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

Percentage Accurate: 70.1% → 99.5%

Time: 6.7s

Alternatives: 11

Speedup: 5.0×

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: 70.1% 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, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)\\ \mathbf{if}\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), \frac{z}{t\_0} \cdot y, \mathsf{fma}\left(\frac{0.279195317918525}{t\_0}, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (- z -6.012459259764103) z 3.350343815022304)))
   (if (<=
        (+
         x
         (/
          (*
           y
           (+
            (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
            0.279195317918525))
          (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
        INFINITY)
     (fma
      (fma 0.0692910599291889 z 0.4917317610505968)
      (* (/ z t_0) y)
      (fma (/ 0.279195317918525 t_0) y x))
     (+
      x
      (fma
       -1.0
       (/ (- (* -0.4917317610505968 y) (* -0.4166096748901212 y)) z)
       (* 0.0692910599291889 y))))))

C

double code(double x, double y, double z) {
	double t_0 = fma((z - -6.012459259764103), z, 3.350343815022304);
	double tmp;
	if ((x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))) <= ((double) INFINITY)) {
		tmp = fma(fma(0.0692910599291889, z, 0.4917317610505968), ((z / t_0) * y), fma((0.279195317918525 / t_0), y, x));
	} else {
		tmp = x + fma(-1.0, (((-0.4917317610505968 * y) - (-0.4166096748901212 * y)) / z), (0.0692910599291889 * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(z - -6.012459259764103), z, 3.350343815022304)
	tmp = 0.0
	if (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))) <= Inf)
		tmp = fma(fma(0.0692910599291889, z, 0.4917317610505968), Float64(Float64(z / t_0) * y), fma(Float64(0.279195317918525 / t_0), y, x));
	else
		tmp = Float64(x + fma(-1.0, Float64(Float64(Float64(-0.4917317610505968 * y) - Float64(-0.4166096748901212 * y)) / z), Float64(0.0692910599291889 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - -6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]}, If[LessEqual[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], Infinity], N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * N[(N[(z / t$95$0), $MachinePrecision] * y), $MachinePrecision] + N[(N[(0.279195317918525 / t$95$0), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(N[(-0.4917317610505968 * y), $MachinePrecision] - N[(-0.4166096748901212 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))) < +inf.0

   1. Initial program 70.1%

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

   3. Applied rewrites 87.9%

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

   if +inf.0 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))))

   1. Initial program 70.1%

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

   2. Taylor expanded in z around -inf

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      2. lower-/.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      3. lower--.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      6. lower-*.f64 63.6

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right) \]

   4. Applied rewrites 63.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)\\ \mathbf{if}\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(z, \mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right) \cdot \frac{y}{t\_0}, \mathsf{fma}\left(\frac{0.279195317918525}{t\_0}, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fma (- z -6.012459259764103) z 3.350343815022304)))
   (if (<=
        (+
         x
         (/
          (*
           y
           (+
            (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
            0.279195317918525))
          (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
        INFINITY)
     (fma
      z
      (* (fma 0.0692910599291889 z 0.4917317610505968) (/ y t_0))
      (fma (/ 0.279195317918525 t_0) y x))
     (+
      x
      (fma
       -1.0
       (/ (- (* -0.4917317610505968 y) (* -0.4166096748901212 y)) z)
       (* 0.0692910599291889 y))))))

C

double code(double x, double y, double z) {
	double t_0 = fma((z - -6.012459259764103), z, 3.350343815022304);
	double tmp;
	if ((x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))) <= ((double) INFINITY)) {
		tmp = fma(z, (fma(0.0692910599291889, z, 0.4917317610505968) * (y / t_0)), fma((0.279195317918525 / t_0), y, x));
	} else {
		tmp = x + fma(-1.0, (((-0.4917317610505968 * y) - (-0.4166096748901212 * y)) / z), (0.0692910599291889 * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(z - -6.012459259764103), z, 3.350343815022304)
	tmp = 0.0
	if (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))) <= Inf)
		tmp = fma(z, Float64(fma(0.0692910599291889, z, 0.4917317610505968) * Float64(y / t_0)), fma(Float64(0.279195317918525 / t_0), y, x));
	else
		tmp = Float64(x + fma(-1.0, Float64(Float64(Float64(-0.4917317610505968 * y) - Float64(-0.4166096748901212 * y)) / z), Float64(0.0692910599291889 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z - -6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]}, If[LessEqual[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], Infinity], N[(z * N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * N[(y / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[(0.279195317918525 / t$95$0), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(N[(-0.4917317610505968 * y), $MachinePrecision] - N[(-0.4166096748901212 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))) < +inf.0

