(- z0 (* (- (* z2 (- (* (* z1 z1) 330733645533703/8000000000000) 12566370964050293/2000000000000000)) (* (* -9869604950382893/500000000000000 z0) z1)) z1))

Percentage Accurate: 93.5% → 99.6%

Time: 2.3s

Alternatives: 9

Speedup: 1.0×

• 63.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (-
 z0
 (*
  (-
   (* z2 (- (* (* z1 z1) 41.341705691712875) 6.2831854820251465))
   (* (* -19.739209900765786 z0) z1))
  z1)))

C

double code(double z0, double z2, double z1) {
	return z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1);
}

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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    code = z0 - (((z2 * (((z1 * z1) * 41.341705691712875d0) - 6.2831854820251465d0)) - (((-19.739209900765786d0) * z0) * z1)) * z1)
end function

Java

public static double code(double z0, double z2, double z1) {
	return z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1);
}

Python

def code(z0, z2, z1):
	return z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1)

Julia

function code(z0, z2, z1)
	return Float64(z0 - Float64(Float64(Float64(z2 * Float64(Float64(Float64(z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - Float64(Float64(-19.739209900765786 * z0) * z1)) * z1))
end

MATLAB

function tmp = code(z0, z2, z1)
	tmp = z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1);
end

Wolfram

code[z0_, z2_, z1_] := N[(z0 - N[(N[(N[(z2 * N[(N[(N[(z1 * z1), $MachinePrecision] * 41.341705691712875), $MachinePrecision] - 6.2831854820251465), $MachinePrecision]), $MachinePrecision] - N[(N[(-19.739209900765786 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]

Initial Program: 93.5% accurate, 1.0× speedup

Math

\[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (-
 z0
 (*
  (-
   (* z2 (- (* (* z1 z1) 41.341705691712875) 6.2831854820251465))
   (* (* -19.739209900765786 z0) z1))
  z1)))

C

double code(double z0, double z2, double z1) {
	return z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1);
}

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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    code = z0 - (((z2 * (((z1 * z1) * 41.341705691712875d0) - 6.2831854820251465d0)) - (((-19.739209900765786d0) * z0) * z1)) * z1)
end function

Java

public static double code(double z0, double z2, double z1) {
	return z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1);
}

Python

def code(z0, z2, z1):
	return z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1)

Julia

function code(z0, z2, z1)
	return Float64(z0 - Float64(Float64(Float64(z2 * Float64(Float64(Float64(z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - Float64(Float64(-19.739209900765786 * z0) * z1)) * z1))
end

MATLAB

function tmp = code(z0, z2, z1)
	tmp = z0 - (((z2 * (((z1 * z1) * 41.341705691712875) - 6.2831854820251465)) - ((-19.739209900765786 * z0) * z1)) * z1);
end

Wolfram

code[z0_, z2_, z1_] := N[(z0 - N[(N[(N[(z2 * N[(N[(N[(z1 * z1), $MachinePrecision] * 41.341705691712875), $MachinePrecision] - 6.2831854820251465), $MachinePrecision]), $MachinePrecision] - N[(N[(-19.739209900765786 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[z0 - \left(z1 \cdot \left(19.739209900765786 \cdot z0 + \left(z1 \cdot z2\right) \cdot 41.341705691712875\right) - 6.2831854820251465 \cdot z2\right) \cdot z1 \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (-
 z0
 (*
  (-
   (*
    z1
    (+ (* 19.739209900765786 z0) (* (* z1 z2) 41.341705691712875)))
   (* 6.2831854820251465 z2))
  z1)))

C

double code(double z0, double z2, double z1) {
	return z0 - (((z1 * ((19.739209900765786 * z0) + ((z1 * z2) * 41.341705691712875))) - (6.2831854820251465 * z2)) * z1);
}

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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    code = z0 - (((z1 * ((19.739209900765786d0 * z0) + ((z1 * z2) * 41.341705691712875d0))) - (6.2831854820251465d0 * z2)) * z1)
end function

Java

public static double code(double z0, double z2, double z1) {
	return z0 - (((z1 * ((19.739209900765786 * z0) + ((z1 * z2) * 41.341705691712875))) - (6.2831854820251465 * z2)) * z1);
}

Python

def code(z0, z2, z1):
	return z0 - (((z1 * ((19.739209900765786 * z0) + ((z1 * z2) * 41.341705691712875))) - (6.2831854820251465 * z2)) * z1)

Julia

function code(z0, z2, z1)
	return Float64(z0 - Float64(Float64(Float64(z1 * Float64(Float64(19.739209900765786 * z0) + Float64(Float64(z1 * z2) * 41.341705691712875))) - Float64(6.2831854820251465 * z2)) * z1))
end

MATLAB

function tmp = code(z0, z2, z1)
	tmp = z0 - (((z1 * ((19.739209900765786 * z0) + ((z1 * z2) * 41.341705691712875))) - (6.2831854820251465 * z2)) * z1);
end

Wolfram

code[z0_, z2_, z1_] := N[(z0 - N[(N[(N[(z1 * N[(N[(19.739209900765786 * z0), $MachinePrecision] + N[(N[(z1 * z2), $MachinePrecision] * 41.341705691712875), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.2831854820251465 * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.5%

   \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
2. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right)} \cdot z1 \]

   2. lift-*.f64 N/A

      \[\leadsto z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \color{blue}{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}\right) \cdot z1 \]

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

      \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) + \left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1\right)} \cdot z1 \]

   4. +-commutative N/A

      \[\leadsto z0 - \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)} \cdot z1 \]

   5. lift-*.f64 N/A

      \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

   6. lift--.f64 N/A

      \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

   7. sub-flip N/A

      \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} + \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

   8. distribute-lft-in N/A

      \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

   9. associate-+r+ N/A

      \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

   10. add-flip N/A

       \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

   11. lower--.f64 N/A

       \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

3. Applied rewrites 99.6%

   \[\leadsto z0 - \color{blue}{\left(z1 \cdot \left(19.739209900765786 \cdot z0 + \left(z1 \cdot z2\right) \cdot 41.341705691712875\right) - 6.2831854820251465 \cdot z2\right)} \cdot z1 \]
4. Add Preprocessing

Alternative 2: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(\frac{z0}{z1} \cdot -19.739209900765786 - 41.341705691712875 \cdot z2\right) \cdot z1\right) \cdot \left(z1 \cdot z1\right)\\ \mathbf{if}\;z1 \leq -800000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z1 \leq 11000:\\ \;\;\;\;z0 - \left(z1 \cdot \left(41.341705691712875 \cdot \left(z1 \cdot z2\right)\right) - 6.2831854820251465 \cdot z2\right) \cdot z1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (let* ((t_0
        (*
         (*
          (-
           (* (/ z0 z1) -19.739209900765786)
           (* 41.341705691712875 z2))
          z1)
         (* z1 z1))))
  (if (<= z1 -800000000.0)
    t_0
    (if (<= z1 11000.0)
      (-
       z0
       (*
        (-
         (* z1 (* 41.341705691712875 (* z1 z2)))
         (* 6.2831854820251465 z2))
        z1))
      t_0))))

