(/ z0 (+ (/ z3 (* z4 z4)) (/ z1 (* z2 z2))))

Percentage Accurate: 76.6% → 88.4%

Time: 3.2s

Alternatives: 12

Speedup: 0.7×

Specification

Math

\[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (/ z0 (+ (/ z3 (* z4 z4)) (/ z1 (* z2 z2)))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	return z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * 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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    code = z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)))
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	return z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)));
}

Python

def code(z0, z3, z4, z1, z2):
	return z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)))

Julia

function code(z0, z3, z4, z1, z2)
	return Float64(z0 / Float64(Float64(z3 / Float64(z4 * z4)) + Float64(z1 / Float64(z2 * z2))))
end

MATLAB

function tmp = code(z0, z3, z4, z1, z2)
	tmp = z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)));
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := N[(z0 / N[(N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision] + N[(z1 / N[(z2 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.6% accurate, 1.0× speedup

Math

\[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (/ z0 (+ (/ z3 (* z4 z4)) (/ z1 (* z2 z2)))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	return z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * 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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    code = z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)))
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	return z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)));
}

Python

def code(z0, z3, z4, z1, z2):
	return z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)))

Julia

function code(z0, z3, z4, z1, z2)
	return Float64(z0 / Float64(Float64(z3 / Float64(z4 * z4)) + Float64(z1 / Float64(z2 * z2))))
end

MATLAB

function tmp = code(z0, z3, z4, z1, z2)
	tmp = z0 / ((z3 / (z4 * z4)) + (z1 / (z2 * z2)));
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := N[(z0 / N[(N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision] + N[(z1 / N[(z2 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \frac{z0}{\frac{z3}{\left|z4\right|} \cdot \frac{z2}{\left|z4\right|} + \frac{z1}{z2}} \cdot z2\\ \mathbf{if}\;\left|z4\right| \leq 3.3 \cdot 10^{-208}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\left|z4\right| \leq 4.1 \cdot 10^{-8}:\\ \;\;\;\;\left(z2 \cdot \left|z4\right|\right) \cdot \left(\left|z4\right| \cdot \frac{z0}{z2 \cdot z3 + \frac{z1 \cdot \left(\left|z4\right| \cdot \left|z4\right|\right)}{z2}}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0
        (*
         (/ z0 (+ (* (/ z3 (fabs z4)) (/ z2 (fabs z4))) (/ z1 z2)))
         z2)))
  (if (<= (fabs z4) 3.3e-208)
    t_0
    (if (<= (fabs z4) 4.1e-8)
      (*
       (* z2 (fabs z4))
       (*
        (fabs z4)
        (/ z0 (+ (* z2 z3) (/ (* z1 (* (fabs z4) (fabs z4))) z2)))))
      t_0))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = (z0 / (((z3 / fabs(z4)) * (z2 / fabs(z4))) + (z1 / z2))) * z2;
	double tmp;
	if (fabs(z4) <= 3.3e-208) {
		tmp = t_0;
	} else if (fabs(z4) <= 4.1e-8) {
		tmp = (z2 * fabs(z4)) * (fabs(z4) * (z0 / ((z2 * z3) + ((z1 * (fabs(z4) * fabs(z4))) / 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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z0 / (((z3 / abs(z4)) * (z2 / abs(z4))) + (z1 / z2))) * z2
    if (abs(z4) <= 3.3d-208) then
        tmp = t_0
    else if (abs(z4) <= 4.1d-8) then
        tmp = (z2 * abs(z4)) * (abs(z4) * (z0 / ((z2 * z3) + ((z1 * (abs(z4) * abs(z4))) / z2))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = (z0 / (((z3 / Math.abs(z4)) * (z2 / Math.abs(z4))) + (z1 / z2))) * z2;
	double tmp;
	if (Math.abs(z4) <= 3.3e-208) {
		tmp = t_0;
	} else if (Math.abs(z4) <= 4.1e-8) {
		tmp = (z2 * Math.abs(z4)) * (Math.abs(z4) * (z0 / ((z2 * z3) + ((z1 * (Math.abs(z4) * Math.abs(z4))) / z2))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = (z0 / (((z3 / math.fabs(z4)) * (z2 / math.fabs(z4))) + (z1 / z2))) * z2
	tmp = 0
	if math.fabs(z4) <= 3.3e-208:
		tmp = t_0
	elif math.fabs(z4) <= 4.1e-8:
		tmp = (z2 * math.fabs(z4)) * (math.fabs(z4) * (z0 / ((z2 * z3) + ((z1 * (math.fabs(z4) * math.fabs(z4))) / z2))))
	else:
		tmp = t_0
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(Float64(z0 / Float64(Float64(Float64(z3 / abs(z4)) * Float64(z2 / abs(z4))) + Float64(z1 / z2))) * z2)
	tmp = 0.0
	if (abs(z4) <= 3.3e-208)
		tmp = t_0;
	elseif (abs(z4) <= 4.1e-8)
		tmp = Float64(Float64(z2 * abs(z4)) * Float64(abs(z4) * Float64(z0 / Float64(Float64(z2 * z3) + Float64(Float64(z1 * Float64(abs(z4) * abs(z4))) / z2)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = (z0 / (((z3 / abs(z4)) * (z2 / abs(z4))) + (z1 / z2))) * z2;
	tmp = 0.0;
	if (abs(z4) <= 3.3e-208)
		tmp = t_0;
	elseif (abs(z4) <= 4.1e-8)
		tmp = (z2 * abs(z4)) * (abs(z4) * (z0 / ((z2 * z3) + ((z1 * (abs(z4) * abs(z4))) / z2))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(N[(z0 / N[(N[(N[(z3 / N[Abs[z4], $MachinePrecision]), $MachinePrecision] * N[(z2 / N[Abs[z4], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z1 / z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z2), $MachinePrecision]}, If[LessEqual[N[Abs[z4], $MachinePrecision], 3.3e-208], t$95$0, If[LessEqual[N[Abs[z4], $MachinePrecision], 4.1e-8], N[(N[(z2 * N[Abs[z4], $MachinePrecision]), $MachinePrecision] * N[(N[Abs[z4], $MachinePrecision] * N[(z0 / N[(N[(z2 * z3), $MachinePrecision] + N[(N[(z1 * N[(N[Abs[z4], $MachinePrecision] * N[Abs[z4], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z4 < 3.3000000000000001e-208 or 4.1000000000000003e-8 < z4

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. add-to-fraction N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}{z2}}} \]

      5. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \cdot z2 \]

      9. lower-+.f64 80.8%

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

   5. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \cdot z2 \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} \cdot z2 + \frac{z1}{z2}} \cdot z2 \]

      3. associate-*l/ N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 \cdot z2}{z4 \cdot z4}} + \frac{z1}{z2}} \cdot z2 \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3 \cdot z2}{\color{blue}{z4 \cdot z4}} + \frac{z1}{z2}} \cdot z2 \]

      5. times-frac N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4} \cdot \frac{z2}{z4}} + \frac{z1}{z2}} \cdot z2 \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4} \cdot \frac{z2}{z4}} + \frac{z1}{z2}} \cdot z2 \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4}} \cdot \frac{z2}{z4} + \frac{z1}{z2}} \cdot z2 \]

      8. lower-/.f64 86.3%

         \[\leadsto \frac{z0}{\frac{z3}{z4} \cdot \color{blue}{\frac{z2}{z4}} + \frac{z1}{z2}} \cdot z2 \]