   1. Initial program 70.1%

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

   3. Applied rewrites 87.2%

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

   if +inf.0 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))))

   1. Initial program 70.1%

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

   2. Taylor expanded in z around -inf

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      2. lower-/.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      3. lower--.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      6. lower-*.f64 63.6

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right) \]

   4. Applied rewrites 63.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right) \cdot 0.16632129330041143}, \frac{y}{6.012459259764103}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (+
       x
       (/
        (*
         y
         (+
          (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
          0.279195317918525))
        (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
      5e+303)
   (fma
    (/
     (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
     (*
      (fma (- z -6.012459259764103) z 3.350343815022304)
      0.16632129330041143))
    (/ y 6.012459259764103)
    x)
   (+
    x
    (fma
     -1.0
     (/ (- (* -0.4917317610505968 y) (* -0.4166096748901212 y)) z)
     (* 0.0692910599291889 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))) <= 5e+303) {
		tmp = fma((fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525) / (fma((z - -6.012459259764103), z, 3.350343815022304) * 0.16632129330041143)), (y / 6.012459259764103), x);
	} else {
		tmp = x + fma(-1.0, (((-0.4917317610505968 * y) - (-0.4166096748901212 * y)) / z), (0.0692910599291889 * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (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))) <= 5e+303)
		tmp = fma(Float64(fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525) / Float64(fma(Float64(z - -6.012459259764103), z, 3.350343815022304) * 0.16632129330041143)), Float64(y / 6.012459259764103), x);
	else
		tmp = Float64(x + fma(-1.0, Float64(Float64(Float64(-0.4917317610505968 * y) - Float64(-0.4166096748901212 * y)) / z), Float64(0.0692910599291889 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[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], 5e+303], N[(N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] / N[(N[(N[(z - -6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision] * 0.16632129330041143), $MachinePrecision]), $MachinePrecision] * N[(y / 6.012459259764103), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(N[(-0.4917317610505968 * y), $MachinePrecision] - N[(-0.4166096748901212 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))) < 4.9999999999999997e303

   1. Initial program 70.1%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. distribute-lft-in N/A

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

      8. associate--l+ N/A

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

      9. sum-to-mult N/A

         \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\color{blue}{\left(1 + \frac{z \cdot z - \left(\mathsf{neg}\left(\frac{104698244219447}{31250000000000}\right)\right)}{z \cdot \frac{6012459259764103}{1000000000000000}}\right) \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)}} \]

      10. lower-special-*.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\color{blue}{\left(1 + \frac{z \cdot z - \left(\mathsf{neg}\left(\frac{104698244219447}{31250000000000}\right)\right)}{z \cdot \frac{6012459259764103}{1000000000000000}}\right) \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)}} \]

      11. lower-special-+.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\color{blue}{\left(1 + \frac{z \cdot z - \left(\mathsf{neg}\left(\frac{104698244219447}{31250000000000}\right)\right)}{z \cdot \frac{6012459259764103}{1000000000000000}}\right)} \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)} \]

      12. lower-special-/.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(1 + \color{blue}{\frac{z \cdot z - \left(\mathsf{neg}\left(\frac{104698244219447}{31250000000000}\right)\right)}{z \cdot \frac{6012459259764103}{1000000000000000}}}\right) \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)} \]

      13. add-flip-rev N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(1 + \frac{\color{blue}{z \cdot z + \frac{104698244219447}{31250000000000}}}{z \cdot \frac{6012459259764103}{1000000000000000}}\right) \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)} \]

      14. lower-fma.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(1 + \frac{\color{blue}{\mathsf{fma}\left(z, z, \frac{104698244219447}{31250000000000}\right)}}{z \cdot \frac{6012459259764103}{1000000000000000}}\right) \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)} \]

      15. *-commutative N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(1 + \frac{\mathsf{fma}\left(z, z, \frac{104698244219447}{31250000000000}\right)}{\color{blue}{\frac{6012459259764103}{1000000000000000} \cdot z}}\right) \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)} \]

      16. lower-*.f64 N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(1 + \frac{\mathsf{fma}\left(z, z, \frac{104698244219447}{31250000000000}\right)}{\color{blue}{\frac{6012459259764103}{1000000000000000} \cdot z}}\right) \cdot \left(z \cdot \frac{6012459259764103}{1000000000000000}\right)} \]