C

double code(double z0, double z2, double z1) {
	double t_0 = ((((z0 / z1) * -19.739209900765786) - (41.341705691712875 * z2)) * z1) * (z1 * z1);
	double tmp;
	if (z1 <= -800000000.0) {
		tmp = t_0;
	} else if (z1 <= 11000.0) {
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	} 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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((((z0 / z1) * (-19.739209900765786d0)) - (41.341705691712875d0 * z2)) * z1) * (z1 * z1)
    if (z1 <= (-800000000.0d0)) then
        tmp = t_0
    else if (z1 <= 11000.0d0) then
        tmp = z0 - (((z1 * (41.341705691712875d0 * (z1 * z2))) - (6.2831854820251465d0 * z2)) * z1)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z2, double z1) {
	double t_0 = ((((z0 / z1) * -19.739209900765786) - (41.341705691712875 * z2)) * z1) * (z1 * z1);
	double tmp;
	if (z1 <= -800000000.0) {
		tmp = t_0;
	} else if (z1 <= 11000.0) {
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z2, z1):
	t_0 = ((((z0 / z1) * -19.739209900765786) - (41.341705691712875 * z2)) * z1) * (z1 * z1)
	tmp = 0
	if z1 <= -800000000.0:
		tmp = t_0
	elif z1 <= 11000.0:
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z2, z1)
	t_0 = Float64(Float64(Float64(Float64(Float64(z0 / z1) * -19.739209900765786) - Float64(41.341705691712875 * z2)) * z1) * Float64(z1 * z1))
	tmp = 0.0
	if (z1 <= -800000000.0)
		tmp = t_0;
	elseif (z1 <= 11000.0)
		tmp = Float64(z0 - Float64(Float64(Float64(z1 * Float64(41.341705691712875 * Float64(z1 * z2))) - Float64(6.2831854820251465 * z2)) * z1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z2, z1)
	t_0 = ((((z0 / z1) * -19.739209900765786) - (41.341705691712875 * z2)) * z1) * (z1 * z1);
	tmp = 0.0;
	if (z1 <= -800000000.0)
		tmp = t_0;
	elseif (z1 <= 11000.0)
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z2_, z1_] := Block[{t$95$0 = N[(N[(N[(N[(N[(z0 / z1), $MachinePrecision] * -19.739209900765786), $MachinePrecision] - N[(41.341705691712875 * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision] * N[(z1 * z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z1, -800000000.0], t$95$0, If[LessEqual[z1, 11000.0], N[(z0 - N[(N[(N[(z1 * N[(41.341705691712875 * N[(z1 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.2831854820251465 * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z1 < -8e8 or 11000 < z1

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

   2. Taylor expanded in z1 around inf

      \[\leadsto \color{blue}{{z1}^{3} \cdot \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z1}^{3} \cdot \color{blue}{\left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z1}^{3} \cdot \left(\color{blue}{\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1}} - \frac{330733645533703}{8000000000000} \cdot z2\right) \]

      3. lower--.f64 N/A

         \[\leadsto {z1}^{3} \cdot \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \color{blue}{\frac{330733645533703}{8000000000000} \cdot z2}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z1}^{3} \cdot \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \color{blue}{\frac{330733645533703}{8000000000000}} \cdot z2\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z1}^{3} \cdot \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \]

      6. lower-*.f64 48.5%

         \[\leadsto {z1}^{3} \cdot \left(-19.739209900765786 \cdot \frac{z0}{z1} - 41.341705691712875 \cdot \color{blue}{z2}\right) \]

   4. Applied rewrites 48.5%

      \[\leadsto \color{blue}{{z1}^{3} \cdot \left(-19.739209900765786 \cdot \frac{z0}{z1} - 41.341705691712875 \cdot z2\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z1}^{3} \cdot \color{blue}{\left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot \color{blue}{{z1}^{3}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot {z1}^{\color{blue}{3}} \]

      4. cube-mult N/A

         \[\leadsto \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot \left(z1 \cdot \color{blue}{\left(z1 \cdot z1\right)}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot \left(z1 \cdot \left(z1 \cdot \color{blue}{z1}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \left(\left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot z1\right) \cdot \color{blue}{\left(z1 \cdot z1\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot z1\right) \cdot \color{blue}{\left(z1 \cdot z1\right)} \]

      8. lower-*.f64 50.0%

         \[\leadsto \left(\left(-19.739209900765786 \cdot \frac{z0}{z1} - 41.341705691712875 \cdot z2\right) \cdot z1\right) \cdot \left(\color{blue}{z1} \cdot z1\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{-9869604950382893}{500000000000000} \cdot \frac{z0}{z1} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot z1\right) \cdot \left(z1 \cdot z1\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\frac{z0}{z1} \cdot \frac{-9869604950382893}{500000000000000} - \frac{330733645533703}{8000000000000} \cdot z2\right) \cdot z1\right) \cdot \left(z1 \cdot z1\right) \]

      11. lower-*.f64 50.0%

          \[\leadsto \left(\left(\frac{z0}{z1} \cdot -19.739209900765786 - 41.341705691712875 \cdot z2\right) \cdot z1\right) \cdot \left(z1 \cdot z1\right) \]

   6. Applied rewrites 50.0%

      \[\leadsto \left(\left(\frac{z0}{z1} \cdot -19.739209900765786 - 41.341705691712875 \cdot z2\right) \cdot z1\right) \cdot \color{blue}{\left(z1 \cdot z1\right)} \]

   if -8e8 < z1 < 11000

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right)} \cdot z1 \]

      2. lift-*.f64 N/A

         \[\leadsto z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \color{blue}{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}\right) \cdot z1 \]

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

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) + \left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1\right)} \cdot z1 \]

      4. +-commutative N/A

         \[\leadsto z0 - \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)} \cdot z1 \]

      5. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

      6. lift--.f64 N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

      7. sub-flip N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} + \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

      8. distribute-lft-in N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

      9. associate-+r+ N/A

         \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

      10. add-flip N/A

          \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

      11. lower--.f64 N/A

          \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

   3. Applied rewrites 99.6%

      \[\leadsto z0 - \color{blue}{\left(z1 \cdot \left(19.739209900765786 \cdot z0 + \left(z1 \cdot z2\right) \cdot 41.341705691712875\right) - 6.2831854820251465 \cdot z2\right)} \cdot z1 \]

