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

Percentage Accurate: 99.9% → 100.0%

Time: 7.2s

Alternatives: 10

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 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. 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: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3 + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e-45)
   (+ z (* x 3.0))
   (if (<= x 1.7e+135) (+ z (* y 2.0)) (+ (* x 3.0) (* y 2.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-45) {
		tmp = z + (x * 3.0);
	} else if (x <= 1.7e+135) {
		tmp = z + (y * 2.0);
	} else {
		tmp = (x * 3.0) + (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 (x <= (-2.6d-45)) then
        tmp = z + (x * 3.0d0)
    else if (x <= 1.7d+135) then
        tmp = z + (y * 2.0d0)
    else
        tmp = (x * 3.0d0) + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e-45) {
		tmp = z + (x * 3.0);
	} else if (x <= 1.7e+135) {
		tmp = z + (y * 2.0);
	} else {
		tmp = (x * 3.0) + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e-45:
		tmp = z + (x * 3.0)
	elif x <= 1.7e+135:
		tmp = z + (y * 2.0)
	else:
		tmp = (x * 3.0) + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e-45)
		tmp = Float64(z + Float64(x * 3.0));
	elseif (x <= 1.7e+135)
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(Float64(x * 3.0) + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e-45)
		tmp = z + (x * 3.0);
	elseif (x <= 1.7e+135)
		tmp = z + (y * 2.0);
	else
		tmp = (x * 3.0) + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e-45], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+135], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * 3.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.59999999999999987e-45

   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 83.9%

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

   7. Simplified 83.9%

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

   if -2.59999999999999987e-45 < x < 1.70000000000000005e135

   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 92.1%

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

   7. Simplified 92.1%

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

   if 1.70000000000000005e135 < x

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   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 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{z + \left(y \cdot 2 + x \cdot 3\right)} \]
   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 95.3%

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

   7. Simplified 95.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3 + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + x \cdot 3\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{-46}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+157}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* x 3.0))))
   (if (<= x -8.8e-46) t_0 (if (<= x 1.05e+157) (+ z (* y 2.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z + (x * 3.0);
	double tmp;
	if (x <= -8.8e-46) {
		tmp = t_0;
	} else if (x <= 1.05e+157) {
		tmp = z + (y * 2.0);
	} 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 + (x * 3.0d0)
    if (x <= (-8.8d-46)) then
        tmp = t_0
    else if (x <= 1.05d+157) then
        tmp = z + (y * 2.0d0)
    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 + (x * 3.0);
	double tmp;
	if (x <= -8.8e-46) {
		tmp = t_0;
	} else if (x <= 1.05e+157) {
		tmp = z + (y * 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z + (x * 3.0)
	tmp = 0
	if x <= -8.8e-46:
		tmp = t_0
	elif x <= 1.05e+157:
		tmp = z + (y * 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z + Float64(x * 3.0))
	tmp = 0.0
	if (x <= -8.8e-46)
		tmp = t_0;
	elseif (x <= 1.05e+157)
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z + (x * 3.0);
	tmp = 0.0;
	if (x <= -8.8e-46)
		tmp = t_0;
	elseif (x <= 1.05e+157)
		tmp = z + (y * 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e-46], t$95$0, If[LessEqual[x, 1.05e+157], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.8000000000000004e-46 or 1.05e157 < 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 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 83.4%

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

   7. Simplified 83.4%

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

   if -8.8000000000000004e-46 < x < 1.05e157

   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 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{-46}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+157}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+141}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+157}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e+141)
   (* x 3.0)
   (if (<= x 1.25e+157) (+ z (* y 2.0)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e+141) {
		tmp = x * 3.0;
	} else if (x <= 1.25e+157) {
		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 <= (-5.4d+141)) then
        tmp = x * 3.0d0
    else if (x <= 1.25d+157) 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 <= -5.4e+141) {
		tmp = x * 3.0;
	} else if (x <= 1.25e+157) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e+141:
		tmp = x * 3.0
	elif x <= 1.25e+157:
		tmp = z + (y * 2.0)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e+141)
		tmp = Float64(x * 3.0);
	elseif (x <= 1.25e+157)
		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 <= -5.4e+141)
		tmp = x * 3.0;
	elseif (x <= 1.25e+157)
		tmp = z + (y * 2.0);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e+141], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 1.25e+157], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4000000000000002e141 or 1.24999999999999994e157 < x

