Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1

Percentage Accurate: 67.8% → 99.6%

Time: 16.3s

Alternatives: 9

Speedup: 1.0×

• 51.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 67.8% accurate, 1.0× speedup

Math

\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * x), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.8× speedup

Math

\[\frac{z}{t} \cdot \frac{z}{t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (- (* (/ z t) (/ z t)) (* (- (/ x y)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	return ((z / t) * (z / t)) - (-(x / y) * (x / y));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((z / t) * (z / t)) - (-(x / y) * (x / y))
end function

Java

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

Python

def code(x, y, z, t):
	return ((z / t) * (z / t)) - (-(x / y) * (x / y))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(z / t) * Float64(z / t)) - Float64(Float64(-Float64(x / y)) * Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((z / t) * (z / t)) - (-(x / y) * (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[((-N[(x / y), $MachinePrecision]) * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.8%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

   3. lift-/.f64 N/A

      \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

   4. lift-*.f64 N/A

      \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{\color{blue}{y \cdot y}} \]

   6. times-frac N/A

      \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} \]

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

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

   8. lower--.f64 N/A

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

   9. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

   11. associate-/l* N/A

       \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

   12. *-commutative N/A

       \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

   13. lower-*.f64 N/A

       \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

   14. lower-/.f64 N/A

       \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

   15. lower-*.f64 N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

   16. lower-neg.f64 N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(-\frac{x}{y}\right)} \cdot \frac{x}{y} \]

   17. lower-/.f64 N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\color{blue}{\frac{x}{y}}\right) \cdot \frac{x}{y} \]

   18. lower-/.f64 89.9%

       \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \color{blue}{\frac{x}{y}} \]

3. Applied rewrites 89.9%

   \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]
4. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   2. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   3. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   4. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   6. lift-*.f64 N/A

      \[\leadsto \frac{z \cdot z}{\color{blue}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   7. times-frac N/A

      \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   8. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{z}{t}} \cdot \frac{z}{t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   9. lift-/.f64 N/A

      \[\leadsto \frac{z}{t} \cdot \color{blue}{\frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   10. lower-*.f64 99.6%

       \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

5. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]
6. Add Preprocessing

Alternative 2: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 5000000000000000164943055170434837427135440057522539318423791570869012863893044939457394359293162206430058690814701199200294101105758807930912040583618895295566352963538529190225559103961304787468696490024321895827150961861074155612506360583410417131562672326958643646649953541871894528:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + \frac{\frac{z \cdot z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\left(-y\right) \cdot y} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     (/ (* z z) (* t t))
     5000000000000000164943055170434837427135440057522539318423791570869012863893044939457394359293162206430058690814701199200294101105758807930912040583618895295566352963538529190225559103961304787468696490024321895827150961861074155612506360583410417131562672326958643646649953541871894528)
  (+ (* (/ x y) (/ x y)) (/ (/ (* z z) t) t))
  (- (* (/ z t) (/ z t)) (* (/ x (* (- y) y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e+285) {
		tmp = ((x / y) * (x / y)) + (((z * z) / t) / t);
	} else {
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 5d+285) then
        tmp = ((x / y) * (x / y)) + (((z * z) / t) / t)
    else
        tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 5e+285) {
		tmp = ((x / y) * (x / y)) + (((z * z) / t) / t);
	} else {
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 5e+285:
		tmp = ((x / y) * (x / y)) + (((z * z) / t) / t)
	else:
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 5e+285)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + Float64(Float64(Float64(z * z) / t) / t));
	else
		tmp = Float64(Float64(Float64(z / t) * Float64(z / t)) - Float64(Float64(x / Float64(Float64(-y) * y)) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 5e+285)
		tmp = ((x / y) * (x / y)) + (((z * z) / t) / t);
	else
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 5000000000000000164943055170434837427135440057522539318423791570869012863893044939457394359293162206430058690814701199200294101105758807930912040583618895295566352963538529190225559103961304787468696490024321895827150961861074155612506360583410417131562672326958643646649953541871894528], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x / N[((-y) * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 5.0000000000000002e285

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{z \cdot z}{t \cdot t}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{z \cdot z}}{t \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{\color{blue}{t \cdot t}} \]

      4. times-frac N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} \]

