Initial program 45.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 99.7%

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

   if -245000 < z < 5.0999999999999996

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 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

   5. Applied rewrites 99.3%

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

   if 5.0999999999999996 < z

   1. Initial program 44.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.07512208616047561, \frac{y}{z}, \mathsf{fma}\left(0.0692910599291889, y, x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.07512208616047561}{z} - -0.0692910599291889, y, x\right)\\ \mathbf{elif}\;z \leq 5.1:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.07512208616047561, \frac{y}{z}, \mathsf{fma}\left(0.0692910599291889, y, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 5.1\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{0.07512208616047561}{z} - -0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -245000.0) (not (<= z 5.1)))
   (fma (- (/ 0.07512208616047561 z) -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 <= -245000.0) || !(z <= 5.1)) {
		tmp = fma(((0.07512208616047561 / z) - -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 <= -245000.0) || !(z <= 5.1))
		tmp = fma(Float64(Float64(0.07512208616047561 / z) - -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, -245000.0], N[Not[LessEqual[z, 5.1]], $MachinePrecision]], N[(N[(N[(0.07512208616047561 / z), $MachinePrecision] - -0.0692910599291889), $MachinePrecision] * 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 < -245000 or 5.0999999999999996 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 99.2%

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

   if -245000 < z < 5.0999999999999996

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 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

   5. Applied rewrites 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 5.1\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{0.07512208616047561}{z} - -0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245000:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{elif}\;z \leq 5.1:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -245000.0)
   (+ x (* 0.0692910599291889 y))
   (if (<= z 5.1)
     (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 <= -245000.0) {
		tmp = x + (0.0692910599291889 * y);
	} else if (z <= 5.1) {
		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 <= -245000.0)
		tmp = Float64(x + Float64(0.0692910599291889 * y));
	elseif (z <= 5.1)
		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, -245000.0], N[(x + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1], 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 < -245000

   1. Initial program 45.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.4%

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

   if -245000 < z < 5.0999999999999996

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 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

   5. Applied rewrites 99.3%

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

   if 5.0999999999999996 < z

   1. Initial program 44.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 98.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{elif}\;z \leq 5.1:\\ \;\;\;\;\mathsf{fma}\left(-0.00277777777751721 \cdot y, z, \mathsf{fma}\left(0.08333333333333323, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 6.1\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -245000.0) (not (<= z 6.1)))
   (fma 0.0692910599291889 y x)
   (fma 0.08333333333333323 y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -245000.0) || !(z <= 6.1)) {
		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 <= -245000.0) || !(z <= 6.1))
		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, -245000.0], N[Not[LessEqual[z, 6.1]], $MachinePrecision]], N[(0.0692910599291889 * y + x), $MachinePrecision], N[(0.08333333333333323 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -245000 or 6.0999999999999996 < z

   1. Initial program 44.8%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 98.7%

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

   if -245000 < z < 6.0999999999999996

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000 \lor \neg \left(z \leq 6.1\right):\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -245000:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{elif}\;z \leq 6.1:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -245000.0)
   (+ x (* 0.0692910599291889 y))
   (if (<= z 6.1) (fma 0.08333333333333323 y x) (fma 0.0692910599291889 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -245000.0) {
		tmp = x + (0.0692910599291889 * y);
	} else if (z <= 6.1) {
		tmp = 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 <= -245000.0)
		tmp = Float64(x + Float64(0.0692910599291889 * y));
	elseif (z <= 6.1)
		tmp = fma(0.08333333333333323, y, x);
	else
		tmp = fma(0.0692910599291889, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -245000.0], N[(x + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1], N[(0.08333333333333323 * y + x), $MachinePrecision], N[(0.0692910599291889 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -245000

   1. Initial program 45.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 99.4%

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

   if -245000 < z < 6.0999999999999996

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.8%

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

   if 6.0999999999999996 < z

   1. Initial program 44.5%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 98.3%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -245000:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \mathbf{elif}\;z \leq 6.1:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+59} \lor \neg \left(y \leq 7.5 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+59) (not (<= y 7.5e+31))) (* y 0.0692910599291889) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+59) || !(y <= 7.5e+31)) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = 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 <= (-2.7d+59)) .or. (.not. (y <= 7.5d+31))) then
        tmp = y * 0.0692910599291889d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+59) || !(y <= 7.5e+31)) {
		tmp = y * 0.0692910599291889;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+59) or not (y <= 7.5e+31):
		tmp = y * 0.0692910599291889
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+59) || !(y <= 7.5e+31))
		tmp = Float64(y * 0.0692910599291889);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.7e+59) || ~((y <= 7.5e+31)))
		tmp = y * 0.0692910599291889;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+59], N[Not[LessEqual[y, 7.5e+31]], $MachinePrecision]], N[(y * 0.0692910599291889), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e59 or 7.5e31 < y

   1. Initial program 58.7%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 72.4%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 53.4%

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

   if -2.7000000000000001e59 < y < 7.5e31

   1. Initial program 81.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 80.1%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+59} \lor \neg \left(y \leq 7.5 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot 0.0692910599291889\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.6% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.0692910599291889, y, x\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z)
	return fma(0.0692910599291889, y, x)
end

Wolfram

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

Derivation

1. Initial program 72.1%

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

3. Taylor expanded in z around inf

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

5. Applied rewrites 83.0%

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

6. Final simplification 83.0%

   \[\leadsto \mathsf{fma}\left(0.0692910599291889, y, x\right) \]
7. Add Preprocessing

Alternative 12: 51.1% accurate, 47.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 72.1%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Applied rewrites 55.8%

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

6. Final simplification 55.8%

   \[\leadsto x \]
7. 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 2025018 
(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))))