   4. Taylor expanded in z0 around 0

      \[\leadsto z0 - \left(z1 \cdot \color{blue}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z2\right)\right)} - 6.2831854820251465 \cdot z2\right) \cdot z1 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 - \left(z1 \cdot \left(\frac{330733645533703}{8000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)}\right) - \frac{12566370964050293}{2000000000000000} \cdot z2\right) \cdot z1 \]

      2. lower-*.f64 86.9%

         \[\leadsto z0 - \left(z1 \cdot \left(41.341705691712875 \cdot \left(z1 \cdot \color{blue}{z2}\right)\right) - 6.2831854820251465 \cdot z2\right) \cdot z1 \]

   6. Applied rewrites 86.9%

      \[\leadsto z0 - \left(z1 \cdot \color{blue}{\left(41.341705691712875 \cdot \left(z1 \cdot z2\right)\right)} - 6.2831854820251465 \cdot z2\right) \cdot z1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z2 \leq -1.4 \cdot 10^{-131}:\\ \;\;\;\;z0 - \left(1 \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1\\ \mathbf{elif}\;z2 \leq 2.6 \cdot 10^{-252}:\\ \;\;\;\;\left(1 - z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot z1\right)\right) \cdot z0\\ \mathbf{else}:\\ \;\;\;\;z0 - \left(z1 \cdot \left(41.341705691712875 \cdot \left(z1 \cdot z2\right)\right) - 6.2831854820251465 \cdot z2\right) \cdot z1\\ \end{array} \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (if (<= z2 -1.4e-131)
  (-
   z0
   (*
    (*
     1.0
     (* (- (* 41.341705691712875 (* z1 z1)) 6.2831854820251465) z2))
    z1))
  (if (<= z2 2.6e-252)
    (*
     (-
      1.0
      (*
       z1
       (+
        (* -6.2831854820251465 (/ z2 z0))
        (* 19.739209900765786 z1))))
     z0)
    (-
     z0
     (*
      (-
       (* z1 (* 41.341705691712875 (* z1 z2)))
       (* 6.2831854820251465 z2))
      z1)))))

C

double code(double z0, double z2, double z1) {
	double tmp;
	if (z2 <= -1.4e-131) {
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	} else if (z2 <= 2.6e-252) {
		tmp = (1.0 - (z1 * ((-6.2831854820251465 * (z2 / z0)) + (19.739209900765786 * z1)))) * z0;
	} else {
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	}
	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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8) :: tmp
    if (z2 <= (-1.4d-131)) then
        tmp = z0 - ((1.0d0 * (((41.341705691712875d0 * (z1 * z1)) - 6.2831854820251465d0) * z2)) * z1)
    else if (z2 <= 2.6d-252) then
        tmp = (1.0d0 - (z1 * (((-6.2831854820251465d0) * (z2 / z0)) + (19.739209900765786d0 * z1)))) * z0
    else
        tmp = z0 - (((z1 * (41.341705691712875d0 * (z1 * z2))) - (6.2831854820251465d0 * z2)) * z1)
    end if
    code = tmp
end function

Java

public static double code(double z0, double z2, double z1) {
	double tmp;
	if (z2 <= -1.4e-131) {
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	} else if (z2 <= 2.6e-252) {
		tmp = (1.0 - (z1 * ((-6.2831854820251465 * (z2 / z0)) + (19.739209900765786 * z1)))) * z0;
	} else {
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	}
	return tmp;
}

Python

def code(z0, z2, z1):
	tmp = 0
	if z2 <= -1.4e-131:
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1)
	elif z2 <= 2.6e-252:
		tmp = (1.0 - (z1 * ((-6.2831854820251465 * (z2 / z0)) + (19.739209900765786 * z1)))) * z0
	else:
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1)
	return tmp

Julia

function code(z0, z2, z1)
	tmp = 0.0
	if (z2 <= -1.4e-131)
		tmp = Float64(z0 - Float64(Float64(1.0 * Float64(Float64(Float64(41.341705691712875 * Float64(z1 * z1)) - 6.2831854820251465) * z2)) * z1));
	elseif (z2 <= 2.6e-252)
		tmp = Float64(Float64(1.0 - Float64(z1 * Float64(Float64(-6.2831854820251465 * Float64(z2 / z0)) + Float64(19.739209900765786 * z1)))) * z0);
	else
		tmp = Float64(z0 - Float64(Float64(Float64(z1 * Float64(41.341705691712875 * Float64(z1 * z2))) - Float64(6.2831854820251465 * z2)) * z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z2, z1)
	tmp = 0.0;
	if (z2 <= -1.4e-131)
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	elseif (z2 <= 2.6e-252)
		tmp = (1.0 - (z1 * ((-6.2831854820251465 * (z2 / z0)) + (19.739209900765786 * z1)))) * z0;
	else
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z2_, z1_] := If[LessEqual[z2, -1.4e-131], N[(z0 - N[(N[(1.0 * N[(N[(N[(41.341705691712875 * N[(z1 * z1), $MachinePrecision]), $MachinePrecision] - 6.2831854820251465), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z2, 2.6e-252], N[(N[(1.0 - N[(z1 * N[(N[(-6.2831854820251465 * N[(z2 / z0), $MachinePrecision]), $MachinePrecision] + N[(19.739209900765786 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision], N[(z0 - N[(N[(N[(z1 * N[(41.341705691712875 * N[(z1 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.2831854820251465 * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z2 < -1.4e-131

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right)} \cdot z1 \]

      2. sub-to-mult N/A

         \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

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

         \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

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

         \[\leadsto z0 - \left(\color{blue}{\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right)} \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      5. lower-unsound-/.f64 85.9%

         \[\leadsto z0 - \left(\left(1 - \color{blue}{\frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      6. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\color{blue}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      7. *-commutative N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      8. lower-*.f64 85.9%

         \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\color{blue}{\left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) \cdot z2}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      9. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\color{blue}{\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      10. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\color{blue}{\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right)} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      11. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(\color{blue}{41.341705691712875 \cdot \left(z1 \cdot z1\right)} - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      12. lift-*.f64 N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)}\right) \cdot z1 \]

      13. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \color{blue}{\left(\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)}\right) \cdot z1 \]

      14. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \color{blue}{\left(\left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) \cdot z2\right)}\right) \cdot z1 \]

      15. lift-*.f64 N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)\right) \cdot z1 \]

      16. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right)} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)\right) \cdot z1 \]

      17. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{41.341705691712875 \cdot \left(z1 \cdot z1\right)} - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]

   3. Applied rewrites 85.9%

      \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right)} \cdot z1 \]