   7. Applied rewrites 86.3%

      \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4} \cdot \frac{z2}{z4}} + \frac{z1}{z2}} \cdot z2 \]

   if 3.3000000000000001e-208 < z4 < 4.1000000000000003e-8

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} + \frac{\frac{z1}{z2}}{z2}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. common-denominator N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}{\left(z4 \cdot z4\right) \cdot z2}}} \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2}} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      12. associate-*l/ N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{\color{blue}{z1 \cdot \left(z4 \cdot z4\right)}}{z2} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      15. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      17. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      18. lower-*.f64 53.2%

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right) \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(z2 \cdot \color{blue}{\left(z4 \cdot z4\right)}\right) \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(z2 \cdot z4\right) \cdot z4\right)} \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3}\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3}\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right)} \cdot \left(z4 \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3}\right) \]

      9. lower-*.f64 64.6%

         \[\leadsto \left(z2 \cdot z4\right) \cdot \color{blue}{\left(z4 \cdot \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3}\right)} \]

      10. lift-+.f64 N/A

          \[\leadsto \left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3}}\right) \]

      11. +-commutative N/A

          \[\leadsto \left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{\color{blue}{z2 \cdot z3 + \frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}}}\right) \]

      12. lower-+.f64 64.6%

          \[\leadsto \left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{\color{blue}{z2 \cdot z3 + \frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}}}\right) \]

   7. Applied rewrites 64.6%

      \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3 + \frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3}{z4 \cdot z4}\\ \mathbf{if}\;\left|z2\right| \leq 1.5 \cdot 10^{-103}:\\ \;\;\;\;\left(\frac{\left|z2\right|}{\left(\left|z2\right| \cdot t\_0\right) \cdot \left|z2\right| + z1} \cdot z0\right) \cdot \left|z2\right|\\ \mathbf{elif}\;\left|z2\right| \leq 10^{+140}:\\ \;\;\;\;\frac{z0}{\frac{\frac{z3}{z4}}{z4} + \frac{z1}{\left|z2\right| \cdot \left|z2\right|}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{t\_0 + \frac{\frac{z1}{\left|z2\right|}}{\left|z2\right|}}\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0 (/ z3 (* z4 z4))))
  (if (<= (fabs z2) 1.5e-103)
    (*
     (* (/ (fabs z2) (+ (* (* (fabs z2) t_0) (fabs z2)) z1)) z0)
     (fabs z2))
    (if (<= (fabs z2) 1e+140)
      (/ z0 (+ (/ (/ z3 z4) z4) (/ z1 (* (fabs z2) (fabs z2)))))
      (/ z0 (+ t_0 (/ (/ z1 (fabs z2)) (fabs z2))))))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double tmp;
	if (fabs(z2) <= 1.5e-103) {
		tmp = ((fabs(z2) / (((fabs(z2) * t_0) * fabs(z2)) + z1)) * z0) * fabs(z2);
	} else if (fabs(z2) <= 1e+140) {
		tmp = z0 / (((z3 / z4) / z4) + (z1 / (fabs(z2) * fabs(z2))));
	} else {
		tmp = z0 / (t_0 + ((z1 / fabs(z2)) / fabs(z2)));
	}
	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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z3 / (z4 * z4)
    if (abs(z2) <= 1.5d-103) then
        tmp = ((abs(z2) / (((abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2)
    else if (abs(z2) <= 1d+140) then
        tmp = z0 / (((z3 / z4) / z4) + (z1 / (abs(z2) * abs(z2))))
    else
        tmp = z0 / (t_0 + ((z1 / abs(z2)) / abs(z2)))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double tmp;
	if (Math.abs(z2) <= 1.5e-103) {
		tmp = ((Math.abs(z2) / (((Math.abs(z2) * t_0) * Math.abs(z2)) + z1)) * z0) * Math.abs(z2);
	} else if (Math.abs(z2) <= 1e+140) {
		tmp = z0 / (((z3 / z4) / z4) + (z1 / (Math.abs(z2) * Math.abs(z2))));
	} else {
		tmp = z0 / (t_0 + ((z1 / Math.abs(z2)) / Math.abs(z2)));
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = z3 / (z4 * z4)
	tmp = 0
	if math.fabs(z2) <= 1.5e-103:
		tmp = ((math.fabs(z2) / (((math.fabs(z2) * t_0) * math.fabs(z2)) + z1)) * z0) * math.fabs(z2)
	elif math.fabs(z2) <= 1e+140:
		tmp = z0 / (((z3 / z4) / z4) + (z1 / (math.fabs(z2) * math.fabs(z2))))
	else:
		tmp = z0 / (t_0 + ((z1 / math.fabs(z2)) / math.fabs(z2)))
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(z3 / Float64(z4 * z4))
	tmp = 0.0
	if (abs(z2) <= 1.5e-103)
		tmp = Float64(Float64(Float64(abs(z2) / Float64(Float64(Float64(abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2));
	elseif (abs(z2) <= 1e+140)
		tmp = Float64(z0 / Float64(Float64(Float64(z3 / z4) / z4) + Float64(z1 / Float64(abs(z2) * abs(z2)))));
	else
		tmp = Float64(z0 / Float64(t_0 + Float64(Float64(z1 / abs(z2)) / abs(z2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = z3 / (z4 * z4);
	tmp = 0.0;
	if (abs(z2) <= 1.5e-103)
		tmp = ((abs(z2) / (((abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2);
	elseif (abs(z2) <= 1e+140)
		tmp = z0 / (((z3 / z4) / z4) + (z1 / (abs(z2) * abs(z2))));
	else
		tmp = z0 / (t_0 + ((z1 / abs(z2)) / abs(z2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Abs[z2], $MachinePrecision], 1.5e-103], N[(N[(N[(N[Abs[z2], $MachinePrecision] / N[(N[(N[(N[Abs[z2], $MachinePrecision] * t$95$0), $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision] + z1), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[z2], $MachinePrecision], 1e+140], N[(z0 / N[(N[(N[(z3 / z4), $MachinePrecision] / z4), $MachinePrecision] + N[(z1 / N[(N[Abs[z2], $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z0 / N[(t$95$0 + N[(N[(z1 / N[Abs[z2], $MachinePrecision]), $MachinePrecision] / N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z2 < 1.5e-103

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. add-to-fraction N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}{z2}}} \]

      5. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \cdot z2 \]

      9. lower-+.f64 80.8%

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

   5. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      2. mult-flip N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}\right)} \cdot z2 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

   7. Applied rewrites 78.8%

      \[\leadsto \color{blue}{\left(\frac{z2}{\left(z2 \cdot \frac{z3}{z4 \cdot z4}\right) \cdot z2 + z1} \cdot z0\right)} \cdot z2 \]

   if 1.5e-103 < z2 < 1.0000000000000001e140

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} + \frac{z1}{z2 \cdot z2}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{\color{blue}{z4 \cdot z4}} + \frac{z1}{z2 \cdot z2}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4}}{z4}} + \frac{z1}{z2 \cdot z2}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4}}{z4}} + \frac{z1}{z2 \cdot z2}} \]

      5. lower-/.f64 81.2%

         \[\leadsto \frac{z0}{\frac{\color{blue}{\frac{z3}{z4}}}{z4} + \frac{z1}{z2 \cdot z2}} \]

