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

Percentage Accurate: 69.6% → 99.3%

Time: 8.1s

Alternatives: 11

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: 69.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{1}{\frac{1}{\frac{y}{14.431876219268936}}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z \cdot y, 0.279195317918525 \cdot y\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+47)
   (+ x (/ 1.0 (/ 1.0 (/ y 14.431876219268936))))
   (if (<= z 5.2e-5)
     (+
      x
      (/
       (fma
        (fma 0.0692910599291889 z 0.4917317610505968)
        (* z y)
        (* 0.279195317918525 y))
       (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
     (- x (/ -1.0 (/ 14.431876219268936 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+47) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = x + (fma(fma(0.0692910599291889, z, 0.4917317610505968), (z * y), (0.279195317918525 * y)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+47)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(y / 14.431876219268936))));
	elseif (z <= 5.2e-5)
		tmp = Float64(x + Float64(fma(fma(0.0692910599291889, z, 0.4917317610505968), Float64(z * y), Float64(0.279195317918525 * y)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304)));
	else
		tmp = Float64(x - Float64(-1.0 / Float64(14.431876219268936 / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+47], N[(x + N[(1.0 / N[(1.0 / N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], N[(x + N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * N[(z * y), $MachinePrecision] + N[(0.279195317918525 * y), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e47

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{\color{blue}{y}}} \]

      2. div-flip N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      4. lower-unsound-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{1}{\frac{y}{\color{blue}{14.431876219268936}}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{14.431876219268936}}}} \]

   if -1.55e47 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

      1. lift-*.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. distribute-lft-in N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 74.7

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

   3. Applied rewrites 74.7%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{1}{\frac{1}{\frac{y}{14.431876219268936}}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e+47)
   (+ x (/ 1.0 (/ 1.0 (/ y 14.431876219268936))))
   (if (<= z 5.2e-5)
     (+
      x
      (/
       (*
        y
        (+
         (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
         0.279195317918525))
       (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
     (- x (/ -1.0 (/ 14.431876219268936 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+47) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.55d+47)) then
        tmp = x + (1.0d0 / (1.0d0 / (y / 14.431876219268936d0)))
    else if (z <= 5.2d-5) then
        tmp = x + ((y * ((((z * 0.0692910599291889d0) + 0.4917317610505968d0) * z) + 0.279195317918525d0)) / (((z + 6.012459259764103d0) * z) + 3.350343815022304d0))
    else
        tmp = x - ((-1.0d0) / (14.431876219268936d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e+47) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e+47:
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)))
	elif z <= 5.2e-5:
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))
	else:
		tmp = x - (-1.0 / (14.431876219268936 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e+47)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(y / 14.431876219268936))));
	elseif (z <= 5.2e-5)
		tmp = 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)));
	else
		tmp = Float64(x - Float64(-1.0 / Float64(14.431876219268936 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e+47)
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	elseif (z <= 5.2e-5)
		tmp = x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304));
	else
		tmp = x - (-1.0 / (14.431876219268936 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e+47], N[(x + N[(1.0 / N[(1.0 / N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], 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], N[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e47

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{\color{blue}{y}}} \]

      2. div-flip N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      4. lower-unsound-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{1}{\frac{y}{\color{blue}{14.431876219268936}}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{14.431876219268936}}}} \]

   if -1.55e47 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{1}{\frac{1}{\frac{y}{14.431876219268936}}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.0692910599291889, z, 0.4917317610505968\right), z, 0.279195317918525\right), \frac{y}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4e+17)
   (+ x (/ 1.0 (/ 1.0 (/ y 14.431876219268936))))
   (if (<= z 5.2e-5)
     (fma
      (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
      (/ y (fma (- z -6.012459259764103) z 3.350343815022304))
      x)
     (- x (/ -1.0 (/ 14.431876219268936 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4e+17) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = fma(fma(fma(0.0692910599291889, z, 0.4917317610505968), z, 0.279195317918525), (y / fma((z - -6.012459259764103), z, 3.350343815022304)), x);
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4e+17)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(y / 14.431876219268936))));
	elseif (z <= 5.2e-5)
		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(-1.0 / Float64(14.431876219268936 / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4e+17], N[(x + N[(1.0 / N[(1.0 / N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], N[(N[(N[(0.0692910599291889 * z + 0.4917317610505968), $MachinePrecision] * z + 0.279195317918525), $MachinePrecision] * N[(y / N[(N[(z - -6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e17

