Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4

Percentage Accurate: 99.9% → 100.0%

Time: 6.5s

Alternatives: 7

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x + y) + y) + x) + z) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x + y) + y) + x) + z) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 3, z + y \cdot 2\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x 3.0 (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	return fma(x, 3.0, (z + (y * 2.0)));
}

Julia

function code(x, y, z)
	return fma(x, 3.0, Float64(z + Float64(y * 2.0)))
end

Wolfram

code[x_, y_, z_] := N[(x * 3.0 + N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
2. Step-by-step derivation

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

   6. associate-+l+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

   7. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

   8. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

   10. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

   11. count-2 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   14. count-2 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

   15. distribute-rgt1-in N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

   17. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

   18. metadata-eval 100.0%

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-+r+ N/A

      \[\leadsto \left(z + y \cdot 2\right) + \color{blue}{x \cdot 3} \]

   2. +-commutative N/A

      \[\leadsto x \cdot 3 + \color{blue}{\left(z + y \cdot 2\right)} \]

   3. fma-define N/A

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{3}, z + y \cdot 2\right) \]

   4. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(x, \color{blue}{3}, \left(z + y \cdot 2\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(x, 3, \mathsf{+.f64}\left(z, \left(y \cdot 2\right)\right)\right) \]

   6. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{fma.f64}\left(x, 3, \mathsf{+.f64}\left(z, \mathsf{*.f64}\left(y, 2\right)\right)\right) \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z + y \cdot 2\right)} \]
7. Add Preprocessing

Alternative 2: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot 2 + x \cdot 3\\ \mathbf{if}\;y \leq -1 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+158}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y 2.0) (* x 3.0))))
   (if (<= y -1e+153)
     t_0
     (if (<= y 2.4e+19)
       (+ z (* x 3.0))
       (if (<= y 2.35e+158) t_0 (+ z (* y 2.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 2.0) + (x * 3.0);
	double tmp;
	if (y <= -1e+153) {
		tmp = t_0;
	} else if (y <= 2.4e+19) {
		tmp = z + (x * 3.0);
	} else if (y <= 2.35e+158) {
		tmp = t_0;
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * 2.0d0) + (x * 3.0d0)
    if (y <= (-1d+153)) then
        tmp = t_0
    else if (y <= 2.4d+19) then
        tmp = z + (x * 3.0d0)
    else if (y <= 2.35d+158) then
        tmp = t_0
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * 2.0) + (x * 3.0);
	double tmp;
	if (y <= -1e+153) {
		tmp = t_0;
	} else if (y <= 2.4e+19) {
		tmp = z + (x * 3.0);
	} else if (y <= 2.35e+158) {
		tmp = t_0;
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 2.0) + (x * 3.0)
	tmp = 0
	if y <= -1e+153:
		tmp = t_0
	elif y <= 2.4e+19:
		tmp = z + (x * 3.0)
	elif y <= 2.35e+158:
		tmp = t_0
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 2.0) + Float64(x * 3.0))
	tmp = 0.0
	if (y <= -1e+153)
		tmp = t_0;
	elseif (y <= 2.4e+19)
		tmp = Float64(z + Float64(x * 3.0));
	elseif (y <= 2.35e+158)
		tmp = t_0;
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * 2.0) + (x * 3.0);
	tmp = 0.0;
	if (y <= -1e+153)
		tmp = t_0;
	elseif (y <= 2.4e+19)
		tmp = z + (x * 3.0);
	elseif (y <= 2.35e+158)
		tmp = t_0;
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 2.0), $MachinePrecision] + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+153], t$95$0, If[LessEqual[y, 2.4e+19], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+158], t$95$0, N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e153 or 2.4e19 < y < 2.35e158

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{2 \cdot y + 3 \cdot x} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot y\right), \color{blue}{\left(3 \cdot x\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, y\right), \left(\color{blue}{3} \cdot x\right)\right) \]