   3. Applied rewrites 81.2%

      \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4}}{z4}} + \frac{z1}{z2 \cdot z2}} \]

   if 1.0000000000000001e140 < z2

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3}{z4 \cdot z4}\\ \mathbf{if}\;\left|z2\right| \leq 1.5 \cdot 10^{-103}:\\ \;\;\;\;\left(\frac{\left|z2\right|}{\left(\left|z2\right| \cdot t\_0\right) \cdot \left|z2\right| + z1} \cdot z0\right) \cdot \left|z2\right|\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{t\_0 + \frac{\frac{z1}{\left|z2\right|}}{\left|z2\right|}}\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0 (/ z3 (* z4 z4))))
  (if (<= (fabs z2) 1.5e-103)
    (*
     (* (/ (fabs z2) (+ (* (* (fabs z2) t_0) (fabs z2)) z1)) z0)
     (fabs z2))
    (/ z0 (+ t_0 (/ (/ z1 (fabs z2)) (fabs z2)))))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double tmp;
	if (fabs(z2) <= 1.5e-103) {
		tmp = ((fabs(z2) / (((fabs(z2) * t_0) * fabs(z2)) + z1)) * z0) * fabs(z2);
	} else {
		tmp = z0 / (t_0 + ((z1 / fabs(z2)) / fabs(z2)));
	}
	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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z3 / (z4 * z4)
    if (abs(z2) <= 1.5d-103) then
        tmp = ((abs(z2) / (((abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2)
    else
        tmp = z0 / (t_0 + ((z1 / abs(z2)) / abs(z2)))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double tmp;
	if (Math.abs(z2) <= 1.5e-103) {
		tmp = ((Math.abs(z2) / (((Math.abs(z2) * t_0) * Math.abs(z2)) + z1)) * z0) * Math.abs(z2);
	} else {
		tmp = z0 / (t_0 + ((z1 / Math.abs(z2)) / Math.abs(z2)));
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = z3 / (z4 * z4)
	tmp = 0
	if math.fabs(z2) <= 1.5e-103:
		tmp = ((math.fabs(z2) / (((math.fabs(z2) * t_0) * math.fabs(z2)) + z1)) * z0) * math.fabs(z2)
	else:
		tmp = z0 / (t_0 + ((z1 / math.fabs(z2)) / math.fabs(z2)))
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(z3 / Float64(z4 * z4))
	tmp = 0.0
	if (abs(z2) <= 1.5e-103)
		tmp = Float64(Float64(Float64(abs(z2) / Float64(Float64(Float64(abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2));
	else
		tmp = Float64(z0 / Float64(t_0 + Float64(Float64(z1 / abs(z2)) / abs(z2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = z3 / (z4 * z4);
	tmp = 0.0;
	if (abs(z2) <= 1.5e-103)
		tmp = ((abs(z2) / (((abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2);
	else
		tmp = z0 / (t_0 + ((z1 / abs(z2)) / abs(z2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Abs[z2], $MachinePrecision], 1.5e-103], N[(N[(N[(N[Abs[z2], $MachinePrecision] / N[(N[(N[(N[Abs[z2], $MachinePrecision] * t$95$0), $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision] + z1), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision], N[(z0 / N[(t$95$0 + N[(N[(z1 / N[Abs[z2], $MachinePrecision]), $MachinePrecision] / N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z2 < 1.5e-103

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. add-to-fraction N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}{z2}}} \]

      5. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \cdot z2 \]

      9. lower-+.f64 80.8%

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

   5. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      2. mult-flip N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}\right)} \cdot z2 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

   7. Applied rewrites 78.8%

      \[\leadsto \color{blue}{\left(\frac{z2}{\left(z2 \cdot \frac{z3}{z4 \cdot z4}\right) \cdot z2 + z1} \cdot z0\right)} \cdot z2 \]

   if 1.5e-103 < z2

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3}{z4 \cdot z4}\\ t_1 := \frac{z0}{t\_0 + \frac{z1}{z2 \cdot z2}}\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-195}:\\ \;\;\;\;\left(z2 \cdot z0\right) \cdot \frac{z2}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0 (/ z3 (* z4 z4))) (t_1 (/ z0 (+ t_0 (/ z1 (* z2 z2))))))
  (if (<= t_0 (- INFINITY))
    (* (* z2 z4) (* z4 (/ z0 (* z2 z3))))
    (if (<= t_0 -1e-307)
      t_1
      (if (<= t_0 5e-195) (* (* z2 z0) (/ z2 z1)) t_1)))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = z0 / (t_0 + (z1 / (z2 * z2)));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = (z2 * z4) * (z4 * (z0 / (z2 * z3)));
	} else if (t_0 <= -1e-307) {
		tmp = t_1;
	} else if (t_0 <= 5e-195) {
		tmp = (z2 * z0) * (z2 / z1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = z0 / (t_0 + (z1 / (z2 * z2)));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = (z2 * z4) * (z4 * (z0 / (z2 * z3)));
	} else if (t_0 <= -1e-307) {
		tmp = t_1;
	} else if (t_0 <= 5e-195) {
		tmp = (z2 * z0) * (z2 / z1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = z3 / (z4 * z4)
	t_1 = z0 / (t_0 + (z1 / (z2 * z2)))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = (z2 * z4) * (z4 * (z0 / (z2 * z3)))
	elif t_0 <= -1e-307:
		tmp = t_1
	elif t_0 <= 5e-195:
		tmp = (z2 * z0) * (z2 / z1)
	else:
		tmp = t_1
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(z3 / Float64(z4 * z4))
	t_1 = Float64(z0 / Float64(t_0 + Float64(z1 / Float64(z2 * z2))))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(Float64(z2 * z4) * Float64(z4 * Float64(z0 / Float64(z2 * z3))));
	elseif (t_0 <= -1e-307)
		tmp = t_1;
	elseif (t_0 <= 5e-195)
		tmp = Float64(Float64(z2 * z0) * Float64(z2 / z1));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = z3 / (z4 * z4);
	t_1 = z0 / (t_0 + (z1 / (z2 * z2)));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = (z2 * z4) * (z4 * (z0 / (z2 * z3)));
	elseif (t_0 <= -1e-307)
		tmp = t_1;
	elseif (t_0 <= 5e-195)
		tmp = (z2 * z0) * (z2 / z1);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z0 / N[(t$95$0 + N[(z1 / N[(z2 * z2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[(z2 * z4), $MachinePrecision] * N[(z4 * N[(z0 / N[(z2 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -1e-307], t$95$1, If[LessEqual[t$95$0, 5e-195], N[(N[(z2 * z0), $MachinePrecision] * N[(z2 / z1), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z3 (*.f64 z4 z4)) < -inf.0

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} + \frac{\frac{z1}{z2}}{z2}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. common-denominator N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}{\left(z4 \cdot z4\right) \cdot z2}}} \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2}} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      12. associate-*l/ N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{\color{blue}{z1 \cdot \left(z4 \cdot z4\right)}}{z2} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      15. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      17. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      18. lower-*.f64 53.2%

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   6. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      2. lower-*.f64 40.1%

         \[\leadsto \frac{z0}{z2 \cdot \color{blue}{z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   8. Applied rewrites 40.1%