      17. *-commutative N/A

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot \frac{692910599291889}{10000000000000000} + \frac{307332350656623}{625000000000000}\right) \cdot z + \frac{11167812716741}{40000000000000}\right)}{\left(1 + \frac{\mathsf{fma}\left(z, z, \frac{104698244219447}{31250000000000}\right)}{\frac{6012459259764103}{1000000000000000} \cdot z}\right) \cdot \color{blue}{\left(\frac{6012459259764103}{1000000000000000} \cdot z\right)}} \]

      18. lower-*.f64 70.1

          \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(1 + \frac{\mathsf{fma}\left(z, z, 3.350343815022304\right)}{6.012459259764103 \cdot z}\right) \cdot \color{blue}{\left(6.012459259764103 \cdot z\right)}} \]

   3. Applied rewrites 70.1%

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\color{blue}{\left(1 + \frac{\mathsf{fma}\left(z, z, 3.350343815022304\right)}{6.012459259764103 \cdot z}\right) \cdot \left(6.012459259764103 \cdot z\right)}} \]

   5. Applied rewrites 75.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right)}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right) \cdot 0.16632129330041143}, \frac{y}{6.012459259764103}, x\right)} \]

   if 4.9999999999999997e303 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))))

   1. Initial program 70.1%

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

   2. Taylor expanded in z around -inf

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      2. lower-/.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      3. lower--.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      6. lower-*.f64 63.6

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right) \]

   4. Applied rewrites 63.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (+
       x
       (/
        (*
         y
         (+
          (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
          0.279195317918525))
        (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
      INFINITY)
   (fma
    (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
    (/ y (fma (- z -6.012459259764103) z 3.350343815022304))
    x)
   (+
    x
    (fma
     -1.0
     (/ (- (* -0.4917317610505968 y) (* -0.4166096748901212 y)) z)
     (* 0.0692910599291889 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))) <= ((double) INFINITY)) {
		tmp = fma(fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525), (y / fma((z - -6.012459259764103), z, 3.350343815022304)), x);
	} else {
		tmp = x + fma(-1.0, (((-0.4917317610505968 * y) - (-0.4166096748901212 * y)) / z), (0.0692910599291889 * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (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))) <= Inf)
		tmp = fma(fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525), Float64(y / fma(Float64(z - -6.012459259764103), z, 3.350343815022304)), x);
	else
		tmp = Float64(x + fma(-1.0, Float64(Float64(Float64(-0.4917317610505968 * y) - Float64(-0.4166096748901212 * y)) / z), Float64(0.0692910599291889 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[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], Infinity], N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] * N[(y / N[(N[(z - -6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(-1.0 * N[(N[(N[(-0.4917317610505968 * y), $MachinePrecision] - N[(-0.4166096748901212 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))) < +inf.0

   1. Initial program 70.1%

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

   3. Applied rewrites 74.7%

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

   if +inf.0 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64))))

   1. Initial program 70.1%

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

   2. Taylor expanded in z around -inf

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z} + \frac{692910599291889}{10000000000000000} \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \color{blue}{\frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      2. lower-/.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{\color{blue}{z}}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      3. lower--.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{\frac{-307332350656623}{625000000000000} \cdot y - \frac{-4166096748901211929300981260567}{10000000000000000000000000000000} \cdot y}{z}, \frac{692910599291889}{10000000000000000} \cdot y\right) \]

      6. lower-*.f64 63.6

         \[\leadsto x + \mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right) \]

   4. Applied rewrites 63.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(-1, \frac{-0.4917317610505968 \cdot y - -0.4166096748901212 \cdot y}{z}, 0.0692910599291889 \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}, y, x\right)\\ \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323 + z \cdot \left(z \cdot \left(0.0007936505811533442 + -0.0005951669793454025 \cdot z\right) - 0.00277777777751721\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma (+ 0.0692910599291889 (* 0.07512208616047561 (/ 1.0 z))) y x)))
   (if (<= z -16200000000.0)
     t_0
     (if (<= z 3.0)
       (fma
        (+
         0.08333333333333323
         (*
          z
          (-
           (* z (+ 0.0007936505811533442 (* -0.0005951669793454025 z)))
           0.00277777777751721)))
        y
        x)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((0.0692910599291889 + (0.07512208616047561 * (1.0 / z))), y, x);
	double tmp;
	if (z <= -16200000000.0) {
		tmp = t_0;
	} else if (z <= 3.0) {
		tmp = fma((0.08333333333333323 + (z * ((z * (0.0007936505811533442 + (-0.0005951669793454025 * z))) - 0.00277777777751721))), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(0.0692910599291889 + Float64(0.07512208616047561 * Float64(1.0 / z))), y, x)
	tmp = 0.0
	if (z <= -16200000000.0)
		tmp = t_0;
	elseif (z <= 3.0)
		tmp = fma(Float64(0.08333333333333323 + Float64(z * Float64(Float64(z * Float64(0.0007936505811533442 + Float64(-0.0005951669793454025 * z))) - 0.00277777777751721))), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.0692910599291889 + N[(0.07512208616047561 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -16200000000.0], t$95$0, If[LessEqual[z, 3.0], N[(N[(0.08333333333333323 + N[(z * N[(N[(z * N[(0.0007936505811533442 + N[(-0.0005951669793454025 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.62e10 or 3 < z