      5. associate-*r/ N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{\frac{z}{t} \cdot z}{t}} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{\frac{z}{t} \cdot z}{t}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t} \cdot z}}{t} \]

      8. lower-/.f64 79.3%

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t}} \cdot z}{t} \]

   3. Applied rewrites 79.3%

      \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{\frac{z}{t} \cdot z}{t}} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t} \cdot z}}{t} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t}} \cdot z}{t} \]

      3. associate-*l/ N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z \cdot z}{t}}}{t} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z \cdot z}{t}}}{t} \]

      5. lower-*.f64 74.0%

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\frac{\color{blue}{z \cdot z}}{t}}{t} \]

   5. Applied rewrites 74.0%

      \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z \cdot z}{t}}}{t} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y}} + \frac{\frac{z \cdot z}{t}}{t} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot y} + \frac{\frac{z \cdot z}{t}}{t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{\color{blue}{y \cdot y}} + \frac{\frac{z \cdot z}{t}}{t} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{\frac{z \cdot z}{t}}{t} \]

      5. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{x}{y} + \frac{\frac{z \cdot z}{t}}{t} \]

      6. lift-/.f64 N/A

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{x}{y}} + \frac{\frac{z \cdot z}{t}}{t} \]

      7. lower-*.f64 90.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{\frac{z \cdot z}{t}}{t} \]

   7. Applied rewrites 90.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{\frac{z \cdot z}{t}}{t} \]

   if 5.0000000000000002e285 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{\color{blue}{y \cdot y}} \]

      6. times-frac N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} \]

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

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      8. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      9. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      11. associate-/l* N/A

          \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      12. *-commutative N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      14. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      16. lower-neg.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(-\frac{x}{y}\right)} \cdot \frac{x}{y} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\color{blue}{\frac{x}{y}}\right) \cdot \frac{x}{y} \]

      18. lower-/.f64 89.9%

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \color{blue}{\frac{x}{y}} \]

   3. Applied rewrites 89.9%

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{\color{blue}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      7. times-frac N/A

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      8. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t}} \cdot \frac{z}{t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \color{blue}{\frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      10. lower-*.f64 99.6%

          \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   5. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]

      2. lift-neg.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} \cdot \frac{x}{y} \]

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

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y} \cdot \frac{x}{y}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y}} \cdot \frac{x}{y}\right)\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{x}{y} \cdot \color{blue}{\frac{x}{y}}\right)\right) \]

      6. times-frac N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x \cdot x}{y \cdot y}}\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{\color{blue}{x \cdot x}}{y \cdot y}\right)\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{x \cdot x}{\color{blue}{y \cdot y}}\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{\color{blue}{x \cdot x}}{y \cdot y}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y} \cdot x}\right)\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y}} \cdot x\right)\right) \]

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

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y \cdot y}\right)\right) \cdot x} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y \cdot y}\right)\right) \cdot x} \]

      14. lift-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y}}\right)\right) \cdot x \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\frac{x}{\mathsf{neg}\left(y \cdot y\right)}} \cdot x \]

      16. lower-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\frac{x}{\mathsf{neg}\left(y \cdot y\right)}} \cdot x \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\mathsf{neg}\left(\color{blue}{y \cdot y}\right)} \cdot x \]

      18. distribute-lft-neg-in N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot y}} \cdot x \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot y}} \cdot x \]

      20. lower-neg.f64 89.6%

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(-y\right)} \cdot y} \cdot x \]

   7. Applied rewrites 89.6%

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

Alternative 3: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\left(-y\right) \cdot y} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     (/ (* z z) (* t t))
     199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680)
  (- (* (/ z (* t t)) z) (* (- (/ x y)) (/ x y)))
  (- (* (/ z t) (/ z t)) (* (/ x (* (- y) y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e+197) {
		tmp = ((z / (t * t)) * z) - (-(x / y) * (x / y));
	} else {
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 2d+197) then
        tmp = ((z / (t * t)) * z) - (-(x / y) * (x / y))
    else
        tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 2e+197) {
		tmp = ((z / (t * t)) * z) - (-(x / y) * (x / y));
	} else {
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 2e+197:
		tmp = ((z / (t * t)) * z) - (-(x / y) * (x / y))
	else:
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 2e+197)
		tmp = Float64(Float64(Float64(z / Float64(t * t)) * z) - Float64(Float64(-Float64(x / y)) * Float64(x / y)));
	else
		tmp = Float64(Float64(Float64(z / t) * Float64(z / t)) - Float64(Float64(x / Float64(Float64(-y) * y)) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 2e+197)
		tmp = ((z / (t * t)) * z) - (-(x / y) * (x / y));
	else
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680], N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[((-N[(x / y), $MachinePrecision]) * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x / N[((-y) * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999999e197