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right) \cdot \frac{z0}{z2 \cdot z3}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \cdot \frac{z0}{z2 \cdot z3} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(z2 \cdot \color{blue}{\left(z4 \cdot z4\right)}\right) \cdot \frac{z0}{z2 \cdot z3} \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(z2 \cdot z4\right) \cdot z4\right)} \cdot \frac{z0}{z2 \cdot z3} \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right)} \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right) \]

      9. lower-*.f64 44.0%

         \[\leadsto \left(z2 \cdot z4\right) \cdot \color{blue}{\left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

   10. Applied rewrites 44.0%

       \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

   if -inf.0 < (/.f64 z3 (*.f64 z4 z4)) < -9.9999999999999991e-308 or 5.0000000000000001e-195 < (/.f64 z3 (*.f64 z4 z4))

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

   if -9.9999999999999991e-308 < (/.f64 z3 (*.f64 z4 z4)) < 5.0000000000000001e-195

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

   2. Taylor expanded in z3 around 0

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lower-pow.f64 50.2%

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   4. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lift-pow.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      4. pow2 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      9. lower-/.f64 49.8%

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   6. Applied rewrites 49.8%

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      2. *-commutative N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

      3. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z2 \cdot z2}{\color{blue}{z1}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z2 \cdot z2}{z1} \]

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 55.9%

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

   8. Applied rewrites 55.9%

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

Alternative 5: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3}{z4 \cdot z4}\\ t_1 := \left|z2\right| \cdot t\_0\\ \mathbf{if}\;\left|z2\right| \leq 1.5 \cdot 10^{-103}:\\ \;\;\;\;\left(\frac{\left|z2\right|}{t\_1 \cdot \left|z2\right| + z1} \cdot z0\right) \cdot \left|z2\right|\\ \mathbf{elif}\;\left|z2\right| \leq 1.28 \cdot 10^{+238}:\\ \;\;\;\;z0 \cdot \frac{\left|z2\right|}{t\_1 + \frac{z1}{\left|z2\right|}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{t\_0 + \frac{z1}{\left|z2\right| \cdot \left|z2\right|}}\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0 (/ z3 (* z4 z4))) (t_1 (* (fabs z2) t_0)))
  (if (<= (fabs z2) 1.5e-103)
    (* (* (/ (fabs z2) (+ (* t_1 (fabs z2)) z1)) z0) (fabs z2))
    (if (<= (fabs z2) 1.28e+238)
      (* z0 (/ (fabs z2) (+ t_1 (/ z1 (fabs z2)))))
      (/ z0 (+ t_0 (/ z1 (* (fabs z2) (fabs z2)))))))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = fabs(z2) * t_0;
	double tmp;
	if (fabs(z2) <= 1.5e-103) {
		tmp = ((fabs(z2) / ((t_1 * fabs(z2)) + z1)) * z0) * fabs(z2);
	} else if (fabs(z2) <= 1.28e+238) {
		tmp = z0 * (fabs(z2) / (t_1 + (z1 / fabs(z2))));
	} else {
		tmp = z0 / (t_0 + (z1 / (fabs(z2) * fabs(z2))));
	}
	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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z3 / (z4 * z4)
    t_1 = abs(z2) * t_0
    if (abs(z2) <= 1.5d-103) then
        tmp = ((abs(z2) / ((t_1 * abs(z2)) + z1)) * z0) * abs(z2)
    else if (abs(z2) <= 1.28d+238) then
        tmp = z0 * (abs(z2) / (t_1 + (z1 / abs(z2))))
    else
        tmp = z0 / (t_0 + (z1 / (abs(z2) * abs(z2))))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = Math.abs(z2) * t_0;
	double tmp;
	if (Math.abs(z2) <= 1.5e-103) {
		tmp = ((Math.abs(z2) / ((t_1 * Math.abs(z2)) + z1)) * z0) * Math.abs(z2);
	} else if (Math.abs(z2) <= 1.28e+238) {
		tmp = z0 * (Math.abs(z2) / (t_1 + (z1 / Math.abs(z2))));
	} else {
		tmp = z0 / (t_0 + (z1 / (Math.abs(z2) * Math.abs(z2))));
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = z3 / (z4 * z4)
	t_1 = math.fabs(z2) * t_0
	tmp = 0
	if math.fabs(z2) <= 1.5e-103:
		tmp = ((math.fabs(z2) / ((t_1 * math.fabs(z2)) + z1)) * z0) * math.fabs(z2)
	elif math.fabs(z2) <= 1.28e+238:
		tmp = z0 * (math.fabs(z2) / (t_1 + (z1 / math.fabs(z2))))
	else:
		tmp = z0 / (t_0 + (z1 / (math.fabs(z2) * math.fabs(z2))))
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(z3 / Float64(z4 * z4))
	t_1 = Float64(abs(z2) * t_0)
	tmp = 0.0
	if (abs(z2) <= 1.5e-103)
		tmp = Float64(Float64(Float64(abs(z2) / Float64(Float64(t_1 * abs(z2)) + z1)) * z0) * abs(z2));
	elseif (abs(z2) <= 1.28e+238)
		tmp = Float64(z0 * Float64(abs(z2) / Float64(t_1 + Float64(z1 / abs(z2)))));
	else
		tmp = Float64(z0 / Float64(t_0 + Float64(z1 / Float64(abs(z2) * abs(z2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = z3 / (z4 * z4);
	t_1 = abs(z2) * t_0;
	tmp = 0.0;
	if (abs(z2) <= 1.5e-103)
		tmp = ((abs(z2) / ((t_1 * abs(z2)) + z1)) * z0) * abs(z2);
	elseif (abs(z2) <= 1.28e+238)
		tmp = z0 * (abs(z2) / (t_1 + (z1 / abs(z2))));
	else
		tmp = z0 / (t_0 + (z1 / (abs(z2) * abs(z2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Abs[z2], $MachinePrecision] * t$95$0), $MachinePrecision]}, If[LessEqual[N[Abs[z2], $MachinePrecision], 1.5e-103], N[(N[(N[(N[Abs[z2], $MachinePrecision] / N[(N[(t$95$1 * N[Abs[z2], $MachinePrecision]), $MachinePrecision] + z1), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[z2], $MachinePrecision], 1.28e+238], N[(z0 * N[(N[Abs[z2], $MachinePrecision] / N[(t$95$1 + N[(z1 / N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z0 / N[(t$95$0 + N[(z1 / N[(N[Abs[z2], $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z2 < 1.5e-103

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. add-to-fraction N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}{z2}}} \]

      5. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \cdot z2 \]

      9. lower-+.f64 80.8%

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

   5. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      2. mult-flip N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}\right)} \cdot z2 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

   7. Applied rewrites 78.8%

      \[\leadsto \color{blue}{\left(\frac{z2}{\left(z2 \cdot \frac{z3}{z4 \cdot z4}\right) \cdot z2 + z1} \cdot z0\right)} \cdot z2 \]

   if 1.5e-103 < z2 < 1.2800000000000001e238

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. add-to-fraction N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}{z2}}} \]

      5. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \cdot z2 \]

      9. lower-+.f64 80.8%

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

   5. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{z0 \cdot z2}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{z0 \cdot \frac{z2}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{z0 \cdot \frac{z2}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \]

      6. lower-/.f64 80.1%

         \[\leadsto z0 \cdot \color{blue}{\frac{z2}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \]

      7. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z2}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \]

      8. *-commutative N/A

         \[\leadsto z0 \cdot \frac{z2}{\color{blue}{z2 \cdot \frac{z3}{z4 \cdot z4}} + \frac{z1}{z2}} \]