   4. Taylor expanded in z0 around 0

      \[\leadsto z0 - \left(\color{blue}{1} \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.9%

      \[\leadsto z0 - \left(\color{blue}{1} \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]

   if -1.4e-131 < z2 < 2.5999999999999999e-252

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1} \]

      2. sub-to-mult N/A

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

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

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

   3. Applied rewrites 88.3%

      \[\leadsto \color{blue}{\left(1 - \frac{\left(\left(19.739209900765786 \cdot z0\right) \cdot z1 - \left(6.2831854820251465 - 41.341705691712875 \cdot \left(z1 \cdot z1\right)\right) \cdot z2\right) \cdot z1}{z0}\right) \cdot z0} \]

   4. Taylor expanded in z1 around 0

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \color{blue}{\left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000} \cdot z1}\right)\right) \cdot z0 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000}} \cdot z1\right)\right) \cdot z0 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)\right) \cdot z0 \]

      5. lower-*.f64 66.4%

         \[\leadsto \left(1 - z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]

   6. Applied rewrites 66.4%

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot z1\right)}\right) \cdot z0 \]

   if 2.5999999999999999e-252 < z2

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right)} \cdot z1 \]

      2. lift-*.f64 N/A

         \[\leadsto z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \color{blue}{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}\right) \cdot z1 \]

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

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) + \left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1\right)} \cdot z1 \]

      4. +-commutative N/A

         \[\leadsto z0 - \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)} \cdot z1 \]

      5. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

      6. lift--.f64 N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

      7. sub-flip N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} + \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

      8. distribute-lft-in N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

      9. associate-+r+ N/A

         \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

      10. add-flip N/A

          \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

      11. lower--.f64 N/A

          \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

   3. Applied rewrites 99.6%

      \[\leadsto z0 - \color{blue}{\left(z1 \cdot \left(19.739209900765786 \cdot z0 + \left(z1 \cdot z2\right) \cdot 41.341705691712875\right) - 6.2831854820251465 \cdot z2\right)} \cdot z1 \]

   4. Taylor expanded in z0 around 0

      \[\leadsto z0 - \left(z1 \cdot \color{blue}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z2\right)\right)} - 6.2831854820251465 \cdot z2\right) \cdot z1 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 - \left(z1 \cdot \left(\frac{330733645533703}{8000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)}\right) - \frac{12566370964050293}{2000000000000000} \cdot z2\right) \cdot z1 \]

      2. lower-*.f64 86.9%

         \[\leadsto z0 - \left(z1 \cdot \left(41.341705691712875 \cdot \left(z1 \cdot \color{blue}{z2}\right)\right) - 6.2831854820251465 \cdot z2\right) \cdot z1 \]

   6. Applied rewrites 86.9%

      \[\leadsto z0 - \left(z1 \cdot \color{blue}{\left(41.341705691712875 \cdot \left(z1 \cdot z2\right)\right)} - 6.2831854820251465 \cdot z2\right) \cdot z1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z2 \leq -1.4 \cdot 10^{-131}:\\ \;\;\;\;z0 - \left(1 \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1\\ \mathbf{elif}\;z2 \leq 2.6 \cdot 10^{-252}:\\ \;\;\;\;\left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0\\ \mathbf{else}:\\ \;\;\;\;z0 - \left(z1 \cdot \left(41.341705691712875 \cdot \left(z1 \cdot z2\right)\right) - 6.2831854820251465 \cdot z2\right) \cdot z1\\ \end{array} \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (if (<= z2 -1.4e-131)
  (-
   z0
   (*
    (*
     1.0
     (* (- (* 41.341705691712875 (* z1 z1)) 6.2831854820251465) z2))
    z1))
  (if (<= z2 2.6e-252)
    (* (- 1.0 (* z1 (* 19.739209900765786 z1))) z0)
    (-
     z0
     (*
      (-
       (* z1 (* 41.341705691712875 (* z1 z2)))
       (* 6.2831854820251465 z2))
      z1)))))

C

double code(double z0, double z2, double z1) {
	double tmp;
	if (z2 <= -1.4e-131) {
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	} else if (z2 <= 2.6e-252) {
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	} else {
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	}
	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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8) :: tmp
    if (z2 <= (-1.4d-131)) then
        tmp = z0 - ((1.0d0 * (((41.341705691712875d0 * (z1 * z1)) - 6.2831854820251465d0) * z2)) * z1)
    else if (z2 <= 2.6d-252) then
        tmp = (1.0d0 - (z1 * (19.739209900765786d0 * z1))) * z0
    else
        tmp = z0 - (((z1 * (41.341705691712875d0 * (z1 * z2))) - (6.2831854820251465d0 * z2)) * z1)
    end if
    code = tmp
end function

Java

public static double code(double z0, double z2, double z1) {
	double tmp;
	if (z2 <= -1.4e-131) {
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	} else if (z2 <= 2.6e-252) {
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	} else {
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	}
	return tmp;
}

Python

def code(z0, z2, z1):
	tmp = 0
	if z2 <= -1.4e-131:
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1)
	elif z2 <= 2.6e-252:
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0
	else:
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1)
	return tmp

Julia

function code(z0, z2, z1)
	tmp = 0.0
	if (z2 <= -1.4e-131)
		tmp = Float64(z0 - Float64(Float64(1.0 * Float64(Float64(Float64(41.341705691712875 * Float64(z1 * z1)) - 6.2831854820251465) * z2)) * z1));
	elseif (z2 <= 2.6e-252)
		tmp = Float64(Float64(1.0 - Float64(z1 * Float64(19.739209900765786 * z1))) * z0);
	else
		tmp = Float64(z0 - Float64(Float64(Float64(z1 * Float64(41.341705691712875 * Float64(z1 * z2))) - Float64(6.2831854820251465 * z2)) * z1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z2, z1)
	tmp = 0.0;
	if (z2 <= -1.4e-131)
		tmp = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	elseif (z2 <= 2.6e-252)
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	else
		tmp = z0 - (((z1 * (41.341705691712875 * (z1 * z2))) - (6.2831854820251465 * z2)) * z1);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z2_, z1_] := If[LessEqual[z2, -1.4e-131], N[(z0 - N[(N[(1.0 * N[(N[(N[(41.341705691712875 * N[(z1 * z1), $MachinePrecision]), $MachinePrecision] - 6.2831854820251465), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z2, 2.6e-252], N[(N[(1.0 - N[(z1 * N[(19.739209900765786 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision], N[(z0 - N[(N[(N[(z1 * N[(41.341705691712875 * N[(z1 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.2831854820251465 * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z2 < -1.4e-131

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right)} \cdot z1 \]