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{\color{blue}{y \cdot y}} \]

      6. times-frac N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} \]

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

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      8. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      9. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      11. associate-/l* N/A

          \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      12. *-commutative N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      14. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      16. lower-neg.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(-\frac{x}{y}\right)} \cdot \frac{x}{y} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\color{blue}{\frac{x}{y}}\right) \cdot \frac{x}{y} \]

      18. lower-/.f64 89.9%

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \color{blue}{\frac{x}{y}} \]

   3. Applied rewrites 89.9%

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]

   if 1.9999999999999999e197 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{\color{blue}{y \cdot y}} \]

      6. times-frac N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} \]

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

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      8. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      9. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      11. associate-/l* N/A

          \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      12. *-commutative N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      14. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      16. lower-neg.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(-\frac{x}{y}\right)} \cdot \frac{x}{y} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\color{blue}{\frac{x}{y}}\right) \cdot \frac{x}{y} \]

      18. lower-/.f64 89.9%

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \color{blue}{\frac{x}{y}} \]

   3. Applied rewrites 89.9%

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{\color{blue}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      7. times-frac N/A

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      8. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t}} \cdot \frac{z}{t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \color{blue}{\frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      10. lower-*.f64 99.6%

          \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   5. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]

      2. lift-neg.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} \cdot \frac{x}{y} \]

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

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y} \cdot \frac{x}{y}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y}} \cdot \frac{x}{y}\right)\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{x}{y} \cdot \color{blue}{\frac{x}{y}}\right)\right) \]

      6. times-frac N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x \cdot x}{y \cdot y}}\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{\color{blue}{x \cdot x}}{y \cdot y}\right)\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{x \cdot x}{\color{blue}{y \cdot y}}\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{\color{blue}{x \cdot x}}{y \cdot y}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y} \cdot x}\right)\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y}} \cdot x\right)\right) \]

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

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y \cdot y}\right)\right) \cdot x} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y \cdot y}\right)\right) \cdot x} \]

      14. lift-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y}}\right)\right) \cdot x \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\frac{x}{\mathsf{neg}\left(y \cdot y\right)}} \cdot x \]

      16. lower-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\frac{x}{\mathsf{neg}\left(y \cdot y\right)}} \cdot x \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\mathsf{neg}\left(\color{blue}{y \cdot y}\right)} \cdot x \]

      18. distribute-lft-neg-in N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot y}} \cdot x \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot y}} \cdot x \]

      20. lower-neg.f64 89.6%

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(-y\right)} \cdot y} \cdot x \]

   7. Applied rewrites 89.6%

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

Alternative 4: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\left(-y\right) \cdot y} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* z z) (* t t))))
  (if (<=
       t_1
       199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680)
    (+ (* (/ x y) (/ x y)) t_1)
    (- (* (/ z t) (/ z t)) (* (/ x (* (- y) y)) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+197) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+197) then
        tmp = ((x / y) * (x / y)) + t_1
    else
        tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+197) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+197:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 2e+197)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = Float64(Float64(Float64(z / t) * Float64(z / t)) - Float64(Float64(x / Float64(Float64(-y) * y)) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 2e+197)
		tmp = ((x / y) * (x / y)) + t_1;
	else
		tmp = ((z / t) * (z / t)) - ((x / (-y * y)) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(N[(x / N[((-y) * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999999e197

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{\color{blue}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{x}{y} + \frac{z \cdot z}{t \cdot t} \]

      7. lower-/.f64 82.3%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

   3. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

   if 1.9999999999999999e197 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{\color{blue}{y \cdot y}} \]

      6. times-frac N/A

         \[\leadsto \frac{z \cdot z}{t \cdot t} + \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} \]