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{\color{blue}{y}}} \]

      2. div-flip N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      4. lower-unsound-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{1}{\frac{y}{\color{blue}{14.431876219268936}}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{14.431876219268936}}}} \]

   if -1.4e17 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. lower-fma.f64 N/A

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

   3. Applied rewrites 74.6%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000:\\ \;\;\;\;x + \frac{1}{\frac{1}{\frac{y}{14.431876219268936}}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \mathsf{fma}\left(0.08333333333333323, y, z \cdot \mathsf{fma}\left(y, -0.14954831483277858, 0.14677053705526136 \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -10000.0)
   (+ x (/ 1.0 (/ 1.0 (/ y 14.431876219268936))))
   (if (<= z 5.2e-5)
     (+
      x
      (fma
       0.08333333333333323
       y
       (* z (fma y -0.14954831483277858 (* 0.14677053705526136 y)))))
     (- x (/ -1.0 (/ 14.431876219268936 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -10000.0) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = x + fma(0.08333333333333323, y, (z * fma(y, -0.14954831483277858, (0.14677053705526136 * y))));
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -10000.0)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(y / 14.431876219268936))));
	elseif (z <= 5.2e-5)
		tmp = Float64(x + fma(0.08333333333333323, y, Float64(z * fma(y, -0.14954831483277858, Float64(0.14677053705526136 * y)))));
	else
		tmp = Float64(x - Float64(-1.0 / Float64(14.431876219268936 / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -10000.0], N[(x + N[(1.0 / N[(1.0 / N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], N[(x + N[(0.08333333333333323 * y + N[(z * N[(y * -0.14954831483277858 + N[(0.14677053705526136 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e4

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{\color{blue}{y}}} \]

      2. div-flip N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      4. lower-unsound-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{1}{\frac{y}{\color{blue}{14.431876219268936}}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{14.431876219268936}}}} \]

   if -1e4 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

   2. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 65.6

         \[\leadsto x + \mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right) \]

   4. Applied rewrites 65.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. metadata-eval 65.6

         \[\leadsto x + \mathsf{fma}\left(0.08333333333333323, y, z \cdot \mathsf{fma}\left(y, -0.14954831483277858, 0.14677053705526136 \cdot y\right)\right) \]

   6. Applied rewrites 65.6%

      \[\leadsto x + \mathsf{fma}\left(0.08333333333333323, y, z \cdot \mathsf{fma}\left(y, -0.14954831483277858, 0.14677053705526136 \cdot y\right)\right) \]

   if 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 99.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000:\\ \;\;\;\;x + \frac{1}{\frac{1}{\frac{y}{14.431876219268936}}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \mathsf{fma}\left(y \cdot z, -0.00277777777751721, 0.08333333333333323 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -10000.0)
   (+ x (/ 1.0 (/ 1.0 (/ y 14.431876219268936))))
   (if (<= z 5.2e-5)
     (+ x (fma (* y z) -0.00277777777751721 (* 0.08333333333333323 y)))
     (- x (/ -1.0 (/ 14.431876219268936 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -10000.0) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = x + fma((y * z), -0.00277777777751721, (0.08333333333333323 * y));
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -10000.0)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(y / 14.431876219268936))));
	elseif (z <= 5.2e-5)
		tmp = Float64(x + fma(Float64(y * z), -0.00277777777751721, Float64(0.08333333333333323 * y)));
	else
		tmp = Float64(x - Float64(-1.0 / Float64(14.431876219268936 / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -10000.0], N[(x + N[(1.0 / N[(1.0 / N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], N[(x + N[(N[(y * z), $MachinePrecision] * -0.00277777777751721 + N[(0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e4

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{\color{blue}{y}}} \]

      2. div-flip N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      4. lower-unsound-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{1}{\frac{y}{\color{blue}{14.431876219268936}}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{14.431876219268936}}}} \]

   if -1e4 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

   2. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 65.6

         \[\leadsto x + \mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right) \]