      2. sub-to-mult N/A

         \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

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

         \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

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

         \[\leadsto z0 - \left(\color{blue}{\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right)} \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      5. lower-unsound-/.f64 85.9%

         \[\leadsto z0 - \left(\left(1 - \color{blue}{\frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      6. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\color{blue}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      7. *-commutative N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      8. lower-*.f64 85.9%

         \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\color{blue}{\left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) \cdot z2}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      9. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\color{blue}{\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      10. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\color{blue}{\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right)} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      11. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(\color{blue}{41.341705691712875 \cdot \left(z1 \cdot z1\right)} - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      12. lift-*.f64 N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)}\right) \cdot z1 \]

      13. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \color{blue}{\left(\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)}\right) \cdot z1 \]

      14. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \color{blue}{\left(\left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) \cdot z2\right)}\right) \cdot z1 \]

      15. lift-*.f64 N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)\right) \cdot z1 \]

      16. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right)} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)\right) \cdot z1 \]

      17. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{41.341705691712875 \cdot \left(z1 \cdot z1\right)} - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]

   3. Applied rewrites 85.9%

      \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right)} \cdot z1 \]

   4. Taylor expanded in z0 around 0

      \[\leadsto z0 - \left(\color{blue}{1} \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.9%

      \[\leadsto z0 - \left(\color{blue}{1} \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]

   if -1.4e-131 < z2 < 2.5999999999999999e-252

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1} \]

      2. sub-to-mult N/A

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

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

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

   3. Applied rewrites 88.3%

      \[\leadsto \color{blue}{\left(1 - \frac{\left(\left(19.739209900765786 \cdot z0\right) \cdot z1 - \left(6.2831854820251465 - 41.341705691712875 \cdot \left(z1 \cdot z1\right)\right) \cdot z2\right) \cdot z1}{z0}\right) \cdot z0} \]

   4. Taylor expanded in z1 around 0

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \color{blue}{\left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000} \cdot z1}\right)\right) \cdot z0 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000}} \cdot z1\right)\right) \cdot z0 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)\right) \cdot z0 \]

      5. lower-*.f64 66.4%

         \[\leadsto \left(1 - z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]

   6. Applied rewrites 66.4%

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot z1\right)}\right) \cdot z0 \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \left(1 - z1 \cdot \left(\frac{9869604950382893}{500000000000000} \cdot \color{blue}{z1}\right)\right) \cdot z0 \]
   8. Step-by-step derivation

      1. lower-*.f64 60.9%

         \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0 \]

   9. Applied rewrites 60.9%

      \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]

   if 2.5999999999999999e-252 < z2

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right)} \cdot z1 \]

      2. lift-*.f64 N/A

         \[\leadsto z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \color{blue}{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}\right) \cdot z1 \]

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

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) + \left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1\right)} \cdot z1 \]

      4. +-commutative N/A

         \[\leadsto z0 - \color{blue}{\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)} \cdot z1 \]

      5. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

      6. lift--.f64 N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot z1 \]

      7. sub-flip N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} + \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

      8. distribute-lft-in N/A

         \[\leadsto z0 - \left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)}\right) \cdot z1 \]

      9. associate-+r+ N/A

         \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) + z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

      10. add-flip N/A

          \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

      11. lower--.f64 N/A

          \[\leadsto z0 - \color{blue}{\left(\left(\left(\mathsf{neg}\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right)\right) \cdot z1 + z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}\right)\right) - \left(\mathsf{neg}\left(z2 \cdot \left(\mathsf{neg}\left(\frac{12566370964050293}{2000000000000000}\right)\right)\right)\right)\right)} \cdot z1 \]

   3. Applied rewrites 99.6%

      \[\leadsto z0 - \color{blue}{\left(z1 \cdot \left(19.739209900765786 \cdot z0 + \left(z1 \cdot z2\right) \cdot 41.341705691712875\right) - 6.2831854820251465 \cdot z2\right)} \cdot z1 \]

   4. Taylor expanded in z0 around 0

      \[\leadsto z0 - \left(z1 \cdot \color{blue}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z2\right)\right)} - 6.2831854820251465 \cdot z2\right) \cdot z1 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 - \left(z1 \cdot \left(\frac{330733645533703}{8000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)}\right) - \frac{12566370964050293}{2000000000000000} \cdot z2\right) \cdot z1 \]

      2. lower-*.f64 86.9%

         \[\leadsto z0 - \left(z1 \cdot \left(41.341705691712875 \cdot \left(z1 \cdot \color{blue}{z2}\right)\right) - 6.2831854820251465 \cdot z2\right) \cdot z1 \]

   6. Applied rewrites 86.9%

      \[\leadsto z0 - \left(z1 \cdot \color{blue}{\left(41.341705691712875 \cdot \left(z1 \cdot z2\right)\right)} - 6.2831854820251465 \cdot z2\right) \cdot z1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := z0 - \left(1 \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1\\ \mathbf{if}\;z2 \leq -1.4 \cdot 10^{-131}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z2 \leq 2.6 \cdot 10^{-252}:\\ \;\;\;\;\left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (let* ((t_0
        (-
         z0
         (*
          (*
           1.0
           (*
            (- (* 41.341705691712875 (* z1 z1)) 6.2831854820251465)
            z2))
          z1))))
  (if (<= z2 -1.4e-131)
    t_0
    (if (<= z2 2.6e-252)
      (* (- 1.0 (* z1 (* 19.739209900765786 z1))) z0)
      t_0))))

C

double code(double z0, double z2, double z1) {
	double t_0 = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	double tmp;
	if (z2 <= -1.4e-131) {
		tmp = t_0;
	} else if (z2 <= 2.6e-252) {
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	} 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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z0 - ((1.0d0 * (((41.341705691712875d0 * (z1 * z1)) - 6.2831854820251465d0) * z2)) * z1)
    if (z2 <= (-1.4d-131)) then
        tmp = t_0
    else if (z2 <= 2.6d-252) then
        tmp = (1.0d0 - (z1 * (19.739209900765786d0 * z1))) * z0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z2, double z1) {
	double t_0 = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	double tmp;
	if (z2 <= -1.4e-131) {
		tmp = t_0;
	} else if (z2 <= 2.6e-252) {
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z2, z1):
	t_0 = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1)
	tmp = 0
	if z2 <= -1.4e-131:
		tmp = t_0
	elif z2 <= 2.6e-252:
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z2, z1)
	t_0 = Float64(z0 - Float64(Float64(1.0 * Float64(Float64(Float64(41.341705691712875 * Float64(z1 * z1)) - 6.2831854820251465) * z2)) * z1))
	tmp = 0.0
	if (z2 <= -1.4e-131)
		tmp = t_0;
	elseif (z2 <= 2.6e-252)
		tmp = Float64(Float64(1.0 - Float64(z1 * Float64(19.739209900765786 * z1))) * z0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z2, z1)
	t_0 = z0 - ((1.0 * (((41.341705691712875 * (z1 * z1)) - 6.2831854820251465) * z2)) * z1);
	tmp = 0.0;
	if (z2 <= -1.4e-131)
		tmp = t_0;
	elseif (z2 <= 2.6e-252)
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z2_, z1_] := Block[{t$95$0 = N[(z0 - N[(N[(1.0 * N[(N[(N[(41.341705691712875 * N[(z1 * z1), $MachinePrecision]), $MachinePrecision] - 6.2831854820251465), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z2, -1.4e-131], t$95$0, If[LessEqual[z2, 2.6e-252], N[(N[(1.0 - N[(z1 * N[(19.739209900765786 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z2 < -1.4e-131 or 2.5999999999999999e-252 < z2