      9. lower-*.f64 80.1%

         \[\leadsto z0 \cdot \frac{z2}{\color{blue}{z2 \cdot \frac{z3}{z4 \cdot z4}} + \frac{z1}{z2}} \]

   7. Applied rewrites 80.1%

      \[\leadsto \color{blue}{z0 \cdot \frac{z2}{z2 \cdot \frac{z3}{z4 \cdot z4} + \frac{z1}{z2}}} \]

   if 1.2800000000000001e238 < z2

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3}{z4 \cdot z4}\\ \mathbf{if}\;\left|z2\right| \leq 7.8 \cdot 10^{+211}:\\ \;\;\;\;\left(\frac{\left|z2\right|}{\left(\left|z2\right| \cdot t\_0\right) \cdot \left|z2\right| + z1} \cdot z0\right) \cdot \left|z2\right|\\ \mathbf{else}:\\ \;\;\;\;\frac{z0}{t\_0 + \frac{z1}{\left|z2\right| \cdot \left|z2\right|}}\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0 (/ z3 (* z4 z4))))
  (if (<= (fabs z2) 7.8e+211)
    (*
     (* (/ (fabs z2) (+ (* (* (fabs z2) t_0) (fabs z2)) z1)) z0)
     (fabs z2))
    (/ z0 (+ t_0 (/ z1 (* (fabs z2) (fabs z2))))))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double tmp;
	if (fabs(z2) <= 7.8e+211) {
		tmp = ((fabs(z2) / (((fabs(z2) * t_0) * fabs(z2)) + z1)) * z0) * fabs(z2);
	} else {
		tmp = z0 / (t_0 + (z1 / (fabs(z2) * fabs(z2))));
	}
	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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z3 / (z4 * z4)
    if (abs(z2) <= 7.8d+211) then
        tmp = ((abs(z2) / (((abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2)
    else
        tmp = z0 / (t_0 + (z1 / (abs(z2) * abs(z2))))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double tmp;
	if (Math.abs(z2) <= 7.8e+211) {
		tmp = ((Math.abs(z2) / (((Math.abs(z2) * t_0) * Math.abs(z2)) + z1)) * z0) * Math.abs(z2);
	} else {
		tmp = z0 / (t_0 + (z1 / (Math.abs(z2) * Math.abs(z2))));
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = z3 / (z4 * z4)
	tmp = 0
	if math.fabs(z2) <= 7.8e+211:
		tmp = ((math.fabs(z2) / (((math.fabs(z2) * t_0) * math.fabs(z2)) + z1)) * z0) * math.fabs(z2)
	else:
		tmp = z0 / (t_0 + (z1 / (math.fabs(z2) * math.fabs(z2))))
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(z3 / Float64(z4 * z4))
	tmp = 0.0
	if (abs(z2) <= 7.8e+211)
		tmp = Float64(Float64(Float64(abs(z2) / Float64(Float64(Float64(abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2));
	else
		tmp = Float64(z0 / Float64(t_0 + Float64(z1 / Float64(abs(z2) * abs(z2)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = z3 / (z4 * z4);
	tmp = 0.0;
	if (abs(z2) <= 7.8e+211)
		tmp = ((abs(z2) / (((abs(z2) * t_0) * abs(z2)) + z1)) * z0) * abs(z2);
	else
		tmp = z0 / (t_0 + (z1 / (abs(z2) * abs(z2))));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Abs[z2], $MachinePrecision], 7.8e+211], N[(N[(N[(N[Abs[z2], $MachinePrecision] / N[(N[(N[(N[Abs[z2], $MachinePrecision] * t$95$0), $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision] + z1), $MachinePrecision]), $MachinePrecision] * z0), $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision], N[(z0 / N[(t$95$0 + N[(z1 / N[(N[Abs[z2], $MachinePrecision] * N[Abs[z2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z2 < 7.8000000000000005e211

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. add-to-fraction N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}{z2}}} \]

      5. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]

      7. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2} + \frac{z1}{z2}} \cdot z2 \]

      9. lower-+.f64 80.8%

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

   5. Applied rewrites 80.8%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z2} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}} \cdot z2 \]

      2. mult-flip N/A

         \[\leadsto \color{blue}{\left(z0 \cdot \frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}}\right)} \cdot z2 \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{1}{\frac{z3}{z4 \cdot z4} \cdot z2 + \frac{z1}{z2}} \cdot z0\right)} \cdot z2 \]

   7. Applied rewrites 78.8%

      \[\leadsto \color{blue}{\left(\frac{z2}{\left(z2 \cdot \frac{z3}{z4 \cdot z4}\right) \cdot z2 + z1} \cdot z0\right)} \cdot z2 \]

   if 7.8000000000000005e211 < z2

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left|z4\right| \leq 5 \cdot 10^{-180}:\\ \;\;\;\;\left(z2 \cdot \left|z4\right|\right) \cdot \left(\left|z4\right| \cdot \frac{z0}{z2 \cdot z3}\right)\\ \mathbf{elif}\;\left|z4\right| \leq 110000000:\\ \;\;\;\;\frac{\frac{z0}{z3}}{z2} \cdot \left(z2 \cdot \left(\left|z4\right| \cdot \left|z4\right|\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{z1} \cdot z2\right) \cdot \left(z2 \cdot z0\right)\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (if (<= (fabs z4) 5e-180)
  (* (* z2 (fabs z4)) (* (fabs z4) (/ z0 (* z2 z3))))
  (if (<= (fabs z4) 110000000.0)
    (* (/ (/ z0 z3) z2) (* z2 (* (fabs z4) (fabs z4))))
    (* (* (/ 1.0 z1) z2) (* z2 z0)))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double tmp;
	if (fabs(z4) <= 5e-180) {
		tmp = (z2 * fabs(z4)) * (fabs(z4) * (z0 / (z2 * z3)));
	} else if (fabs(z4) <= 110000000.0) {
		tmp = ((z0 / z3) / z2) * (z2 * (fabs(z4) * fabs(z4)));
	} else {
		tmp = ((1.0 / z1) * z2) * (z2 * 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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: tmp
    if (abs(z4) <= 5d-180) then
        tmp = (z2 * abs(z4)) * (abs(z4) * (z0 / (z2 * z3)))
    else if (abs(z4) <= 110000000.0d0) then
        tmp = ((z0 / z3) / z2) * (z2 * (abs(z4) * abs(z4)))
    else
        tmp = ((1.0d0 / z1) * z2) * (z2 * z0)
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double tmp;
	if (Math.abs(z4) <= 5e-180) {
		tmp = (z2 * Math.abs(z4)) * (Math.abs(z4) * (z0 / (z2 * z3)));
	} else if (Math.abs(z4) <= 110000000.0) {
		tmp = ((z0 / z3) / z2) * (z2 * (Math.abs(z4) * Math.abs(z4)));
	} else {
		tmp = ((1.0 / z1) * z2) * (z2 * z0);
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	tmp = 0
	if math.fabs(z4) <= 5e-180:
		tmp = (z2 * math.fabs(z4)) * (math.fabs(z4) * (z0 / (z2 * z3)))
	elif math.fabs(z4) <= 110000000.0:
		tmp = ((z0 / z3) / z2) * (z2 * (math.fabs(z4) * math.fabs(z4)))
	else:
		tmp = ((1.0 / z1) * z2) * (z2 * z0)
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	tmp = 0.0
	if (abs(z4) <= 5e-180)
		tmp = Float64(Float64(z2 * abs(z4)) * Float64(abs(z4) * Float64(z0 / Float64(z2 * z3))));
	elseif (abs(z4) <= 110000000.0)
		tmp = Float64(Float64(Float64(z0 / z3) / z2) * Float64(z2 * Float64(abs(z4) * abs(z4))));
	else
		tmp = Float64(Float64(Float64(1.0 / z1) * z2) * Float64(z2 * z0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	tmp = 0.0;
	if (abs(z4) <= 5e-180)
		tmp = (z2 * abs(z4)) * (abs(z4) * (z0 / (z2 * z3)));
	elseif (abs(z4) <= 110000000.0)
		tmp = ((z0 / z3) / z2) * (z2 * (abs(z4) * abs(z4)));
	else
		tmp = ((1.0 / z1) * z2) * (z2 * z0);
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := If[LessEqual[N[Abs[z4], $MachinePrecision], 5e-180], N[(N[(z2 * N[Abs[z4], $MachinePrecision]), $MachinePrecision] * N[(N[Abs[z4], $MachinePrecision] * N[(z0 / N[(z2 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Abs[z4], $MachinePrecision], 110000000.0], N[(N[(N[(z0 / z3), $MachinePrecision] / z2), $MachinePrecision] * N[(z2 * N[(N[Abs[z4], $MachinePrecision] * N[Abs[z4], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / z1), $MachinePrecision] * z2), $MachinePrecision] * N[(z2 * z0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z4 < 5.0000000000000001e-180