   4. Applied rewrites 65.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. metadata-eval N/A

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

      13. lower-*.f64 65.6

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

   6. Applied rewrites 65.6%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 99.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000:\\ \;\;\;\;x + \frac{1}{\frac{1}{\frac{y}{14.431876219268936}}}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + -0.00277777777751721 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -10000.0)
   (+ x (/ 1.0 (/ 1.0 (/ y 14.431876219268936))))
   (if (<= z 5.2e-5)
     (+ x (* y (+ 0.08333333333333323 (* -0.00277777777751721 z))))
     (- x (/ -1.0 (/ 14.431876219268936 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -10000.0) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)));
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-10000.0d0)) then
        tmp = x + (1.0d0 / (1.0d0 / (y / 14.431876219268936d0)))
    else if (z <= 5.2d-5) then
        tmp = x + (y * (0.08333333333333323d0 + ((-0.00277777777751721d0) * z)))
    else
        tmp = x - ((-1.0d0) / (14.431876219268936d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -10000.0) {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	} else if (z <= 5.2e-5) {
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)));
	} else {
		tmp = x - (-1.0 / (14.431876219268936 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -10000.0:
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)))
	elif z <= 5.2e-5:
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)))
	else:
		tmp = x - (-1.0 / (14.431876219268936 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -10000.0)
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(y / 14.431876219268936))));
	elseif (z <= 5.2e-5)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(-0.00277777777751721 * z))));
	else
		tmp = Float64(x - Float64(-1.0 / Float64(14.431876219268936 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -10000.0)
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	elseif (z <= 5.2e-5)
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)));
	else
		tmp = x - (-1.0 / (14.431876219268936 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -10000.0], N[(x + N[(1.0 / N[(1.0 / N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], N[(x + N[(y * N[(0.08333333333333323 + N[(-0.00277777777751721 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e4

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{\color{blue}{y}}} \]

      2. div-flip N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      4. lower-unsound-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{1}{\frac{y}{\color{blue}{14.431876219268936}}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{14.431876219268936}}}} \]

   if -1e4 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

   2. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 65.6

         \[\leadsto x + \mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right) \]

   4. Applied rewrites 65.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right)} \]

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 65.6

         \[\leadsto x + y \cdot \left(0.08333333333333323 + -0.00277777777751721 \cdot z\right) \]

   7. Applied rewrites 65.6%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \mathbf{if}\;z \leq -10000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \left(0.08333333333333323 + -0.00277777777751721 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ -1.0 (/ 14.431876219268936 y)))))
   (if (<= z -10000.0)
     t_0
     (if (<= z 5.2e-5)
       (+ x (* y (+ 0.08333333333333323 (* -0.00277777777751721 z))))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (-1.0 / (14.431876219268936 / y));
	double tmp;
	if (z <= -10000.0) {
		tmp = t_0;
	} else if (z <= 5.2e-5) {
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)));
	} 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 - ((-1.0d0) / (14.431876219268936d0 / y))
    if (z <= (-10000.0d0)) then
        tmp = t_0
    else if (z <= 5.2d-5) then
        tmp = x + (y * (0.08333333333333323d0 + ((-0.00277777777751721d0) * z)))
    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 - (-1.0 / (14.431876219268936 / y));
	double tmp;
	if (z <= -10000.0) {
		tmp = t_0;
	} else if (z <= 5.2e-5) {
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (-1.0 / (14.431876219268936 / y))
	tmp = 0
	if z <= -10000.0:
		tmp = t_0
	elif z <= 5.2e-5:
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(-1.0 / Float64(14.431876219268936 / y)))
	tmp = 0.0
	if (z <= -10000.0)
		tmp = t_0;
	elseif (z <= 5.2e-5)
		tmp = Float64(x + Float64(y * Float64(0.08333333333333323 + Float64(-0.00277777777751721 * z))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (-1.0 / (14.431876219268936 / y));
	tmp = 0.0;
	if (z <= -10000.0)
		tmp = t_0;
	elseif (z <= 5.2e-5)
		tmp = x + (y * (0.08333333333333323 + (-0.00277777777751721 * z)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -10000.0], t$95$0, If[LessEqual[z, 5.2e-5], N[(x + N[(y * N[(0.08333333333333323 + N[(-0.00277777777751721 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e4 or 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]

   if -1e4 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

   2. Taylor expanded in z around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 65.6

         \[\leadsto x + \mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right) \]

   4. Applied rewrites 65.6%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(0.08333333333333323, y, z \cdot \left(0.14677053705526136 \cdot y - 0.14954831483277858 \cdot y\right)\right)} \]