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 - \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right)} \cdot z1 \]

      2. sub-to-mult N/A

         \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

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

         \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right)} \cdot z1 \]

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

         \[\leadsto z0 - \left(\color{blue}{\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}\right)} \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      5. lower-unsound-/.f64 85.9%

         \[\leadsto z0 - \left(\left(1 - \color{blue}{\frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      6. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\color{blue}{z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      7. *-commutative N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\color{blue}{\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      8. lower-*.f64 85.9%

         \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\color{blue}{\left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) \cdot z2}}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      9. lift-*.f64 N/A

         \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\color{blue}{\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      10. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\color{blue}{\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right)} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)\right) \cdot z1 \]

      11. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(\color{blue}{41.341705691712875 \cdot \left(z1 \cdot z1\right)} - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right)\right)\right) \cdot z1 \]

      12. lift-*.f64 N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \color{blue}{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right)\right)}\right) \cdot z1 \]

      13. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \color{blue}{\left(\left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)}\right) \cdot z1 \]

      14. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \color{blue}{\left(\left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) \cdot z2\right)}\right) \cdot z1 \]

      15. lift-*.f64 N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000}} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)\right) \cdot z1 \]

      16. *-commutative N/A

          \[\leadsto z0 - \left(\left(1 - \frac{\left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1}{\left(\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right) - \frac{12566370964050293}{2000000000000000}\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{\frac{330733645533703}{8000000000000} \cdot \left(z1 \cdot z1\right)} - \frac{12566370964050293}{2000000000000000}\right) \cdot z2\right)\right) \cdot z1 \]

      17. lower-*.f64 85.9%

          \[\leadsto z0 - \left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(\left(\color{blue}{41.341705691712875 \cdot \left(z1 \cdot z1\right)} - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]

   3. Applied rewrites 85.9%

      \[\leadsto z0 - \color{blue}{\left(\left(1 - \frac{\left(-19.739209900765786 \cdot z0\right) \cdot z1}{\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2}\right) \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right)} \cdot z1 \]

   4. Taylor expanded in z0 around 0

      \[\leadsto z0 - \left(\color{blue}{1} \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]
   5. Step-by-step derivation

   6. Applied rewrites 86.9%

      \[\leadsto z0 - \left(\color{blue}{1} \cdot \left(\left(41.341705691712875 \cdot \left(z1 \cdot z1\right) - 6.2831854820251465\right) \cdot z2\right)\right) \cdot z1 \]

   if -1.4e-131 < z2 < 2.5999999999999999e-252

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1} \]

      2. sub-to-mult N/A

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

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

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

   3. Applied rewrites 88.3%

      \[\leadsto \color{blue}{\left(1 - \frac{\left(\left(19.739209900765786 \cdot z0\right) \cdot z1 - \left(6.2831854820251465 - 41.341705691712875 \cdot \left(z1 \cdot z1\right)\right) \cdot z2\right) \cdot z1}{z0}\right) \cdot z0} \]

   4. Taylor expanded in z1 around 0

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \color{blue}{\left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000} \cdot z1}\right)\right) \cdot z0 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000}} \cdot z1\right)\right) \cdot z0 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)\right) \cdot z0 \]

      5. lower-*.f64 66.4%

         \[\leadsto \left(1 - z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]

   6. Applied rewrites 66.4%

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot z1\right)}\right) \cdot z0 \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \left(1 - z1 \cdot \left(\frac{9869604950382893}{500000000000000} \cdot \color{blue}{z1}\right)\right) \cdot z0 \]
   8. Step-by-step derivation

      1. lower-*.f64 60.9%

         \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0 \]

   9. Applied rewrites 60.9%

      \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_0 := \left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0\\ \mathbf{if}\;z1 \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z1 \leq 1.65:\\ \;\;\;\;z0 - \left(-6.2831854820251465 \cdot z1\right) \cdot z2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (let* ((t_0 (* (- 1.0 (* z1 (* 19.739209900765786 z1))) z0)))
  (if (<= z1 -1.6e-16)
    t_0
    (if (<= z1 1.65) (- z0 (* (* -6.2831854820251465 z1) z2)) t_0))))

C

double code(double z0, double z2, double z1) {
	double t_0 = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	double tmp;
	if (z1 <= -1.6e-16) {
		tmp = t_0;
	} else if (z1 <= 1.65) {
		tmp = z0 - ((-6.2831854820251465 * z1) * z2);
	} 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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - (z1 * (19.739209900765786d0 * z1))) * z0
    if (z1 <= (-1.6d-16)) then
        tmp = t_0
    else if (z1 <= 1.65d0) then
        tmp = z0 - (((-6.2831854820251465d0) * z1) * z2)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z2, double z1) {
	double t_0 = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	double tmp;
	if (z1 <= -1.6e-16) {
		tmp = t_0;
	} else if (z1 <= 1.65) {
		tmp = z0 - ((-6.2831854820251465 * z1) * z2);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z2, z1):
	t_0 = (1.0 - (z1 * (19.739209900765786 * z1))) * z0
	tmp = 0
	if z1 <= -1.6e-16:
		tmp = t_0
	elif z1 <= 1.65:
		tmp = z0 - ((-6.2831854820251465 * z1) * z2)
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z2, z1)
	t_0 = Float64(Float64(1.0 - Float64(z1 * Float64(19.739209900765786 * z1))) * z0)
	tmp = 0.0
	if (z1 <= -1.6e-16)
		tmp = t_0;
	elseif (z1 <= 1.65)
		tmp = Float64(z0 - Float64(Float64(-6.2831854820251465 * z1) * z2));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z2, z1)
	t_0 = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	tmp = 0.0;
	if (z1 <= -1.6e-16)
		tmp = t_0;
	elseif (z1 <= 1.65)
		tmp = z0 - ((-6.2831854820251465 * z1) * z2);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z2_, z1_] := Block[{t$95$0 = N[(N[(1.0 - N[(z1 * N[(19.739209900765786 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision]}, If[LessEqual[z1, -1.6e-16], t$95$0, If[LessEqual[z1, 1.65], N[(z0 - N[(N[(-6.2831854820251465 * z1), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z1 < -1.6000000000000001e-16 or 1.6499999999999999 < z1