      3. *-lowering-*.f64 91.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, y\right), \mathsf{*.f64}\left(3, \color{blue}{x}\right)\right) \]

   7. Simplified 91.2%

      \[\leadsto \color{blue}{2 \cdot y + 3 \cdot x} \]

   if -1e153 < y < 2.4e19

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + 3 \cdot x} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 3 \cdot x + \color{blue}{z} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(3 \cdot x\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 90.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, x\right), z\right) \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{3 \cdot x + z} \]

   if 2.35e158 < y

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 2 \cdot y + \color{blue}{z} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 94.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, y\right), z\right) \]

   7. Simplified 94.8%

      \[\leadsto \color{blue}{2 \cdot y + z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+153}:\\ \;\;\;\;y \cdot 2 + x \cdot 3\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+19}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+158}:\\ \;\;\;\;y \cdot 2 + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + y \cdot 2\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+138}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-44}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* y 2.0))))
   (if (<= y -3.9e+138) t_0 (if (<= y 4.2e-44) (+ z (* x 3.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z + (y * 2.0);
	double tmp;
	if (y <= -3.9e+138) {
		tmp = t_0;
	} else if (y <= 4.2e-44) {
		tmp = z + (x * 3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z + (y * 2.0d0)
    if (y <= (-3.9d+138)) then
        tmp = t_0
    else if (y <= 4.2d-44) then
        tmp = z + (x * 3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z + (y * 2.0);
	double tmp;
	if (y <= -3.9e+138) {
		tmp = t_0;
	} else if (y <= 4.2e-44) {
		tmp = z + (x * 3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z + (y * 2.0)
	tmp = 0
	if y <= -3.9e+138:
		tmp = t_0
	elif y <= 4.2e-44:
		tmp = z + (x * 3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z + Float64(y * 2.0))
	tmp = 0.0
	if (y <= -3.9e+138)
		tmp = t_0;
	elseif (y <= 4.2e-44)
		tmp = Float64(z + Float64(x * 3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z + (y * 2.0);
	tmp = 0.0;
	if (y <= -3.9e+138)
		tmp = t_0;
	elseif (y <= 4.2e-44)
		tmp = z + (x * 3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+138], t$95$0, If[LessEqual[y, 4.2e-44], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8999999999999998e138 or 4.20000000000000003e-44 < y

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 2 \cdot y + \color{blue}{z} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 86.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, y\right), z\right) \]

   7. Simplified 86.1%

      \[\leadsto \color{blue}{2 \cdot y + z} \]

   if -3.8999999999999998e138 < y < 4.20000000000000003e-44

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z + 3 \cdot x} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 3 \cdot x + \color{blue}{z} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(3 \cdot x\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 91.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, x\right), z\right) \]

   7. Simplified 91.4%

      \[\leadsto \color{blue}{3 \cdot x + z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+138}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-44}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+178}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+174}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.1e+178)
   (* x 3.0)
   (if (<= x 7.1e+174) (+ z (* y 2.0)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e+178) {
		tmp = x * 3.0;
	} else if (x <= 7.1e+174) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.1d+178)) then
        tmp = x * 3.0d0
    else if (x <= 7.1d+174) then
        tmp = z + (y * 2.0d0)
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e+178) {
		tmp = x * 3.0;
	} else if (x <= 7.1e+174) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.1e+178:
		tmp = x * 3.0
	elif x <= 7.1e+174:
		tmp = z + (y * 2.0)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.1e+178)
		tmp = Float64(x * 3.0);
	elseif (x <= 7.1e+174)
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.1e+178)
		tmp = x * 3.0;
	elseif (x <= 7.1e+174)
		tmp = z + (y * 2.0);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.1e+178], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 7.1e+174], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.09999999999999999e178 or 7.1000000000000003e174 < x

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{3 \cdot x} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 79.6%

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{x}\right) \]