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   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 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 74.4%

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

   7. Simplified 74.4%

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

   if -5.4000000000000002e141 < x < 1.24999999999999994e157

   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 87.6%

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

   7. Simplified 87.6%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+141}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+157}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+57}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+103}:\\ \;\;\;\;x + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.22e+57) (+ x z) (if (<= z 3.3e+103) (+ x (* y 2.0)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.22e+57) {
		tmp = x + z;
	} else if (z <= 3.3e+103) {
		tmp = x + (y * 2.0);
	} else {
		tmp = x + z;
	}
	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 (z <= (-1.22d+57)) then
        tmp = x + z
    else if (z <= 3.3d+103) then
        tmp = x + (y * 2.0d0)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.22e+57) {
		tmp = x + z;
	} else if (z <= 3.3e+103) {
		tmp = x + (y * 2.0);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.22e+57:
		tmp = x + z
	elif z <= 3.3e+103:
		tmp = x + (y * 2.0)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.22e+57)
		tmp = Float64(x + z);
	elseif (z <= 3.3e+103)
		tmp = Float64(x + Float64(y * 2.0));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.22e+57)
		tmp = x + z;
	elseif (z <= 3.3e+103)
		tmp = x + (y * 2.0);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.22e+57], N[(x + z), $MachinePrecision], If[LessEqual[z, 3.3e+103], N[(x + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e57 or 3.30000000000000009e103 < z

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 73.5%

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

   if -1.22e57 < z < 3.30000000000000009e103

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot y\right)}, x\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 55.9%

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

   5. Simplified 55.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+57}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+103}:\\ \;\;\;\;x + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+25}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+102}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+25) (* y 2.0) (if (<= y 3.6e+102) (+ x z) (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+25) {
		tmp = y * 2.0;
	} else if (y <= 3.6e+102) {
		tmp = x + 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 <= (-9d+25)) then
        tmp = y * 2.0d0
    else if (y <= 3.6d+102) then
        tmp = x + 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 <= -9e+25) {
		tmp = y * 2.0;
	} else if (y <= 3.6e+102) {
		tmp = x + z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+25:
		tmp = y * 2.0
	elif y <= 3.6e+102:
		tmp = x + z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+25)
		tmp = Float64(y * 2.0);
	elseif (y <= 3.6e+102)
		tmp = Float64(x + z);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+25)
		tmp = y * 2.0;
	elseif (y <= 3.6e+102)
		tmp = x + z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+25], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 3.6e+102], N[(x + z), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000006e25 or 3.6000000000000002e102 < y

   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 inf

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

      1. *-lowering-*.f64 66.3%

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

   7. Simplified 66.3%

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

   if -9.0000000000000006e25 < y < 3.6000000000000002e102

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{z}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 56.7%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+25}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+102}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+23}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+55) z (if (<= z 8e+23) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+55) {
		tmp = z;
	} else if (z <= 8e+23) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	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 (z <= (-3d+55)) then
        tmp = z
    else if (z <= 8d+23) then
        tmp = y * 2.0d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+55) {
		tmp = z;
	} else if (z <= 8e+23) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+55:
		tmp = z
	elif z <= 8e+23:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+55)
		tmp = z;
	elseif (z <= 8e+23)
		tmp = Float64(y * 2.0);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+55)
		tmp = z;
	elseif (z <= 8e+23)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+55], z, If[LessEqual[z, 8e+23], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000017e55 or 7.9999999999999993e23 < z

   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 67.2%

      \[\leadsto \color{blue}{z} \]

   if -3.00000000000000017e55 < z < 7.9999999999999993e23

   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 y around inf

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

      1. *-lowering-*.f64 52.1%

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

   7. Simplified 52.1%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+23}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 + ((x * 3.0d0) + (y * 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z + N[(N[(x * 3.0), $MachinePrecision] + 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 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. Final simplification 99.9%

   \[\leadsto z + \left(x \cdot 3 + y \cdot 2\right) \]
6. Add Preprocessing

Alternative 9: 33.9% 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 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 38.3%

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

Alternative 10: 7.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(2 \cdot y\right)}, x\right) \]
4. Step-by-step derivation

   1. *-lowering-*.f64 40.0%

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

5. Simplified 40.0%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
7. Step-by-step derivation

8. Simplified 7.1%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024161 
(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))