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1} \]

      2. sub-to-mult N/A

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

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

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

   3. Applied rewrites 88.3%

      \[\leadsto \color{blue}{\left(1 - \frac{\left(\left(19.739209900765786 \cdot z0\right) \cdot z1 - \left(6.2831854820251465 - 41.341705691712875 \cdot \left(z1 \cdot z1\right)\right) \cdot z2\right) \cdot z1}{z0}\right) \cdot z0} \]

   4. Taylor expanded in z1 around 0

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \color{blue}{\left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000} \cdot z1}\right)\right) \cdot z0 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000}} \cdot z1\right)\right) \cdot z0 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)\right) \cdot z0 \]

      5. lower-*.f64 66.4%

         \[\leadsto \left(1 - z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]

   6. Applied rewrites 66.4%

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot z1\right)}\right) \cdot z0 \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \left(1 - z1 \cdot \left(\frac{9869604950382893}{500000000000000} \cdot \color{blue}{z1}\right)\right) \cdot z0 \]
   8. Step-by-step derivation

      1. lower-*.f64 60.9%

         \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0 \]

   9. Applied rewrites 60.9%

      \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]

   if -1.6000000000000001e-16 < z1 < 1.6499999999999999

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

   2. Taylor expanded in z1 around 0

      \[\leadsto z0 - \color{blue}{\frac{-12566370964050293}{2000000000000000} \cdot \left(z1 \cdot z2\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 - \frac{-12566370964050293}{2000000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)} \]

      2. lower-*.f64 49.7%

         \[\leadsto z0 - -6.2831854820251465 \cdot \left(z1 \cdot \color{blue}{z2}\right) \]

   4. Applied rewrites 49.7%

      \[\leadsto z0 - \color{blue}{-6.2831854820251465 \cdot \left(z1 \cdot z2\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto z0 - \frac{-12566370964050293}{2000000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto z0 - \frac{-12566370964050293}{2000000000000000} \cdot \left(z1 \cdot \color{blue}{z2}\right) \]

      3. associate-*r* N/A

         \[\leadsto z0 - \left(\frac{-12566370964050293}{2000000000000000} \cdot z1\right) \cdot \color{blue}{z2} \]

      4. lower-*.f64 N/A

         \[\leadsto z0 - \left(\frac{-12566370964050293}{2000000000000000} \cdot z1\right) \cdot \color{blue}{z2} \]

      5. lower-*.f64 49.7%

         \[\leadsto z0 - \left(-6.2831854820251465 \cdot z1\right) \cdot z2 \]

   6. Applied rewrites 49.7%

      \[\leadsto z0 - \left(-6.2831854820251465 \cdot z1\right) \cdot \color{blue}{z2} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 73.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z1 \leq 9 \cdot 10^{-12}:\\ \;\;\;\;z0 - \left(z2 \cdot -6.2831854820251465 - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0\\ \end{array} \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (if (<= z1 9e-12)
  (-
   z0
   (*
    (- (* z2 -6.2831854820251465) (* (* -19.739209900765786 z0) z1))
    z1))
  (* (- 1.0 (* z1 (* 19.739209900765786 z1))) z0)))

C

double code(double z0, double z2, double z1) {
	double tmp;
	if (z1 <= 9e-12) {
		tmp = z0 - (((z2 * -6.2831854820251465) - ((-19.739209900765786 * z0) * z1)) * z1);
	} else {
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	}
	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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    real(8) :: tmp
    if (z1 <= 9d-12) then
        tmp = z0 - (((z2 * (-6.2831854820251465d0)) - (((-19.739209900765786d0) * z0) * z1)) * z1)
    else
        tmp = (1.0d0 - (z1 * (19.739209900765786d0 * z1))) * z0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z2, double z1) {
	double tmp;
	if (z1 <= 9e-12) {
		tmp = z0 - (((z2 * -6.2831854820251465) - ((-19.739209900765786 * z0) * z1)) * z1);
	} else {
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	}
	return tmp;
}

Python

def code(z0, z2, z1):
	tmp = 0
	if z1 <= 9e-12:
		tmp = z0 - (((z2 * -6.2831854820251465) - ((-19.739209900765786 * z0) * z1)) * z1)
	else:
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0
	return tmp

Julia

function code(z0, z2, z1)
	tmp = 0.0
	if (z1 <= 9e-12)
		tmp = Float64(z0 - Float64(Float64(Float64(z2 * -6.2831854820251465) - Float64(Float64(-19.739209900765786 * z0) * z1)) * z1));
	else
		tmp = Float64(Float64(1.0 - Float64(z1 * Float64(19.739209900765786 * z1))) * z0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z2, z1)
	tmp = 0.0;
	if (z1 <= 9e-12)
		tmp = z0 - (((z2 * -6.2831854820251465) - ((-19.739209900765786 * z0) * z1)) * z1);
	else
		tmp = (1.0 - (z1 * (19.739209900765786 * z1))) * z0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z2_, z1_] := If[LessEqual[z1, 9e-12], N[(z0 - N[(N[(N[(z2 * -6.2831854820251465), $MachinePrecision] - N[(N[(-19.739209900765786 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - N[(z1 * N[(19.739209900765786 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z1 < 8.9999999999999996e-12

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

   2. Taylor expanded in z1 around 0

      \[\leadsto z0 - \left(z2 \cdot \color{blue}{\frac{-12566370964050293}{2000000000000000}} - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   3. Step-by-step derivation

   4. Applied rewrites 71.4%

      \[\leadsto z0 - \left(z2 \cdot \color{blue}{-6.2831854820251465} - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

   if 8.9999999999999996e-12 < z1

   1. Initial program 93.5%

      \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1} \]

      2. sub-to-mult N/A

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

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

         \[\leadsto \color{blue}{\left(1 - \frac{\left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot \frac{330733645533703}{8000000000000} - \frac{12566370964050293}{2000000000000000}\right) - \left(\frac{-9869604950382893}{500000000000000} \cdot z0\right) \cdot z1\right) \cdot z1}{z0}\right) \cdot z0} \]

   3. Applied rewrites 88.3%

      \[\leadsto \color{blue}{\left(1 - \frac{\left(\left(19.739209900765786 \cdot z0\right) \cdot z1 - \left(6.2831854820251465 - 41.341705691712875 \cdot \left(z1 \cdot z1\right)\right) \cdot z2\right) \cdot z1}{z0}\right) \cdot z0} \]