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

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      8. lower--.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      9. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      11. associate-/l* N/A

          \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      12. *-commutative N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      13. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      14. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y} \]

      15. lower-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \cdot \frac{x}{y}} \]

      16. lower-neg.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \color{blue}{\left(-\frac{x}{y}\right)} \cdot \frac{x}{y} \]

      17. lower-/.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\color{blue}{\frac{x}{y}}\right) \cdot \frac{x}{y} \]

      18. lower-/.f64 89.9%

          \[\leadsto \frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \color{blue}{\frac{x}{y}} \]

   3. Applied rewrites 89.9%

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{\color{blue}{t \cdot t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      7. times-frac N/A

         \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      8. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t}} \cdot \frac{z}{t} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      9. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \color{blue}{\frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

      10. lower-*.f64 99.6%

          \[\leadsto \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} - \left(-\frac{x}{y}\right) \cdot \frac{x}{y} \]

   5. Applied rewrites 99.6%

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

      1. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(-\frac{x}{y}\right) \cdot \frac{x}{y}} \]

      2. lift-neg.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y}\right)\right)} \cdot \frac{x}{y} \]

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

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y} \cdot \frac{x}{y}\right)\right)} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y}} \cdot \frac{x}{y}\right)\right) \]

      5. lift-/.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{x}{y} \cdot \color{blue}{\frac{x}{y}}\right)\right) \]

      6. times-frac N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x \cdot x}{y \cdot y}}\right)\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{\color{blue}{x \cdot x}}{y \cdot y}\right)\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{x \cdot x}{\color{blue}{y \cdot y}}\right)\right) \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\frac{\color{blue}{x \cdot x}}{y \cdot y}\right)\right) \]

      10. associate-*l/ N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y} \cdot x}\right)\right) \]

      11. lift-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y}} \cdot x\right)\right) \]

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

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y \cdot y}\right)\right) \cdot x} \]

      13. lower-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\left(\mathsf{neg}\left(\frac{x}{y \cdot y}\right)\right) \cdot x} \]

      14. lift-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \left(\mathsf{neg}\left(\color{blue}{\frac{x}{y \cdot y}}\right)\right) \cdot x \]

      15. distribute-neg-frac2 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\frac{x}{\mathsf{neg}\left(y \cdot y\right)}} \cdot x \]

      16. lower-/.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \color{blue}{\frac{x}{\mathsf{neg}\left(y \cdot y\right)}} \cdot x \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\mathsf{neg}\left(\color{blue}{y \cdot y}\right)} \cdot x \]

      18. distribute-lft-neg-in N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot y}} \cdot x \]

      19. lower-*.f64 N/A

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot y}} \cdot x \]

      20. lower-neg.f64 89.6%

          \[\leadsto \frac{z}{t} \cdot \frac{z}{t} - \frac{x}{\color{blue}{\left(-y\right)} \cdot y} \cdot x \]

   7. Applied rewrites 89.6%

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

Alternative 5: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z + \frac{x}{y \cdot y} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* z z) (* t t))))
  (if (<=
       t_1
       199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680)
    (+ (* (/ x y) (/ x y)) t_1)
    (+ (* (/ (/ z t) t) z) (* (/ x (* y y)) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+197) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (((z / t) / t) * z) + ((x / (y * y)) * x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+197) then
        tmp = ((x / y) * (x / y)) + t_1
    else
        tmp = (((z / t) / t) * z) + ((x / (y * y)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+197) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = (((z / t) / t) * z) + ((x / (y * y)) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+197:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = (((z / t) / t) * z) + ((x / (y * y)) * x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 2e+197)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = Float64(Float64(Float64(Float64(z / t) / t) * z) + Float64(Float64(x / Float64(y * y)) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 2e+197)
		tmp = ((x / y) * (x / y)) + t_1;
	else
		tmp = (((z / t) / t) * z) + ((x / (y * y)) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 199999999999999990228658492784702641067783209223724333989331677811470234474999183665567757783446804561917508975342765134138965065011049861852714718525529079875407330767468500015544730764581724487680], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision] + N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 1.9999999999999999e197

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{\color{blue}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{x}{y} + \frac{z \cdot z}{t \cdot t} \]