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000} + \frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{692910599291889}{10000000000000000} + \color{blue}{\frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{692910599291889}{10000000000000000} + \frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \color{blue}{\frac{1}{z}}, y, x\right) \]

      3. lower-/.f64 63.6

         \[\leadsto \mathsf{fma}\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{\color{blue}{z}}, y, x\right) \]

   6. Applied rewrites 63.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}}, y, x\right) \]

   if -1.62e10 < z < 3

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{279195317918525}{3350343815022304} + z \cdot \left(z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} + \frac{-374943941275717765274452559944207169728571246668095556552487}{629981088144543617699065742275429975113587435159029727787745280} \cdot z\right) - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right)}, y, x\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + \color{blue}{z \cdot \left(z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} + \frac{-374943941275717765274452559944207169728571246668095556552487}{629981088144543617699065742275429975113587435159029727787745280} \cdot z\right) - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right)}, y, x\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + z \cdot \color{blue}{\left(z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} + \frac{-374943941275717765274452559944207169728571246668095556552487}{629981088144543617699065742275429975113587435159029727787745280} \cdot z\right) - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right)}, y, x\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + z \cdot \left(z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} + \frac{-374943941275717765274452559944207169728571246668095556552487}{629981088144543617699065742275429975113587435159029727787745280} \cdot z\right) - \color{blue}{\frac{155900051080628738716045985239}{56124018394291031809500087342080}}\right), y, x\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + z \cdot \left(z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} + \frac{-374943941275717765274452559944207169728571246668095556552487}{629981088144543617699065742275429975113587435159029727787745280} \cdot z\right) - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right), y, x\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + z \cdot \left(z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} + \frac{-374943941275717765274452559944207169728571246668095556552487}{629981088144543617699065742275429975113587435159029727787745280} \cdot z\right) - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right), y, x\right) \]

      6. lower-*.f64 57.5

         \[\leadsto \mathsf{fma}\left(0.08333333333333323 + z \cdot \left(z \cdot \left(0.0007936505811533442 + -0.0005951669793454025 \cdot z\right) - 0.00277777777751721\right), y, x\right) \]

   6. Applied rewrites 57.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.08333333333333323 + z \cdot \left(z \cdot \left(0.0007936505811533442 + -0.0005951669793454025 \cdot z\right) - 0.00277777777751721\right)}, y, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 98.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}, y, x\right)\\ \mathbf{if}\;z \leq -16200000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.4:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323 + z \cdot \left(0.0007936505811533442 \cdot z - 0.00277777777751721\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma (+ 0.0692910599291889 (* 0.07512208616047561 (/ 1.0 z))) y x)))
   (if (<= z -16200000000.0)
     t_0
     (if (<= z 4.4)
       (fma
        (+
         0.08333333333333323
         (* z (- (* 0.0007936505811533442 z) 0.00277777777751721)))
        y
        x)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((0.0692910599291889 + (0.07512208616047561 * (1.0 / z))), y, x);
	double tmp;
	if (z <= -16200000000.0) {
		tmp = t_0;
	} else if (z <= 4.4) {
		tmp = fma((0.08333333333333323 + (z * ((0.0007936505811533442 * z) - 0.00277777777751721))), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(0.0692910599291889 + Float64(0.07512208616047561 * Float64(1.0 / z))), y, x)
	tmp = 0.0
	if (z <= -16200000000.0)
		tmp = t_0;
	elseif (z <= 4.4)
		tmp = fma(Float64(0.08333333333333323 + Float64(z * Float64(Float64(0.0007936505811533442 * z) - 0.00277777777751721))), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.0692910599291889 + N[(0.07512208616047561 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -16200000000.0], t$95$0, If[LessEqual[z, 4.4], N[(N[(0.08333333333333323 + N[(z * N[(N[(0.0007936505811533442 * z), $MachinePrecision] - 0.00277777777751721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.62e10 or 4.4000000000000004 < z