   4. Taylor expanded in z1 around 0

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \color{blue}{\left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)}\right) \cdot z0 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000} \cdot z1}\right)\right) \cdot z0 \]

      3. lower-*.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \color{blue}{\frac{9869604950382893}{500000000000000}} \cdot z1\right)\right) \cdot z0 \]

      4. lower-/.f64 N/A

         \[\leadsto \left(1 - z1 \cdot \left(\frac{-12566370964050293}{2000000000000000} \cdot \frac{z2}{z0} + \frac{9869604950382893}{500000000000000} \cdot z1\right)\right) \cdot z0 \]

      5. lower-*.f64 66.4%

         \[\leadsto \left(1 - z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]

   6. Applied rewrites 66.4%

      \[\leadsto \left(1 - \color{blue}{z1 \cdot \left(-6.2831854820251465 \cdot \frac{z2}{z0} + 19.739209900765786 \cdot z1\right)}\right) \cdot z0 \]

   7. Taylor expanded in z0 around inf

      \[\leadsto \left(1 - z1 \cdot \left(\frac{9869604950382893}{500000000000000} \cdot \color{blue}{z1}\right)\right) \cdot z0 \]
   8. Step-by-step derivation

      1. lower-*.f64 60.9%

         \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot z1\right)\right) \cdot z0 \]

   9. Applied rewrites 60.9%

      \[\leadsto \left(1 - z1 \cdot \left(19.739209900765786 \cdot \color{blue}{z1}\right)\right) \cdot z0 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 49.7% accurate, 2.9× speedup

Math

\[z0 - \left(-6.2831854820251465 \cdot z1\right) \cdot z2 \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (- z0 (* (* -6.2831854820251465 z1) z2)))

C

double code(double z0, double z2, double z1) {
	return z0 - ((-6.2831854820251465 * z1) * z2);
}

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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    code = z0 - (((-6.2831854820251465d0) * z1) * z2)
end function

Java

public static double code(double z0, double z2, double z1) {
	return z0 - ((-6.2831854820251465 * z1) * z2);
}

Python

def code(z0, z2, z1):
	return z0 - ((-6.2831854820251465 * z1) * z2)

Julia

function code(z0, z2, z1)
	return Float64(z0 - Float64(Float64(-6.2831854820251465 * z1) * z2))
end

MATLAB

function tmp = code(z0, z2, z1)
	tmp = z0 - ((-6.2831854820251465 * z1) * z2);
end

Wolfram

code[z0_, z2_, z1_] := N[(z0 - N[(N[(-6.2831854820251465 * z1), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.5%

   \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

2. Taylor expanded in z1 around 0

   \[\leadsto z0 - \color{blue}{\frac{-12566370964050293}{2000000000000000} \cdot \left(z1 \cdot z2\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z0 - \frac{-12566370964050293}{2000000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)} \]

   2. lower-*.f64 49.7%

      \[\leadsto z0 - -6.2831854820251465 \cdot \left(z1 \cdot \color{blue}{z2}\right) \]

4. Applied rewrites 49.7%

   \[\leadsto z0 - \color{blue}{-6.2831854820251465 \cdot \left(z1 \cdot z2\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto z0 - \frac{-12566370964050293}{2000000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)} \]

   2. lift-*.f64 N/A

      \[\leadsto z0 - \frac{-12566370964050293}{2000000000000000} \cdot \left(z1 \cdot \color{blue}{z2}\right) \]

   3. associate-*r* N/A

      \[\leadsto z0 - \left(\frac{-12566370964050293}{2000000000000000} \cdot z1\right) \cdot \color{blue}{z2} \]

   4. lower-*.f64 N/A

      \[\leadsto z0 - \left(\frac{-12566370964050293}{2000000000000000} \cdot z1\right) \cdot \color{blue}{z2} \]

   5. lower-*.f64 49.7%

      \[\leadsto z0 - \left(-6.2831854820251465 \cdot z1\right) \cdot z2 \]

6. Applied rewrites 49.7%

   \[\leadsto z0 - \left(-6.2831854820251465 \cdot z1\right) \cdot \color{blue}{z2} \]
7. Add Preprocessing

Alternative 9: 49.7% accurate, 2.9× speedup

Math

\[z0 - -6.2831854820251465 \cdot \left(z1 \cdot z2\right) \]

FPCore

(FPCore (z0 z2 z1)
  :precision binary64
  (- z0 (* -6.2831854820251465 (* z1 z2))))

C

double code(double z0, double z2, double z1) {
	return z0 - (-6.2831854820251465 * (z1 * z2));
}

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(z0, z2, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z2
    real(8), intent (in) :: z1
    code = z0 - ((-6.2831854820251465d0) * (z1 * z2))
end function

Java

public static double code(double z0, double z2, double z1) {
	return z0 - (-6.2831854820251465 * (z1 * z2));
}

Python

def code(z0, z2, z1):
	return z0 - (-6.2831854820251465 * (z1 * z2))

Julia

function code(z0, z2, z1)
	return Float64(z0 - Float64(-6.2831854820251465 * Float64(z1 * z2)))
end

MATLAB

function tmp = code(z0, z2, z1)
	tmp = z0 - (-6.2831854820251465 * (z1 * z2));
end

Wolfram

code[z0_, z2_, z1_] := N[(z0 - N[(-6.2831854820251465 * N[(z1 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.5%

   \[z0 - \left(z2 \cdot \left(\left(z1 \cdot z1\right) \cdot 41.341705691712875 - 6.2831854820251465\right) - \left(-19.739209900765786 \cdot z0\right) \cdot z1\right) \cdot z1 \]

2. Taylor expanded in z1 around 0

   \[\leadsto z0 - \color{blue}{\frac{-12566370964050293}{2000000000000000} \cdot \left(z1 \cdot z2\right)} \]
3. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto z0 - \frac{-12566370964050293}{2000000000000000} \cdot \color{blue}{\left(z1 \cdot z2\right)} \]

   2. lower-*.f64 49.7%

      \[\leadsto z0 - -6.2831854820251465 \cdot \left(z1 \cdot \color{blue}{z2}\right) \]

4. Applied rewrites 49.7%

   \[\leadsto z0 - \color{blue}{-6.2831854820251465 \cdot \left(z1 \cdot z2\right)} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0 z2 z1)
  :name "(- z0 (* (- (* z2 (- (* (* z1 z1) 330733645533703/8000000000000) 12566370964050293/2000000000000000)) (* (* -9869604950382893/500000000000000 z0) z1)) z1))"
  :precision binary64
  (- z0 (* (- (* z2 (- (* (* z1 z1) 41.341705691712875) 6.2831854820251465)) (* (* -19.739209900765786 z0) z1)) z1)))