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

Percentage Accurate: 69.0% → 99.4%

Time: 4.5s

Alternatives: 8

Speedup: 4.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.0% 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: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -0.4166096748901212, y \cdot \left(0.0692910599291889 - \frac{-0.4917317610505968}{z}\right)\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-5}:\\ \;\;\;\;x + 0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -0.4166096748901212, y \cdot \frac{\mathsf{fma}\left(z, 0.0692910599291889, 0.4917317610505968\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (+
    x
    (fma
     (/ y z)
     -0.4166096748901212
     (* y (- 0.0692910599291889 (/ -0.4917317610505968 z)))))
   (if (<= z 1.26e-5)
     (+ x (* 0.08333333333333323 y))
     (+
      x
      (fma
       (/ y z)
       -0.4166096748901212
       (* y (/ (fma z 0.0692910599291889 0.4917317610505968) z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = x + fma((y / z), -0.4166096748901212, (y * (0.0692910599291889 - (-0.4917317610505968 / z))));
	} else if (z <= 1.26e-5) {
		tmp = x + (0.08333333333333323 * y);
	} else {
		tmp = x + fma((y / z), -0.4166096748901212, (y * (fma(z, 0.0692910599291889, 0.4917317610505968) / z)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(x + fma(Float64(y / z), -0.4166096748901212, Float64(y * Float64(0.0692910599291889 - Float64(-0.4917317610505968 / z)))));
	elseif (z <= 1.26e-5)
		tmp = Float64(x + Float64(0.08333333333333323 * y));
	else
		tmp = Float64(x + fma(Float64(y / z), -0.4166096748901212, Float64(y * Float64(fma(z, 0.0692910599291889, 0.4917317610505968) / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(x + N[(N[(y / z), $MachinePrecision] * -0.4166096748901212 + N[(y * N[(0.0692910599291889 - N[(-0.4917317610505968 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e-5], N[(x + N[(0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -0.4166096748901212 + N[(y * N[(N[(z * 0.0692910599291889 + 0.4917317610505968), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.8

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

   4. Applied rewrites 64.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(0.0692910599291889, y, 0.4917317610505968 \cdot \frac{y}{z}\right) - 0.4166096748901212 \cdot \frac{y}{z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. add-flip N/A

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

      6. sub-flip-reverse N/A

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

      7. *-commutative N/A

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

      8. lift-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip N/A

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

      15. +-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. lift-fma.f64 N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval 64.8

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

      20. lift-fma.f64 N/A

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

   6. Applied rewrites 64.8%

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

   if -5.4000000000000004 < z < 1.25999999999999996e-5

   1. Initial program 69.0%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

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

   if 1.25999999999999996e-5 < z

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.8

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

   4. Applied rewrites 64.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(0.0692910599291889, y, 0.4917317610505968 \cdot \frac{y}{z}\right) - 0.4166096748901212 \cdot \frac{y}{z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. add-flip N/A

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

      6. sub-flip-reverse N/A

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

      7. *-commutative N/A

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

      8. lift-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip N/A

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

      15. +-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. lift-fma.f64 N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval 64.8

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

      20. lift-fma.f64 N/A

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

   6. Applied rewrites 64.8%

      \[\leadsto x + \mathsf{fma}\left(\frac{y}{z}, \color{blue}{-0.4166096748901212}, y \cdot \left(0.0692910599291889 - \frac{-0.4917317610505968}{z}\right)\right) \]
   7. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. lift-/.f64 N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. add-to-fraction-rev N/A

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

      7. lift-fma.f64 N/A

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

      8. lower-/.f64 64.8

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

      9. lift-fma.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. add-flip N/A

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

      12. lift-*.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. metadata-eval N/A

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

      16. add-flip N/A

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

      17. lower-fma.f64 64.8

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

   8. Applied rewrites 64.8%

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

Alternative 2: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \mathsf{fma}\left(\frac{y}{z}, -0.4166096748901212, y \cdot \left(0.0692910599291889 - \frac{-0.4917317610505968}{z}\right)\right)\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-5}:\\ \;\;\;\;x + 0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          x
          (fma
           (/ y z)
           -0.4166096748901212
           (* y (- 0.0692910599291889 (/ -0.4917317610505968 z)))))))
   (if (<= z -5.4)
     t_0
     (if (<= z 1.26e-5) (+ x (* 0.08333333333333323 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + fma((y / z), -0.4166096748901212, (y * (0.0692910599291889 - (-0.4917317610505968 / z))));
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 1.26e-5) {
		tmp = x + (0.08333333333333323 * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + fma(Float64(y / z), -0.4166096748901212, Float64(y * Float64(0.0692910599291889 - Float64(-0.4917317610505968 / z)))))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 1.26e-5)
		tmp = Float64(x + Float64(0.08333333333333323 * y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(N[(y / z), $MachinePrecision] * -0.4166096748901212 + N[(y * N[(0.0692910599291889 - N[(-0.4917317610505968 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 1.26e-5], N[(x + N[(0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 1.25999999999999996e-5 < z