   7. Simplified 79.6%

      \[\leadsto \color{blue}{3 \cdot x} \]

   if -1.09999999999999999e178 < x < 7.1000000000000003e174

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{z + 2 \cdot y} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 2 \cdot y + \color{blue}{z} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 84.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, y\right), z\right) \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{2 \cdot y + z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+178}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+174}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+152}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e+152) (* y 2.0) (if (<= y 1.65e+20) z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e+152) {
		tmp = y * 2.0;
	} else if (y <= 1.65e+20) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8.2d+152)) then
        tmp = y * 2.0d0
    else if (y <= 1.65d+20) then
        tmp = z
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e+152) {
		tmp = y * 2.0;
	} else if (y <= 1.65e+20) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.2e+152:
		tmp = y * 2.0
	elif y <= 1.65e+20:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e+152)
		tmp = Float64(y * 2.0);
	elseif (y <= 1.65e+20)
		tmp = z;
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.2e+152)
		tmp = y * 2.0;
	elseif (y <= 1.65e+20)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e+152], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 1.65e+20], z, N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999996e152 or 1.65e20 < y

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 100.0%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 74.5%

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{y}\right) \]

   7. Simplified 74.5%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -8.1999999999999996e152 < y < 1.65e20

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Step-by-step derivation

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

      6. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

      7. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

      8. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

      11. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

      14. count-2 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

      15. distribute-rgt1-in N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

      18. metadata-eval 99.9%

          \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   6. Step-by-step derivation

   7. Simplified 53.0%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+152}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ z + \left(y \cdot 2 + x \cdot 3\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (+ (* y 2.0) (* x 3.0))))

C

double code(double x, double y, double z) {
	return z + ((y * 2.0) + (x * 3.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + ((y * 2.0d0) + (x * 3.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return z + ((y * 2.0) + (x * 3.0));
}

Python

def code(x, y, z):
	return z + ((y * 2.0) + (x * 3.0))

Julia

function code(x, y, z)
	return Float64(z + Float64(Float64(y * 2.0) + Float64(x * 3.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + ((y * 2.0) + (x * 3.0));
end

Wolfram

code[x_, y_, z_] := N[(z + N[(N[(y * 2.0), $MachinePrecision] + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
2. Step-by-step derivation

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

   6. associate-+l+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

   7. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

   8. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

   10. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

   11. count-2 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   14. count-2 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

   15. distribute-rgt1-in N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

   17. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

   18. metadata-eval 100.0%

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 7: 34.0% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

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

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
2. Step-by-step derivation

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(z, \color{blue}{\left(x + \left(\left(\left(x + y\right) + y\right) + x\right)\right)}\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \color{blue}{\left(\left(x + y\right) + y\right)}\right)\right)\right) \]

   6. associate-+l+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(x + \left(x + \color{blue}{\left(y + y\right)}\right)\right)\right)\right) \]

   7. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(x + \left(\left(x + x\right) + \color{blue}{\left(y + y\right)}\right)\right)\right) \]

   8. associate-+r+ N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(\left(x + \left(x + x\right)\right) + \color{blue}{\left(y + y\right)}\right)\right) \]

   9. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(z, \left(\left(y + y\right) + \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

   10. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y + y\right), \color{blue}{\left(x + \left(x + x\right)\right)}\right)\right) \]

   11. count-2 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(2 \cdot y\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\color{blue}{x} + \left(x + x\right)\right)\right)\right) \]

   14. count-2 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x + 2 \cdot \color{blue}{x}\right)\right)\right) \]

   15. distribute-rgt1-in N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(\left(2 + 1\right) \cdot \color{blue}{x}\right)\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \left(x \cdot \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

   17. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, \color{blue}{\left(2 + 1\right)}\right)\right)\right) \]

   18. metadata-eval 100.0%

       \[\leadsto \mathsf{+.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 2\right), \mathsf{*.f64}\left(x, 3\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around inf

   \[\leadsto \color{blue}{z} \]
6. Step-by-step derivation

7. Simplified 38.2%

   \[\leadsto \color{blue}{z} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))