      7. lower-/.f64 82.3%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

   3. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

   if 1.9999999999999999e197 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      3. lower-+.f64 67.8%

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} + \frac{x \cdot x}{y \cdot y} \]

      6. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

      9. lower-/.f64 74.2%

         \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z + \frac{x \cdot x}{y \cdot y} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

      12. associate-/l* N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{x \cdot \frac{x}{y \cdot y}} \]

      13. *-commutative N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

      15. lower-/.f64 81.0%

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y}} \cdot x \]

   3. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z + \frac{x}{y \cdot y} \cdot x} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z + \frac{x}{y \cdot y} \cdot x \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z}{\color{blue}{t \cdot t}} \cdot z + \frac{x}{y \cdot y} \cdot x \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{z}{t}}{t}} \cdot z + \frac{x}{y \cdot y} \cdot x \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{z}{t}}}{t} \cdot z + \frac{x}{y \cdot y} \cdot x \]

      5. lower-/.f64 87.0%

         \[\leadsto \color{blue}{\frac{\frac{z}{t}}{t}} \cdot z + \frac{x}{y \cdot y} \cdot x \]

   5. Applied rewrites 87.0%

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

Alternative 6: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \cdot t \leq \frac{101201127}{202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784}:\\ \;\;\;\;\frac{x}{y \cdot y} \cdot x + \frac{\frac{z \cdot z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{\frac{x}{y}}{y} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     (* t t)
     101201127/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784)
  (+ (* (/ x (* y y)) x) (/ (/ (* z z) t) t))
  (+ (* (/ z (* t t)) z) (* (/ (/ x y) y) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t * t) <= 5e-316) {
		tmp = ((x / (y * y)) * x) + (((z * z) / t) / t);
	} else {
		tmp = ((z / (t * t)) * z) + (((x / y) / y) * x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t * t) <= 5d-316) then
        tmp = ((x / (y * y)) * x) + (((z * z) / t) / t)
    else
        tmp = ((z / (t * t)) * z) + (((x / y) / y) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t * t) <= 5e-316) {
		tmp = ((x / (y * y)) * x) + (((z * z) / t) / t);
	} else {
		tmp = ((z / (t * t)) * z) + (((x / y) / y) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t * t) <= 5e-316:
		tmp = ((x / (y * y)) * x) + (((z * z) / t) / t)
	else:
		tmp = ((z / (t * t)) * z) + (((x / y) / y) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(t * t) <= 5e-316)
		tmp = Float64(Float64(Float64(x / Float64(y * y)) * x) + Float64(Float64(Float64(z * z) / t) / t));
	else
		tmp = Float64(Float64(Float64(z / Float64(t * t)) * z) + Float64(Float64(Float64(x / y) / y) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t * t) <= 5e-316)
		tmp = ((x / (y * y)) * x) + (((z * z) / t) / t);
	else
		tmp = ((z / (t * t)) * z) + (((x / y) / y) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(t * t), $MachinePrecision], 101201127/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784], N[(N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 t t) < 5.0000000171117013e-316

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{z \cdot z}{t \cdot t}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{z \cdot z}}{t \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{\color{blue}{t \cdot t}} \]

      4. times-frac N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} \]

      5. associate-*r/ N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{\frac{z}{t} \cdot z}{t}} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{\frac{z}{t} \cdot z}{t}} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t} \cdot z}}{t} \]

      8. lower-/.f64 79.3%

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t}} \cdot z}{t} \]

   3. Applied rewrites 79.3%

      \[\leadsto \frac{x \cdot x}{y \cdot y} + \color{blue}{\frac{\frac{z}{t} \cdot z}{t}} \]
   4. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t} \cdot z}}{t} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z}{t}} \cdot z}{t} \]

      3. associate-*l/ N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z \cdot z}{t}}}{t} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z \cdot z}{t}}}{t} \]

      5. lower-*.f64 74.0%

         \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\frac{\color{blue}{z \cdot z}}{t}}{t} \]

   5. Applied rewrites 74.0%

      \[\leadsto \frac{x \cdot x}{y \cdot y} + \frac{\color{blue}{\frac{z \cdot z}{t}}}{t} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y}} + \frac{\frac{z \cdot z}{t}}{t} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot y} + \frac{\frac{z \cdot z}{t}}{t} \]