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.8

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

   4. Applied rewrites 64.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(0.0692910599291889, y, 0.4917317610505968 \cdot \frac{y}{z}\right) - 0.4166096748901212 \cdot \frac{y}{z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. add-flip N/A

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

      6. sub-flip-reverse N/A

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

      7. *-commutative N/A

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

      8. lift-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. +-commutative N/A

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

      11. add-flip N/A

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

      12. sub-negate N/A

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

      13. sub-negate-rev N/A

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

      14. add-flip N/A

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

      15. +-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. lift-fma.f64 N/A

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

      18. lower-fma.f64 N/A

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

      19. metadata-eval 64.8

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

      20. lift-fma.f64 N/A

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

   6. Applied rewrites 64.8%

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

   if -5.4000000000000004 < z < 1.25999999999999996e-5

   1. Initial program 69.0%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

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

Alternative 3: 98.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right) + x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-5}:\\ \;\;\;\;x + 0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(y, 0.0692910599291889, \frac{y}{z} \cdot 0.07512208616047561\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4)
   (+ (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))) x)
   (if (<= z 1.26e-5)
     (+ x (* 0.08333333333333323 y))
     (+ x (fma y 0.0692910599291889 (* (/ y z) 0.07512208616047561))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4) {
		tmp = (y * (0.0692910599291889 + (0.07512208616047561 / z))) + x;
	} else if (z <= 1.26e-5) {
		tmp = x + (0.08333333333333323 * y);
	} else {
		tmp = x + fma(y, 0.0692910599291889, ((y / z) * 0.07512208616047561));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4)
		tmp = Float64(Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))) + x);
	elseif (z <= 1.26e-5)
		tmp = Float64(x + Float64(0.08333333333333323 * y));
	else
		tmp = Float64(x + fma(y, 0.0692910599291889, Float64(Float64(y / z) * 0.07512208616047561)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4], N[(N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.26e-5], N[(x + N[(0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 0.0692910599291889 + N[(N[(y / z), $MachinePrecision] * 0.07512208616047561), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000004

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.8

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

   4. Applied rewrites 64.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(0.0692910599291889, y, 0.4917317610505968 \cdot \frac{y}{z}\right) - 0.4166096748901212 \cdot \frac{y}{z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-+l- N/A

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

      9. sub-flip N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. distribute-neg-out N/A

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

      15. metadata-eval N/A

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

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

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. sub-flip N/A

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

   6. Applied rewrites 65.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 65.2

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

   8. Applied rewrites 65.2%

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

   if -5.4000000000000004 < z < 1.25999999999999996e-5

   1. Initial program 69.0%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

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

   if 1.25999999999999996e-5 < z

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.8

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

   4. Applied rewrites 64.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(0.0692910599291889, y, 0.4917317610505968 \cdot \frac{y}{z}\right) - 0.4166096748901212 \cdot \frac{y}{z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-+l- N/A

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

      9. sub-flip N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. distribute-neg-out N/A

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

      15. metadata-eval N/A

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

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

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. sub-flip N/A

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

   6. Applied rewrites 65.2%

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

Alternative 4: 98.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(0.0692910599291889 + \frac{0.07512208616047561}{z}\right) + x\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-5}:\\ \;\;\;\;x + 0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y (+ 0.0692910599291889 (/ 0.07512208616047561 z))) x)))
   (if (<= z -5.4)
     t_0
     (if (<= z 1.26e-5) (+ x (* 0.08333333333333323 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * (0.0692910599291889 + (0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 1.26e-5) {
		tmp = x + (0.08333333333333323 * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * (0.0692910599291889d0 + (0.07512208616047561d0 / z))) + x
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 1.26d-5) then
        tmp = x + (0.08333333333333323d0 * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * (0.0692910599291889 + (0.07512208616047561 / z))) + x;
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 1.26e-5) {
		tmp = x + (0.08333333333333323 * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * (0.0692910599291889 + (0.07512208616047561 / z))) + x
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 1.26e-5:
		tmp = x + (0.08333333333333323 * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * Float64(0.0692910599291889 + Float64(0.07512208616047561 / z))) + x)
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 1.26e-5)
		tmp = Float64(x + Float64(0.08333333333333323 * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * (0.0692910599291889 + (0.07512208616047561 / z))) + x;
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 1.26e-5)
		tmp = x + (0.08333333333333323 * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * N[(0.0692910599291889 + N[(0.07512208616047561 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 1.26e-5], N[(x + N[(0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 1.25999999999999996e-5 < z

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 64.8

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

   4. Applied rewrites 64.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(0.0692910599291889, y, 0.4917317610505968 \cdot \frac{y}{z}\right) - 0.4166096748901212 \cdot \frac{y}{z}\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-+l- N/A

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

      9. sub-flip N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. distribute-neg-out N/A