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000} + \frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{692910599291889}{10000000000000000} + \color{blue}{\frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{692910599291889}{10000000000000000} + \frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \color{blue}{\frac{1}{z}}, y, x\right) \]

      3. lower-/.f64 63.6

         \[\leadsto \mathsf{fma}\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{\color{blue}{z}}, y, x\right) \]

   6. Applied rewrites 63.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}}, y, x\right) \]

   if -1.62e10 < z < 4.4000000000000004

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{279195317918525}{3350343815022304} + z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} \cdot z - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right)}, y, x\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + \color{blue}{z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} \cdot z - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right)}, y, x\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + z \cdot \color{blue}{\left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} \cdot z - \frac{155900051080628738716045985239}{56124018394291031809500087342080}\right)}, y, x\right) \]

      3. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{279195317918525}{3350343815022304} + z \cdot \left(\frac{149233894885562575800992648418763933371314529}{188034757901510979839193143041976607183277752320} \cdot z - \color{blue}{\frac{155900051080628738716045985239}{56124018394291031809500087342080}}\right), y, x\right) \]

      4. lower-*.f64 60.6

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

   6. Applied rewrites 60.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.08333333333333323 + z \cdot \left(0.0007936505811533442 \cdot z - 0.00277777777751721\right)}, y, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 98.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}, y, x\right)\\ \mathbf{if}\;z \leq -180000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, -0.00277777777751721, 0.08333333333333323\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (fma (+ 0.0692910599291889 (* 0.07512208616047561 (/ 1.0 z))) y x)))
   (if (<= z -180000000000.0)
     t_0
     (if (<= z 5.0)
       (fma (fma z -0.00277777777751721 0.08333333333333323) y x)
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma((0.0692910599291889 + (0.07512208616047561 * (1.0 / z))), y, x);
	double tmp;
	if (z <= -180000000000.0) {
		tmp = t_0;
	} else if (z <= 5.0) {
		tmp = fma(fma(z, -0.00277777777751721, 0.08333333333333323), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(Float64(0.0692910599291889 + Float64(0.07512208616047561 * Float64(1.0 / z))), y, x)
	tmp = 0.0
	if (z <= -180000000000.0)
		tmp = t_0;
	elseif (z <= 5.0)
		tmp = fma(fma(z, -0.00277777777751721, 0.08333333333333323), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.0692910599291889 + N[(0.07512208616047561 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -180000000000.0], t$95$0, If[LessEqual[z, 5.0], N[(N[(z * -0.00277777777751721 + 0.08333333333333323), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e11 or 5 < z

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000} + \frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{692910599291889}{10000000000000000} + \color{blue}{\frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{692910599291889}{10000000000000000} + \frac{751220861604756070699018739433}{10000000000000000000000000000000} \cdot \color{blue}{\frac{1}{z}}, y, x\right) \]

      3. lower-/.f64 63.6

         \[\leadsto \mathsf{fma}\left(0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{\color{blue}{z}}, y, x\right) \]

   6. Applied rewrites 63.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.0692910599291889 + 0.07512208616047561 \cdot \frac{1}{z}}, y, x\right) \]

   if -1.8e11 < z < 5

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{279195317918525}{3350343815022304} + \frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot z}, y, x\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 66.7

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

   6. Applied rewrites 66.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.08333333333333323 + -0.00277777777751721 \cdot z}, y, x\right) \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 66.7

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

   8. Applied rewrites 66.7%

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

Alternative 8: 98.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -180000000000:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{elif}\;z \leq 5:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, -0.00277777777751721, 0.08333333333333323\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -180000000000.0)
   (fma 0.0692910599291889 y x)
   (if (<= z 5.0)
     (fma (fma z -0.00277777777751721 0.08333333333333323) y x)
     (fma 0.0692910599291889 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -180000000000.0) {
		tmp = fma(0.0692910599291889, y, x);
	} else if (z <= 5.0) {
		tmp = fma(fma(z, -0.00277777777751721, 0.08333333333333323), y, x);
	} else {
		tmp = fma(0.0692910599291889, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -180000000000.0)
		tmp = fma(0.0692910599291889, y, x);
	elseif (z <= 5.0)
		tmp = fma(fma(z, -0.00277777777751721, 0.08333333333333323), y, x);
	else
		tmp = fma(0.0692910599291889, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -180000000000.0], N[(0.0692910599291889 * y + x), $MachinePrecision], If[LessEqual[z, 5.0], N[(N[(z * -0.00277777777751721 + 0.08333333333333323), $MachinePrecision] * y + x), $MachinePrecision], N[(0.0692910599291889 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e11 or 5 < z