      3. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot y} \cdot x} + \frac{\frac{z \cdot z}{t}}{t} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{y \cdot y}} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      5. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      6. lift-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{y} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      7. mult-flip-rev N/A

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot \frac{1}{y}\right)} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{\frac{1}{y}}\right) \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      9. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot \frac{1}{y}\right)} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      10. lift-*.f64 87.4%

          \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot \frac{1}{y}\right) \cdot x} + \frac{\frac{z \cdot z}{t}}{t} \]

      11. lift-*.f64 N/A

          \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot \frac{1}{y}\right)} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\frac{x}{y} \cdot \color{blue}{\frac{1}{y}}\right) \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      13. mult-flip-rev N/A

          \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      14. lift-/.f64 N/A

          \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{y} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      15. associate-/l/ N/A

          \[\leadsto \color{blue}{\frac{x}{y \cdot y}} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{y \cdot y}} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

      17. lower-/.f64 81.0%

          \[\leadsto \color{blue}{\frac{x}{y \cdot y}} \cdot x + \frac{\frac{z \cdot z}{t}}{t} \]

   7. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot y} \cdot x} + \frac{\frac{z \cdot z}{t}}{t} \]

   if 5.0000000171117013e-316 < (*.f64 t t)

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      3. lower-+.f64 67.8%

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} + \frac{x \cdot x}{y \cdot y} \]

      6. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

      9. lower-/.f64 74.2%

         \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z + \frac{x \cdot x}{y \cdot y} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

      12. associate-/l* N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{x \cdot \frac{x}{y \cdot y}} \]

      13. *-commutative N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

      15. lower-/.f64 81.0%

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y}} \cdot x \]

   3. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z + \frac{x}{y \cdot y} \cdot x} \]
   4. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y}} \cdot x \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{z}{t \cdot t} \cdot z + \frac{x}{\color{blue}{y \cdot y}} \cdot x \]

      3. associate-/r* N/A

         \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{\frac{x}{y}}{y}} \cdot x \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{z}{t \cdot t} \cdot z + \frac{\color{blue}{\frac{x}{y}}}{y} \cdot x \]

      5. lower-/.f64 87.3%

         \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{\frac{x}{y}}{y}} \cdot x \]

   5. Applied rewrites 87.3%

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

Alternative 7: 88.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ \mathbf{if}\;t\_1 \leq 20000000000000001019220591274005456279710505470622733232619203286613548419128326636838181727778134043521316213363512555228359822654904417182365028760483854715262087764856296628876189602931571523608705123012237845488278935519238250121771614208:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z + \frac{x}{y \cdot y} \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* z z) (* t t))))
  (if (<=
       t_1
       20000000000000001019220591274005456279710505470622733232619203286613548419128326636838181727778134043521316213363512555228359822654904417182365028760483854715262087764856296628876189602931571523608705123012237845488278935519238250121771614208)
    (+ (* (/ x y) (/ x y)) t_1)
    (+ (* (/ z (* t t)) z) (* (/ x (* y y)) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+241) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = ((z / (t * t)) * z) + ((x / (y * y)) * x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * z) / (t * t)
    if (t_1 <= 2d+241) then
        tmp = ((x / y) * (x / y)) + t_1
    else
        tmp = ((z / (t * t)) * z) + ((x / (y * y)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * z) / (t * t);
	double tmp;
	if (t_1 <= 2e+241) {
		tmp = ((x / y) * (x / y)) + t_1;
	} else {
		tmp = ((z / (t * t)) * z) + ((x / (y * y)) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * z) / (t * t)
	tmp = 0
	if t_1 <= 2e+241:
		tmp = ((x / y) * (x / y)) + t_1
	else:
		tmp = ((z / (t * t)) * z) + ((x / (y * y)) * x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * z) / Float64(t * t))
	tmp = 0.0
	if (t_1 <= 2e+241)
		tmp = Float64(Float64(Float64(x / y) * Float64(x / y)) + t_1);
	else
		tmp = Float64(Float64(Float64(z / Float64(t * t)) * z) + Float64(Float64(x / Float64(y * y)) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * z) / (t * t);
	tmp = 0.0;
	if (t_1 <= 2e+241)
		tmp = ((x / y) * (x / y)) + t_1;
	else
		tmp = ((z / (t * t)) * z) + ((x / (y * y)) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 20000000000000001019220591274005456279710505470622733232619203286613548419128326636838181727778134043521316213363512555228359822654904417182365028760483854715262087764856296628876189602931571523608705123012237845488278935519238250121771614208], N[(N[(N[(x / y), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2.0000000000000001e241

