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

Percentage Accurate: 99.9% → 100.0%

Time: 7.7s

Alternatives: 9

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: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-237}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.6e+19)
   (* x 3.0)
   (if (<= x -7e-237) (+ x z) (if (<= x 1.25e-42) (* y 2.0) (* x 3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.6e+19) {
		tmp = x * 3.0;
	} else if (x <= -7e-237) {
		tmp = x + z;
	} else if (x <= 1.25e-42) {
		tmp = 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 <= (-7.6d+19)) then
        tmp = x * 3.0d0
    else if (x <= (-7d-237)) then
        tmp = x + z
    else if (x <= 1.25d-42) then
        tmp = 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 <= -7.6e+19) {
		tmp = x * 3.0;
	} else if (x <= -7e-237) {
		tmp = x + z;
	} else if (x <= 1.25e-42) {
		tmp = y * 2.0;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.6e+19:
		tmp = x * 3.0
	elif x <= -7e-237:
		tmp = x + z
	elif x <= 1.25e-42:
		tmp = y * 2.0
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.6e+19)
		tmp = Float64(x * 3.0);
	elseif (x <= -7e-237)
		tmp = Float64(x + z);
	elseif (x <= 1.25e-42)
		tmp = 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 <= -7.6e+19)
		tmp = x * 3.0;
	elseif (x <= -7e-237)
		tmp = x + z;
	elseif (x <= 1.25e-42)
		tmp = y * 2.0;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.6e+19], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -7e-237], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.25e-42], N[(y * 2.0), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.6e19 or 1.25000000000000001e-42 < 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 69.3%

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

   7. Simplified 69.3%

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

   if -7.6e19 < x < -6.99999999999999966e-237

   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 52.7%

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

   if -6.99999999999999966e-237 < x < 1.25000000000000001e-42

   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 60.0%

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

   7. Simplified 60.0%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-237}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-42}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-237}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.2e+17)
   (* x 3.0)
   (if (<= x -3e-237) z (if (<= x 1.35e-42) (* y 2.0) (* x 3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e+17) {
		tmp = x * 3.0;
	} else if (x <= -3e-237) {
		tmp = z;
	} else if (x <= 1.35e-42) {
		tmp = 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 <= (-6.2d+17)) then
        tmp = x * 3.0d0
    else if (x <= (-3d-237)) then
        tmp = z
    else if (x <= 1.35d-42) then
        tmp = 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 <= -6.2e+17) {
		tmp = x * 3.0;
	} else if (x <= -3e-237) {
		tmp = z;
	} else if (x <= 1.35e-42) {
		tmp = y * 2.0;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.2e+17:
		tmp = x * 3.0
	elif x <= -3e-237:
		tmp = z
	elif x <= 1.35e-42:
		tmp = y * 2.0
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.2e+17)
		tmp = Float64(x * 3.0);
	elseif (x <= -3e-237)
		tmp = z;
	elseif (x <= 1.35e-42)
		tmp = 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 <= -6.2e+17)
		tmp = x * 3.0;
	elseif (x <= -3e-237)
		tmp = z;
	elseif (x <= 1.35e-42)
		tmp = y * 2.0;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.2e+17], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, -3e-237], z, If[LessEqual[x, 1.35e-42], N[(y * 2.0), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2e17 or 1.35e-42 < 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 69.3%

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

   7. Simplified 69.3%

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

   if -6.2e17 < x < -3.00000000000000024e-237

   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 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 51.2%

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

   if -3.00000000000000024e-237 < x < 1.35e-42

   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 60.0%

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

   7. Simplified 60.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-237}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-42}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + x \cdot 3\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-42}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* x 3.0))))
   (if (<= x -4.4e+33) t_0 (if (<= x 2.5e-42) (+ 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 <= -4.4e+33) {
		tmp = t_0;
	} else if (x <= 2.5e-42) {
		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 <= (-4.4d+33)) then
        tmp = t_0
    else if (x <= 2.5d-42) 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 <= -4.4e+33) {
		tmp = t_0;
	} else if (x <= 2.5e-42) {
		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 <= -4.4e+33:
		tmp = t_0
	elif x <= 2.5e-42:
		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 <= -4.4e+33)
		tmp = t_0;
	elseif (x <= 2.5e-42)
		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 <= -4.4e+33)
		tmp = t_0;
	elseif (x <= 2.5e-42)
		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, -4.4e+33], t$95$0, If[LessEqual[x, 2.5e-42], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.39999999999999988e33 or 2.50000000000000001e-42 < 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 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 87.4%

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

   7. Simplified 87.4%

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

   if -4.39999999999999988e33 < x < 2.50000000000000001e-42

   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 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-42}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+57}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9e+34) (* x 3.0) (if (<= x 4e+57) (+ z (* y 2.0)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9e+34) {
		tmp = x * 3.0;
	} else if (x <= 4e+57) {
		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 <= (-9d+34)) then
        tmp = x * 3.0d0
    else if (x <= 4d+57) 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 <= -9e+34) {
		tmp = x * 3.0;
	} else if (x <= 4e+57) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9e+34:
		tmp = x * 3.0
	elif x <= 4e+57:
		tmp = z + (y * 2.0)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9e+34)
		tmp = Float64(x * 3.0);
	elseif (x <= 4e+57)
		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 <= -9e+34)
		tmp = x * 3.0;
	elseif (x <= 4e+57)
		tmp = z + (y * 2.0);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9e+34], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 4e+57], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000001e34 or 4.00000000000000019e57 < 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 74.0%

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

   7. Simplified 74.0%

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

   if -9.0000000000000001e34 < x < 4.00000000000000019e57

   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 88.9%

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

   7. Simplified 88.9%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+34}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+57}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+73}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e-26) (* y 2.0) (if (<= y 5.8e+73) z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-26) {
		tmp = y * 2.0;
	} else if (y <= 5.8e+73) {
		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 <= (-1.9d-26)) then
        tmp = y * 2.0d0
    else if (y <= 5.8d+73) 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 <= -1.9e-26) {
		tmp = y * 2.0;
	} else if (y <= 5.8e+73) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e-26:
		tmp = y * 2.0
	elif y <= 5.8e+73:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e-26)
		tmp = Float64(y * 2.0);
	elseif (y <= 5.8e+73)
		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 <= -1.9e-26)
		tmp = y * 2.0;
	elseif (y <= 5.8e+73)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e-26], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 5.8e+73], z, N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000007e-26 or 5.8000000000000005e73 < 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 62.9%

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

   7. Simplified 62.9%

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

   if -1.90000000000000007e-26 < y < 5.8000000000000005e73

   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 42.2%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-26}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+73}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 33.8% 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 30.9%

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

Alternative 9: 8.0% 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 z around inf

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

5. Simplified 36.8%

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

6. Taylor expanded in z around 0

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

8. Simplified 8.8%

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

Reproduce

herbie shell --seed 2024138 
(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))