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 65.6

         \[\leadsto x + y \cdot \left(0.08333333333333323 + -0.00277777777751721 \cdot z\right) \]

   7. Applied rewrites 65.6%

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

Alternative 8: 98.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{-1}{\frac{14.431876219268936}{y}}\\ \mathbf{if}\;z \leq -10000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x - -0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ -1.0 (/ 14.431876219268936 y)))))
   (if (<= z -10000.0)
     t_0
     (if (<= z 5.2e-5) (- x (* -0.08333333333333323 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (-1.0 / (14.431876219268936 / y));
	double tmp;
	if (z <= -10000.0) {
		tmp = t_0;
	} else if (z <= 5.2e-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 = x - ((-1.0d0) / (14.431876219268936d0 / y))
    if (z <= (-10000.0d0)) then
        tmp = t_0
    else if (z <= 5.2d-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 = x - (-1.0 / (14.431876219268936 / y));
	double tmp;
	if (z <= -10000.0) {
		tmp = t_0;
	} else if (z <= 5.2e-5) {
		tmp = x - (-0.08333333333333323 * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (-1.0 / (14.431876219268936 / y))
	tmp = 0
	if z <= -10000.0:
		tmp = t_0
	elif z <= 5.2e-5:
		tmp = x - (-0.08333333333333323 * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(-1.0 / Float64(14.431876219268936 / y)))
	tmp = 0.0
	if (z <= -10000.0)
		tmp = t_0;
	elseif (z <= 5.2e-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 = x - (-1.0 / (14.431876219268936 / y));
	tmp = 0.0;
	if (z <= -10000.0)
		tmp = t_0;
	elseif (z <= 5.2e-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[(x - N[(-1.0 / N[(14.431876219268936 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -10000.0], t$95$0, If[LessEqual[z, 5.2e-5], N[(x - N[(-0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e4 or 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{10000000000000000}{692910599291889}}{y}} \]

      7. lower-/.f64 79.8

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{14.431876219268936}{y}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{14.431876219268936}{y}}} \]

   if -1e4 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around 0

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.6

         \[\leadsto x + \frac{1}{\frac{12.000000000000014}{\color{blue}{y}}} \]

   6. Applied rewrites 79.6%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{12.000000000000014}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{3350343815022304}{279195317918525}}{y}} \]

      7. lower-/.f64 79.6

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{12.000000000000014}{y}}} \]

   8. Applied rewrites 79.6%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{12.000000000000014}{y}}} \]

   9. Taylor expanded in z around 0

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

       1. lower-*.f64 79.7

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

   11. Applied rewrites 79.7%

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

Alternative 9: 98.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - -0.0692910599291889 \cdot y\\ \mathbf{if}\;z \leq -10000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x - -0.08333333333333323 \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (* -0.0692910599291889 y))))
   (if (<= z -10000.0)
     t_0
     (if (<= z 5.2e-5) (- 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 <= -10000.0) {
		tmp = t_0;
	} else if (z <= 5.2e-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 = x - ((-0.0692910599291889d0) * y)
    if (z <= (-10000.0d0)) then
        tmp = t_0
    else if (z <= 5.2d-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 = x - (-0.0692910599291889 * y);
	double tmp;
	if (z <= -10000.0) {
		tmp = t_0;
	} else if (z <= 5.2e-5) {
		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 <= -10000.0:
		tmp = t_0
	elif z <= 5.2e-5:
		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 <= -10000.0)
		tmp = t_0;
	elseif (z <= 5.2e-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 = x - (-0.0692910599291889 * y);
	tmp = 0.0;
	if (z <= -10000.0)
		tmp = t_0;
	elseif (z <= 5.2e-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[(x - N[(-0.0692910599291889 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -10000.0], t$95$0, If[LessEqual[z, 5.2e-5], N[(x - N[(-0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e4 or 5.19999999999999968e-5 < z

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around 0

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.6

         \[\leadsto x + \frac{1}{\frac{12.000000000000014}{\color{blue}{y}}} \]

   6. Applied rewrites 79.6%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{12.000000000000014}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{3350343815022304}{279195317918525}}{y}} \]

      7. lower-/.f64 79.6

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{12.000000000000014}{y}}} \]