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{x \cdot x}{\color{blue}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

      4. times-frac N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

      6. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{x}{y} + \frac{z \cdot z}{t \cdot t} \]

      7. lower-/.f64 82.3%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

   3. Applied rewrites 82.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]

   if 2.0000000000000001e241 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 67.8%

      \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      3. lower-+.f64 67.8%

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} + \frac{x \cdot x}{y \cdot y} \]

      6. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

      8. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

      9. lower-/.f64 74.2%

         \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z + \frac{x \cdot x}{y \cdot y} \]

      10. lift-/.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

      11. lift-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

      12. associate-/l* N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{x \cdot \frac{x}{y \cdot y}} \]

      13. *-commutative N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

      14. lower-*.f64 N/A

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

      15. lower-/.f64 81.0%

          \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y}} \cdot x \]

   3. Applied rewrites 81.0%

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

Alternative 8: 81.0% accurate, 1.0× speedup

Math

\[\frac{z}{t \cdot t} \cdot z + \frac{x}{y \cdot y} \cdot x \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (* (/ z (* t t)) z) (* (/ x (* y y)) x)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.8%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
2. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

   3. lower-+.f64 67.8%

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t} + \frac{x \cdot x}{y \cdot y}} \]

   4. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{z \cdot z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{z \cdot z}}{t \cdot t} + \frac{x \cdot x}{y \cdot y} \]

   6. associate-/l* N/A

      \[\leadsto \color{blue}{z \cdot \frac{z}{t \cdot t}} + \frac{x \cdot x}{y \cdot y} \]

   7. *-commutative N/A

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

   8. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z} + \frac{x \cdot x}{y \cdot y} \]

   9. lower-/.f64 74.2%

      \[\leadsto \color{blue}{\frac{z}{t \cdot t}} \cdot z + \frac{x \cdot x}{y \cdot y} \]

   10. lift-/.f64 N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x \cdot x}{y \cdot y}} \]

   11. lift-*.f64 N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z + \frac{\color{blue}{x \cdot x}}{y \cdot y} \]

   12. associate-/l* N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{x \cdot \frac{x}{y \cdot y}} \]

   13. *-commutative N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

   14. lower-*.f64 N/A

       \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y} \cdot x} \]

   15. lower-/.f64 81.0%

       \[\leadsto \frac{z}{t \cdot t} \cdot z + \color{blue}{\frac{x}{y \cdot y}} \cdot x \]

3. Applied rewrites 81.0%

   \[\leadsto \color{blue}{\frac{z}{t \cdot t} \cdot z + \frac{x}{y \cdot y} \cdot x} \]
4. Add Preprocessing

Alternative 9: 74.2% accurate, 1.0× speedup

Math

\[\frac{x}{y \cdot y} \cdot x + \frac{z \cdot z}{t \cdot t} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (* (/ x (* y y)) x) (/ (* z z) (* t t))))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.8%

   \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x \cdot x}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]

   3. associate-/l* N/A

      \[\leadsto \color{blue}{x \cdot \frac{x}{y \cdot y}} + \frac{z \cdot z}{t \cdot t} \]

   4. *-commutative N/A

      \[\leadsto \color{blue}{\frac{x}{y \cdot y} \cdot x} + \frac{z \cdot z}{t \cdot t} \]

   5. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{x}{y \cdot y} \cdot x} + \frac{z \cdot z}{t \cdot t} \]

   6. lower-/.f64 74.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot y}} \cdot x + \frac{z \cdot z}{t \cdot t} \]

3. Applied rewrites 74.2%

   \[\leadsto \color{blue}{\frac{x}{y \cdot y} \cdot x} + \frac{z \cdot z}{t \cdot t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64
  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))