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} + \frac{\frac{z1}{z2}}{z2}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. common-denominator N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}{\left(z4 \cdot z4\right) \cdot z2}}} \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2}} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      12. associate-*l/ N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{\color{blue}{z1 \cdot \left(z4 \cdot z4\right)}}{z2} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      15. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      17. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      18. lower-*.f64 53.2%

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   6. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      2. lower-*.f64 40.1%

         \[\leadsto \frac{z0}{z2 \cdot \color{blue}{z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   8. Applied rewrites 40.1%

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right) \cdot \frac{z0}{z2 \cdot z3}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \cdot \frac{z0}{z2 \cdot z3} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(z2 \cdot \color{blue}{\left(z4 \cdot z4\right)}\right) \cdot \frac{z0}{z2 \cdot z3} \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(z2 \cdot z4\right) \cdot z4\right)} \cdot \frac{z0}{z2 \cdot z3} \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right)} \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right) \]

      9. lower-*.f64 44.0%

         \[\leadsto \left(z2 \cdot z4\right) \cdot \color{blue}{\left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

   10. Applied rewrites 44.0%

       \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

   if 5.0000000000000001e-180 < z4 < 1.1e8

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} + \frac{\frac{z1}{z2}}{z2}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. common-denominator N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}{\left(z4 \cdot z4\right) \cdot z2}}} \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2}} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      12. associate-*l/ N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{\color{blue}{z1 \cdot \left(z4 \cdot z4\right)}}{z2} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      15. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      17. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      18. lower-*.f64 53.2%

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   6. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      2. lower-*.f64 40.1%

         \[\leadsto \frac{z0}{z2 \cdot \color{blue}{z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   8. Applied rewrites 40.1%

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{z2 \cdot \color{blue}{z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \frac{z0}{z3 \cdot \color{blue}{z2}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \frac{\frac{z0}{z3}}{\color{blue}{z2}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{z0}{z3}}{\color{blue}{z2}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      6. lower-/.f64 43.5%

         \[\leadsto \frac{\frac{z0}{z3}}{z2} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   10. Applied rewrites 43.5%

       \[\leadsto \frac{\frac{z0}{z3}}{\color{blue}{z2}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   if 1.1e8 < z4

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

   2. Taylor expanded in z3 around 0

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lower-pow.f64 50.2%

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   4. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lift-pow.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      4. pow2 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      9. lower-/.f64 49.8%

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   6. Applied rewrites 49.8%

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

      3. associate-*l/ N/A

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

      4. lift-*.f64 N/A

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

      5. mult-flip-rev N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{z1} \cdot \left(\left(z2 \cdot z2\right) \cdot z0\right) \]

      10. associate-*l* N/A

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

      11. associate-*r* N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 55.8%

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

   8. Applied rewrites 55.8%

      \[\leadsto \left(\frac{1}{z1} \cdot z2\right) \cdot \color{blue}{\left(z2 \cdot z0\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3}{z4 \cdot z4}\\ t_1 := \left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+23}:\\ \;\;\;\;\left(z2 \cdot z0\right) \cdot \frac{z2}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0 (/ z3 (* z4 z4)))
       (t_1 (* (* z2 z4) (* z4 (/ z0 (* z2 z3))))))
  (if (<= t_0 -5e+138)
    t_1
    (if (<= t_0 1e+23) (* (* z2 z0) (/ z2 z1)) t_1))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = (z2 * z4) * (z4 * (z0 / (z2 * z3)));
	double tmp;
	if (t_0 <= -5e+138) {
		tmp = t_1;
	} else if (t_0 <= 1e+23) {
		tmp = (z2 * z0) * (z2 / z1);
	} else {
		tmp = t_1;
	}
	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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z3 / (z4 * z4)
    t_1 = (z2 * z4) * (z4 * (z0 / (z2 * z3)))
    if (t_0 <= (-5d+138)) then
        tmp = t_1
    else if (t_0 <= 1d+23) then
        tmp = (z2 * z0) * (z2 / z1)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = (z2 * z4) * (z4 * (z0 / (z2 * z3)));
	double tmp;
	if (t_0 <= -5e+138) {
		tmp = t_1;
	} else if (t_0 <= 1e+23) {
		tmp = (z2 * z0) * (z2 / z1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = z3 / (z4 * z4)
	t_1 = (z2 * z4) * (z4 * (z0 / (z2 * z3)))
	tmp = 0
	if t_0 <= -5e+138:
		tmp = t_1
	elif t_0 <= 1e+23:
		tmp = (z2 * z0) * (z2 / z1)
	else:
		tmp = t_1
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(z3 / Float64(z4 * z4))
	t_1 = Float64(Float64(z2 * z4) * Float64(z4 * Float64(z0 / Float64(z2 * z3))))
	tmp = 0.0
	if (t_0 <= -5e+138)
		tmp = t_1;
	elseif (t_0 <= 1e+23)
		tmp = Float64(Float64(z2 * z0) * Float64(z2 / z1));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = z3 / (z4 * z4);
	t_1 = (z2 * z4) * (z4 * (z0 / (z2 * z3)));
	tmp = 0.0;
	if (t_0 <= -5e+138)
		tmp = t_1;
	elseif (t_0 <= 1e+23)
		tmp = (z2 * z0) * (z2 / z1);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z2 * z4), $MachinePrecision] * N[(z4 * N[(z0 / N[(z2 * z3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+138], t$95$1, If[LessEqual[t$95$0, 1e+23], N[(N[(z2 * z0), $MachinePrecision] * N[(z2 / z1), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z3 (*.f64 z4 z4)) < -5.0000000000000002e138 or 9.9999999999999992e22 < (/.f64 z3 (*.f64 z4 z4))