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000}}, y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 78.6%

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

   if -1.8e11 < z < 5

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{279195317918525}{3350343815022304} + \frac{-155900051080628738716045985239}{56124018394291031809500087342080} \cdot z}, y, x\right) \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 66.7

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

   6. Applied rewrites 66.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{0.08333333333333323 + -0.00277777777751721 \cdot z}, y, x\right) \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 66.7

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

   8. Applied rewrites 66.7%

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

Alternative 9: 98.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -180000000000:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{elif}\;z \leq 5.8:\\ \;\;\;\;x - -0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -180000000000.0)
   (fma 0.0692910599291889 y x)
   (if (<= z 5.8)
     (- x (* -0.08333333333333323 y))
     (fma 0.0692910599291889 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -180000000000.0) {
		tmp = fma(0.0692910599291889, y, x);
	} else if (z <= 5.8) {
		tmp = x - (-0.08333333333333323 * y);
	} else {
		tmp = fma(0.0692910599291889, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -180000000000.0)
		tmp = fma(0.0692910599291889, y, x);
	elseif (z <= 5.8)
		tmp = Float64(x - Float64(-0.08333333333333323 * y));
	else
		tmp = fma(0.0692910599291889, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -180000000000.0], N[(0.0692910599291889 * y + x), $MachinePrecision], If[LessEqual[z, 5.8], N[(x - N[(-0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], N[(0.0692910599291889 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e11 or 5.79999999999999982 < z

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000}}, y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 78.6%

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

   if -1.8e11 < z < 5.79999999999999982

   1. Initial program 70.1%

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

   3. Applied rewrites 87.9%

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

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{692910599291889}{10000000000000000}, z, \frac{307332350656623}{625000000000000}\right), \color{blue}{\frac{y}{z}}, \mathsf{fma}\left(\frac{\frac{11167812716741}{40000000000000}}{\mathsf{fma}\left(z - \frac{-6012459259764103}{1000000000000000}, z, \frac{104698244219447}{31250000000000}\right)}, y, x\right)\right) \]
   5. Step-by-step derivation

      1. lower-/.f64 61.6

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

   6. Applied rewrites 61.6%

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

   8. Applied rewrites 61.6%

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

   9. Taylor expanded in z around 0

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

       1. lower-*.f64 80.5

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

   11. Applied rewrites 80.5%

       \[\leadsto x - \color{blue}{-0.08333333333333323 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 98.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -180000000000:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \mathbf{elif}\;z \leq 5.8:\\ \;\;\;\;\mathsf{fma}\left(0.08333333333333323, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0692910599291889, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -180000000000.0)
   (fma 0.0692910599291889 y x)
   (if (<= z 5.8) (fma 0.08333333333333323 y x) (fma 0.0692910599291889 y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -180000000000.0) {
		tmp = fma(0.0692910599291889, y, x);
	} else if (z <= 5.8) {
		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 <= -180000000000.0)
		tmp = fma(0.0692910599291889, y, x);
	elseif (z <= 5.8)
		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, -180000000000.0], N[(0.0692910599291889 * y + x), $MachinePrecision], If[LessEqual[z, 5.8], N[(0.08333333333333323 * y + x), $MachinePrecision], N[(0.0692910599291889 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e11 or 5.79999999999999982 < z

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000}}, y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 78.6%

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

   if -1.8e11 < z < 5.79999999999999982

   1. Initial program 70.1%

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

   3. Applied rewrites 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000}}, y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 78.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{279195317918525}{3350343815022304}}, y, x\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 80.5%

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

Alternative 11: 78.6% accurate, 5.0× 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 70.1%

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

3. Applied rewrites 75.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right), z, -0.279195317918525\right), y, x\right)} \]

4. Taylor expanded in z around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{692910599291889}{10000000000000000}}, y, x\right) \]
5. Step-by-step derivation

6. Applied rewrites 78.6%

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

Reproduce

herbie shell --seed 2025150 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64
  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))