   8. Applied rewrites 79.6%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{12.000000000000014}{y}}} \]

   9. Taylor expanded in z around inf

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

       1. lower-*.f64 79.7

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

   11. Applied rewrites 79.7%

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

   if -1e4 < z < 5.19999999999999968e-5

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around 0

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.6

         \[\leadsto x + \frac{1}{\frac{12.000000000000014}{\color{blue}{y}}} \]

   6. Applied rewrites 79.6%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{12.000000000000014}{y}}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

      2. add-flip N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}}\right)\right) \]

      5. distribute-neg-frac N/A

         \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

      6. metadata-eval N/A

         \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{3350343815022304}{279195317918525}}{y}} \]

      7. lower-/.f64 79.6

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{12.000000000000014}{y}}} \]

   8. Applied rewrites 79.6%

      \[\leadsto \color{blue}{x - \frac{-1}{\frac{12.000000000000014}{y}}} \]

   9. Taylor expanded in z around 0

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

       1. lower-*.f64 79.7

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

   11. Applied rewrites 79.7%

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

Alternative 10: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(-0.0692910599291889, z, -0.4917317610505968\right)}{\mathsf{fma}\left(-6.012459259764103 - z, z, -3.350343815022304\right)}, \mathsf{fma}\left(0.279195317918525, \frac{y}{\mathsf{fma}\left(z - -6.012459259764103, z, 3.350343815022304\right)}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{1}{\frac{y}{14.431876219268936}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (+
       x
       (/
        (*
         y
         (+
          (* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
          0.279195317918525))
        (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
      5e+304)
   (fma
    (* z y)
    (/
     (fma -0.0692910599291889 z -0.4917317610505968)
     (fma (- -6.012459259764103 z) z -3.350343815022304))
    (fma
     0.279195317918525
     (/ y (fma (- z -6.012459259764103) z 3.350343815022304))
     x))
   (+ x (/ 1.0 (/ 1.0 (/ y 14.431876219268936))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x + ((y * ((((z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / (((z + 6.012459259764103) * z) + 3.350343815022304))) <= 5e+304) {
		tmp = fma((z * y), (fma(-0.0692910599291889, z, -0.4917317610505968) / fma((-6.012459259764103 - z), z, -3.350343815022304)), fma(0.279195317918525, (y / fma((z - -6.012459259764103), z, 3.350343815022304)), x));
	} else {
		tmp = x + (1.0 / (1.0 / (y / 14.431876219268936)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(z * 0.0692910599291889) + 0.4917317610505968) * z) + 0.279195317918525)) / Float64(Float64(Float64(z + 6.012459259764103) * z) + 3.350343815022304))) <= 5e+304)
		tmp = fma(Float64(z * y), Float64(fma(-0.0692910599291889, z, -0.4917317610505968) / fma(Float64(-6.012459259764103 - z), z, -3.350343815022304)), fma(0.279195317918525, Float64(y / fma(Float64(z - -6.012459259764103), z, 3.350343815022304)), x));
	else
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(y / 14.431876219268936))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x + N[(N[(y * N[(N[(N[(N[(z * 0.0692910599291889), $MachinePrecision] + 0.4917317610505968), $MachinePrecision] * z), $MachinePrecision] + 0.279195317918525), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(z + 6.012459259764103), $MachinePrecision] * z), $MachinePrecision] + 3.350343815022304), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+304], N[(N[(z * y), $MachinePrecision] * N[(N[(-0.0692910599291889 * z + -0.4917317610505968), $MachinePrecision] / N[(N[(-6.012459259764103 - z), $MachinePrecision] * z + -3.350343815022304), $MachinePrecision]), $MachinePrecision] + N[(0.279195317918525 * N[(y / N[(N[(z - -6.012459259764103), $MachinePrecision] * z + 3.350343815022304), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(1.0 / N[(y / 14.431876219268936), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 692910599291889/10000000000000000 binary64)) #s(literal 307332350656623/625000000000000 binary64)) z) #s(literal 11167812716741/40000000000000 binary64))) (+.f64 (*.f64 (+.f64 z #s(literal 6012459259764103/1000000000000000 binary64)) z) #s(literal 104698244219447/31250000000000 binary64)))) < 4.9999999999999997e304

   1. Initial program 69.6%

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

   3. Applied rewrites 83.4%

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

   if 4.9999999999999997e304 < (+.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 69.6%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 69.5