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} + \frac{\frac{z1}{z2}}{z2}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. common-denominator N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}{\left(z4 \cdot z4\right) \cdot z2}}} \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2}} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      12. associate-*l/ N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{\color{blue}{z1 \cdot \left(z4 \cdot z4\right)}}{z2} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      15. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      17. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      18. lower-*.f64 53.2%

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   6. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      2. lower-*.f64 40.1%

         \[\leadsto \frac{z0}{z2 \cdot \color{blue}{z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   8. Applied rewrites 40.1%

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right) \cdot \frac{z0}{z2 \cdot z3}} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \cdot \frac{z0}{z2 \cdot z3} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(z2 \cdot \color{blue}{\left(z4 \cdot z4\right)}\right) \cdot \frac{z0}{z2 \cdot z3} \]

      5. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(z2 \cdot z4\right) \cdot z4\right)} \cdot \frac{z0}{z2 \cdot z3} \]

      6. associate-*l* N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(z2 \cdot z4\right)} \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right) \]

      9. lower-*.f64 44.0%

         \[\leadsto \left(z2 \cdot z4\right) \cdot \color{blue}{\left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

   10. Applied rewrites 44.0%

       \[\leadsto \color{blue}{\left(z2 \cdot z4\right) \cdot \left(z4 \cdot \frac{z0}{z2 \cdot z3}\right)} \]

   if -5.0000000000000002e138 < (/.f64 z3 (*.f64 z4 z4)) < 9.9999999999999992e22

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

   2. Taylor expanded in z3 around 0

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lower-pow.f64 50.2%

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   4. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lift-pow.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      4. pow2 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      9. lower-/.f64 49.8%

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   6. Applied rewrites 49.8%

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      2. *-commutative N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

      3. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z2 \cdot z2}{\color{blue}{z1}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z2 \cdot z2}{z1} \]

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 55.9%

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

   8. Applied rewrites 55.9%

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

Alternative 9: 69.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := \frac{z3}{z4 \cdot z4}\\ t_1 := \frac{z0}{z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 10^{+23}:\\ \;\;\;\;\left(z2 \cdot z0\right) \cdot \frac{z2}{z1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (let* ((t_0 (/ z3 (* z4 z4)))
       (t_1 (* (/ z0 (* z2 z3)) (* z2 (* z4 z4)))))
  (if (<= t_0 -1e+153)
    t_1
    (if (<= t_0 1e+23) (* (* z2 z0) (/ z2 z1)) t_1))))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = (z0 / (z2 * z3)) * (z2 * (z4 * z4));
	double tmp;
	if (t_0 <= -1e+153) {
		tmp = t_1;
	} else if (t_0 <= 1e+23) {
		tmp = (z2 * z0) * (z2 / z1);
	} else {
		tmp = t_1;
	}
	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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z3 / (z4 * z4)
    t_1 = (z0 / (z2 * z3)) * (z2 * (z4 * z4))
    if (t_0 <= (-1d+153)) then
        tmp = t_1
    else if (t_0 <= 1d+23) then
        tmp = (z2 * z0) * (z2 / z1)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	double t_0 = z3 / (z4 * z4);
	double t_1 = (z0 / (z2 * z3)) * (z2 * (z4 * z4));
	double tmp;
	if (t_0 <= -1e+153) {
		tmp = t_1;
	} else if (t_0 <= 1e+23) {
		tmp = (z2 * z0) * (z2 / z1);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(z0, z3, z4, z1, z2):
	t_0 = z3 / (z4 * z4)
	t_1 = (z0 / (z2 * z3)) * (z2 * (z4 * z4))
	tmp = 0
	if t_0 <= -1e+153:
		tmp = t_1
	elif t_0 <= 1e+23:
		tmp = (z2 * z0) * (z2 / z1)
	else:
		tmp = t_1
	return tmp

Julia

function code(z0, z3, z4, z1, z2)
	t_0 = Float64(z3 / Float64(z4 * z4))
	t_1 = Float64(Float64(z0 / Float64(z2 * z3)) * Float64(z2 * Float64(z4 * z4)))
	tmp = 0.0
	if (t_0 <= -1e+153)
		tmp = t_1;
	elseif (t_0 <= 1e+23)
		tmp = Float64(Float64(z2 * z0) * Float64(z2 / z1));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z3, z4, z1, z2)
	t_0 = z3 / (z4 * z4);
	t_1 = (z0 / (z2 * z3)) * (z2 * (z4 * z4));
	tmp = 0.0;
	if (t_0 <= -1e+153)
		tmp = t_1;
	elseif (t_0 <= 1e+23)
		tmp = (z2 * z0) * (z2 / z1);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := Block[{t$95$0 = N[(z3 / N[(z4 * z4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(z0 / N[(z2 * z3), $MachinePrecision]), $MachinePrecision] * N[(z2 * N[(z4 * z4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+153], t$95$1, If[LessEqual[t$95$0, 1e+23], N[(N[(z2 * z0), $MachinePrecision] * N[(z2 / z1), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z3 (*.f64 z4 z4)) < -1e153 or 9.9999999999999992e22 < (/.f64 z3 (*.f64 z4 z4))

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{z1}{z2 \cdot z2}}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{\color{blue}{z2 \cdot z2}}} \]

      3. associate-/r* N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. lower-/.f64 81.6%

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\color{blue}{\frac{z1}{z2}}}{z2}} \]

   3. Applied rewrites 81.6%

      \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4} + \frac{\frac{z1}{z2}}{z2}}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3}{z4 \cdot z4}} + \frac{\frac{z1}{z2}}{z2}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z0}{\frac{z3}{z4 \cdot z4} + \color{blue}{\frac{\frac{z1}{z2}}{z2}}} \]

      5. common-denominator N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}{\left(z4 \cdot z4\right) \cdot z2}}} \]

      6. associate-/r/ N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      7. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z0}{z3 \cdot z2 + \frac{z1}{z2} \cdot \left(z4 \cdot z4\right)}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      9. +-commutative N/A

         \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      10. lower-+.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1}{z2}} \cdot \left(z4 \cdot z4\right) + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      12. associate-*l/ N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      13. lower-/.f64 N/A

          \[\leadsto \frac{z0}{\color{blue}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2}} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{\color{blue}{z1 \cdot \left(z4 \cdot z4\right)}}{z2} + z3 \cdot z2} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      15. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + \color{blue}{z2 \cdot z3}} \cdot \left(\left(z4 \cdot z4\right) \cdot z2\right) \]

      17. *-commutative N/A

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

      18. lower-*.f64 53.2%

          \[\leadsto \frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \color{blue}{\left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\frac{z0}{\frac{z1 \cdot \left(z4 \cdot z4\right)}{z2} + z2 \cdot z3} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right)} \]

   6. Taylor expanded in z3 around inf

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0}{\color{blue}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

      2. lower-*.f64 40.1%

         \[\leadsto \frac{z0}{z2 \cdot \color{blue}{z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   8. Applied rewrites 40.1%

      \[\leadsto \color{blue}{\frac{z0}{z2 \cdot z3}} \cdot \left(z2 \cdot \left(z4 \cdot z4\right)\right) \]

   if -1e153 < (/.f64 z3 (*.f64 z4 z4)) < 9.9999999999999992e22

   1. Initial program 76.6%

      \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

   2. Taylor expanded in z3 around 0

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lower-pow.f64 50.2%

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   4. Applied rewrites 50.2%