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

      15. metadata-eval N/A

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

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

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. sub-flip N/A

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

   6. Applied rewrites 65.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 65.2

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

   8. Applied rewrites 65.2%

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

   if -5.4000000000000004 < z < 1.25999999999999996e-5

   1. Initial program 69.0%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

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

Alternative 5: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right)}{\mathsf{fma}\left(-6.012459259764103 - z, z, -3.350343815022304\right)} \cdot y, \mathsf{fma}\left(\frac{0.279195317918525}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)}, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (+
       x
       (/
        (*
         y
         (+
          (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
          0.279195317918525))
        (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
      2e+306)
   (fma
    z
    (*
     (/
      (fma -0.0692910599291889 z -0.4917317610505968)
      (fma (- -6.012459259764103 z) z -3.350343815022304))
     y)
    (fma
     (/ 0.279195317918525 (fma (- z -6.012459259764103) z 3.350343815022304))
     y
     x))
   (+ x (* 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))) <= 2e+306) {
		tmp = fma(z, ((fma(-0.0692910599291889, z, -0.4917317610505968) / fma((-6.012459259764103 - z), z, -3.350343815022304)) * y), fma((0.279195317918525 / fma((z - -6.012459259764103), z, 3.350343815022304)), y, x));
	} else {
		tmp = x + (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))) <= 2e+306)
		tmp = fma(z, Float64(Float64(fma(-0.0692910599291889, z, -0.4917317610505968) / fma(Float64(-6.012459259764103 - z), z, -3.350343815022304)) * y), fma(Float64(0.279195317918525 / fma(Float64(z - -6.012459259764103), z, 3.350343815022304)), y, x));
	else
		tmp = Float64(x + 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], 2e+306], N[(z * N[(N[(N[(-0.0692910599291889 * z + -0.4917317610505968), $MachinePrecision] / N[(N[(-6.012459259764103 - z), $MachinePrecision] * z + -3.350343815022304), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + N[(N[(0.279195317918525 / N[(N[(z - -6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.0692910599291889 * y), $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)))) < 2.00000000000000003e306

   1. Initial program 69.0%

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

   3. Applied rewrites 87.3%

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

   if 2.00000000000000003e306 < (+.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 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

      \[\leadsto x + \color{blue}{0.0692910599291889 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 98.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + 0.0692910599291889 \cdot y\\ \mathbf{if}\;z \leq -5.4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.3 \cdot 10^{-20}:\\ \;\;\;\;x + 0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* 0.0692910599291889 y))))
   (if (<= z -5.4)
     t_0
     (if (<= z 8.3e-20) (+ x (* 0.08333333333333323 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (0.0692910599291889 * y);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 8.3e-20) {
		tmp = x + (0.08333333333333323 * y);
	} 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 = x + (0.0692910599291889d0 * y)
    if (z <= (-5.4d0)) then
        tmp = t_0
    else if (z <= 8.3d-20) then
        tmp = x + (0.08333333333333323d0 * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (0.0692910599291889 * y);
	double tmp;
	if (z <= -5.4) {
		tmp = t_0;
	} else if (z <= 8.3e-20) {
		tmp = x + (0.08333333333333323 * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (0.0692910599291889 * y)
	tmp = 0
	if z <= -5.4:
		tmp = t_0
	elif z <= 8.3e-20:
		tmp = x + (0.08333333333333323 * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(0.0692910599291889 * y))
	tmp = 0.0
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 8.3e-20)
		tmp = Float64(x + Float64(0.08333333333333323 * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (0.0692910599291889 * y);
	tmp = 0.0;
	if (z <= -5.4)
		tmp = t_0;
	elseif (z <= 8.3e-20)
		tmp = x + (0.08333333333333323 * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4], t$95$0, If[LessEqual[z, 8.3e-20], N[(x + N[(0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004 or 8.29999999999999989e-20 < z

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

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

   if -5.4000000000000004 < z < 8.29999999999999989e-20

   1. Initial program 69.0%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

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

Alternative 7: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 0.0692910599291889 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (+
       x
       (/
        (*
         y
         (+
          (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
          0.279195317918525))
        (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
      2e+306)
   (fma
    (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
    (/ y (fma (- z -6.012459259764103) z 3.350343815022304))
    x)
   (+ x (* 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))) <= 2e+306) {
		tmp = fma(fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525), (y / fma((z - -6.012459259764103), z, 3.350343815022304)), x);
	} else {
		tmp = x + (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))) <= 2e+306)
		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 + 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], 2e+306], 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[(0.0692910599291889 * y), $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)))) < 2.00000000000000003e306

   1. Initial program 69.0%

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

   3. Applied rewrites 73.8%

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

   if 2.00000000000000003e306 < (+.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 69.0%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 79.3

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

   4. Applied rewrites 79.3%

      \[\leadsto x + \color{blue}{0.0692910599291889 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 79.3% accurate, 4.5× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (0.0692910599291889d0 * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.0%

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

2. Taylor expanded in z around inf

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

   1. lower-*.f64 79.3

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

4. Applied rewrites 79.3%

   \[\leadsto x + \color{blue}{0.0692910599291889 \cdot y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025149 
(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))))