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 69.5

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

      8. lift-+.f64 N/A

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

      9. add-flip N/A

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

      10. lower--.f64 N/A

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

      11. metadata-eval 69.5

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 69.5

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

      15. lift-+.f64 N/A

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

      16. lift-*.f64 N/A

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

      17. lower-fma.f64 69.5

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

      18. lift-+.f64 N/A

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

      19. lift-*.f64 N/A

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

      20. *-commutative N/A

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

      21. lower-fma.f64 69.5

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

   3. Applied rewrites 69.5%

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

   4. Taylor expanded in z around inf

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{10000000000000000}{692910599291889}}{y}}} \]
   5. Step-by-step derivation

      1. lower-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{14.431876219268936}{\color{blue}{y}}} \]

   6. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{14.431876219268936}{y}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\frac{10000000000000000}{692910599291889}}{\color{blue}{y}}} \]

      2. div-flip N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      3. lower-unsound-/.f64 N/A

         \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{\frac{10000000000000000}{692910599291889}}}}} \]

      4. lower-unsound-/.f64 79.8

         \[\leadsto x + \frac{1}{\frac{1}{\frac{y}{\color{blue}{14.431876219268936}}}} \]

   8. Applied rewrites 79.8%

      \[\leadsto x + \frac{1}{\frac{1}{\color{blue}{\frac{y}{14.431876219268936}}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 79.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ x - -0.08333333333333323 \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* -0.08333333333333323 y)))

C

double code(double x, double y, double z) {
	return x - (-0.08333333333333323 * 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 - ((-0.08333333333333323d0) * y)
end function

Java

public static double code(double x, double y, double z) {
	return x - (-0.08333333333333323 * y);
}

Python

def code(x, y, z):
	return x - (-0.08333333333333323 * y)

Julia

function code(x, y, z)
	return Float64(x - Float64(-0.08333333333333323 * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - (-0.08333333333333323 * y);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(-0.08333333333333323 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.6%

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

   1. lift-/.f64 N/A

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

   2. div-flip N/A

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

   3. lower-unsound-/.f64 N/A

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

   4. lower-unsound-/.f64 69.5

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

   5. lift-+.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lower-fma.f64 69.5

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

   8. lift-+.f64 N/A

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

   9. add-flip N/A

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

   10. lower--.f64 N/A

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

   11. metadata-eval 69.5

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

   12. lift-*.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 69.5

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

   15. lift-+.f64 N/A

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

   16. lift-*.f64 N/A

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

   17. lower-fma.f64 69.5

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

   18. lift-+.f64 N/A

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

   19. lift-*.f64 N/A

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

   20. *-commutative N/A

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

   21. lower-fma.f64 69.5

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

3. Applied rewrites 69.5%

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

4. Taylor expanded in z around 0

   \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]
5. Step-by-step derivation

   1. lower-/.f64 79.6

      \[\leadsto x + \frac{1}{\frac{12.000000000000014}{\color{blue}{y}}} \]

6. Applied rewrites 79.6%

   \[\leadsto x + \frac{1}{\color{blue}{\frac{12.000000000000014}{y}}} \]
7. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + \frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

   2. add-flip N/A

      \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

   3. lower--.f64 N/A

      \[\leadsto \color{blue}{x - \left(\mathsf{neg}\left(\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}\right)\right)} \]

   4. lift-/.f64 N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\color{blue}{\frac{1}{\frac{\frac{3350343815022304}{279195317918525}}{y}}}\right)\right) \]

   5. distribute-neg-frac N/A

      \[\leadsto x - \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\frac{\frac{3350343815022304}{279195317918525}}{y}}} \]

   6. metadata-eval N/A

      \[\leadsto x - \frac{\color{blue}{-1}}{\frac{\frac{3350343815022304}{279195317918525}}{y}} \]

   7. lower-/.f64 79.6

      \[\leadsto x - \color{blue}{\frac{-1}{\frac{12.000000000000014}{y}}} \]

8. Applied rewrites 79.6%

   \[\leadsto \color{blue}{x - \frac{-1}{\frac{12.000000000000014}{y}}} \]

9. Taylor expanded in z around 0

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

    1. lower-*.f64 79.7

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

11. Applied rewrites 79.7%

    \[\leadsto x - \color{blue}{-0.08333333333333323 \cdot y} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025155 
(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))))