      \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      3. lift-pow.f64 N/A

         \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

      4. pow2 N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

      7. *-commutative N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      9. lower-/.f64 49.8%

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   6. Applied rewrites 49.8%

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

      2. *-commutative N/A

         \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

      3. lift-/.f64 N/A

         \[\leadsto z0 \cdot \frac{z2 \cdot z2}{\color{blue}{z1}} \]

      4. lift-*.f64 N/A

         \[\leadsto z0 \cdot \frac{z2 \cdot z2}{z1} \]

      5. associate-/l* N/A

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

      6. associate-*r* N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 55.9%

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

   8. Applied rewrites 55.9%

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

Alternative 10: 55.9% accurate, 2.1× speedup

Math

\[\left(z2 \cdot z0\right) \cdot \frac{z2}{z1} \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (* (* z2 z0) (/ z2 z1)))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	return (z2 * z0) * (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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    code = (z2 * z0) * (z2 / z1)
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	return (z2 * z0) * (z2 / z1);
}

Python

def code(z0, z3, z4, z1, z2):
	return (z2 * z0) * (z2 / z1)

Julia

function code(z0, z3, z4, z1, z2)
	return Float64(Float64(z2 * z0) * Float64(z2 / z1))
end

MATLAB

function tmp = code(z0, z3, z4, z1, z2)
	tmp = (z2 * z0) * (z2 / z1);
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := N[(N[(z2 * z0), $MachinePrecision] * N[(z2 / z1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.6%

   \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

2. Taylor expanded in z3 around 0

   \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
3. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   3. lower-pow.f64 50.2%

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

4. Applied rewrites 50.2%

   \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
5. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   3. lift-pow.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   4. pow2 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/l* N/A

      \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

   7. *-commutative N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   9. lower-/.f64 49.8%

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

6. Applied rewrites 49.8%

   \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   2. *-commutative N/A

      \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

   3. lift-/.f64 N/A

      \[\leadsto z0 \cdot \frac{z2 \cdot z2}{\color{blue}{z1}} \]

   4. lift-*.f64 N/A

      \[\leadsto z0 \cdot \frac{z2 \cdot z2}{z1} \]

   5. associate-/l* N/A

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

   6. associate-*r* N/A

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

   7. lower-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-/.f64 55.9%

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

8. Applied rewrites 55.9%

   \[\leadsto \left(z2 \cdot z0\right) \cdot \color{blue}{\frac{z2}{z1}} \]
9. Add Preprocessing

Alternative 11: 55.7% accurate, 2.1× speedup

Math

\[z2 \cdot \left(\frac{z2}{z1} \cdot z0\right) \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (* z2 (* (/ z2 z1) z0)))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	return z2 * ((z2 / z1) * z0);
}

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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    code = z2 * ((z2 / z1) * z0)
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	return z2 * ((z2 / z1) * z0);
}

Python

def code(z0, z3, z4, z1, z2):
	return z2 * ((z2 / z1) * z0)

Julia

function code(z0, z3, z4, z1, z2)
	return Float64(z2 * Float64(Float64(z2 / z1) * z0))
end

MATLAB

function tmp = code(z0, z3, z4, z1, z2)
	tmp = z2 * ((z2 / z1) * z0);
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := N[(z2 * N[(N[(z2 / z1), $MachinePrecision] * z0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.6%

   \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

2. Taylor expanded in z3 around 0

   \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
3. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   3. lower-pow.f64 50.2%

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

4. Applied rewrites 50.2%

   \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
5. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   3. lift-pow.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   4. pow2 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/l* N/A

      \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

   7. *-commutative N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   9. lower-/.f64 49.8%

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

6. Applied rewrites 49.8%

   \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   4. associate-/l* N/A

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

   5. associate-*l* N/A

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

   6. lower-*.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-/.f64 55.7%

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

8. Applied rewrites 55.7%

   \[\leadsto z2 \cdot \color{blue}{\left(\frac{z2}{z1} \cdot z0\right)} \]
9. Add Preprocessing

Alternative 12: 54.0% accurate, 2.1× speedup

Math

\[z2 \cdot \left(\frac{z0}{z1} \cdot z2\right) \]

FPCore

(FPCore (z0 z3 z4 z1 z2)
  :precision binary64
  (* z2 (* (/ z0 z1) z2)))

C

double code(double z0, double z3, double z4, double z1, double z2) {
	return z2 * ((z0 / 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, z3, z4, z1, z2)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z3
    real(8), intent (in) :: z4
    real(8), intent (in) :: z1
    real(8), intent (in) :: z2
    code = z2 * ((z0 / z1) * z2)
end function

Java

public static double code(double z0, double z3, double z4, double z1, double z2) {
	return z2 * ((z0 / z1) * z2);
}

Python

def code(z0, z3, z4, z1, z2):
	return z2 * ((z0 / z1) * z2)

Julia

function code(z0, z3, z4, z1, z2)
	return Float64(z2 * Float64(Float64(z0 / z1) * z2))
end

MATLAB

function tmp = code(z0, z3, z4, z1, z2)
	tmp = z2 * ((z0 / z1) * z2);
end

Wolfram

code[z0_, z3_, z4_, z1_, z2_] := N[(z2 * N[(N[(z0 / z1), $MachinePrecision] * z2), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.6%

   \[\frac{z0}{\frac{z3}{z4 \cdot z4} + \frac{z1}{z2 \cdot z2}} \]

2. Taylor expanded in z3 around 0

   \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
3. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

   2. lower-*.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   3. lower-pow.f64 50.2%

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

4. Applied rewrites 50.2%

   \[\leadsto \color{blue}{\frac{z0 \cdot {z2}^{2}}{z1}} \]
5. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{\color{blue}{z1}} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   3. lift-pow.f64 N/A

      \[\leadsto \frac{z0 \cdot {z2}^{2}}{z1} \]

   4. pow2 N/A

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

   5. lift-*.f64 N/A

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

   6. associate-/l* N/A

      \[\leadsto z0 \cdot \color{blue}{\frac{z2 \cdot z2}{z1}} \]

   7. *-commutative N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   9. lower-/.f64 49.8%

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

6. Applied rewrites 49.8%

   \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot \color{blue}{z0} \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{z2 \cdot z2}{z1} \cdot z0 \]

   4. associate-/l* N/A

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

   5. associate-*l* N/A

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

   6. lower-*.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-/.f64 55.7%

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

8. Applied rewrites 55.7%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. mult-flip N/A

      \[\leadsto z2 \cdot \left(\left(z2 \cdot \frac{1}{z1}\right) \cdot z0\right) \]

   4. lift-/.f64 N/A

      \[\leadsto z2 \cdot \left(\left(z2 \cdot \frac{1}{z1}\right) \cdot z0\right) \]

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 N/A

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

   9. lift-/.f64 N/A

      \[\leadsto z2 \cdot \left(\left(z0 \cdot \frac{1}{z1}\right) \cdot z2\right) \]

   10. mult-flip-rev N/A

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

   11. lower-/.f64 54.0%

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

10. Applied rewrites 54.0%

    \[\leadsto z2 \cdot \left(\frac{z0}{z1} \cdot \color{blue}{z2}\right) \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0 z3 z4 z1 z2)
  :name "(/ z0 (+ (/ z3 (* z4 z4)) (/ z1 (* z2 z2))))"
  :precision binary64
  (/ z0 (+ (/ z3 (* z4 z4)) (/ z1 (* z2 z2)))))