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

Percentage Accurate: 99.9% → 99.9%

Time: 9.6s

Alternatives: 12

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: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+r+ 99.9%

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

   9. +-commutative 99.9%

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

   10. +-commutative 99.9%

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

   11. associate-+l+ 99.9%

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

   12. +-commutative 99.9%

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

   13. associate-+r+ 99.9%

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

   14. count-2 99.9%

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

   15. distribute-rgt1-in 99.9%

       \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

   16. fma-def 99.9%

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

   17. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 56.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + 3 \cdot x\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-193}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-236}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-176}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (* 3.0 x))))
   (if (<= x -3.8e+38)
     t_0
     (if (<= x -1.05e-193)
       (+ y z)
       (if (<= x -8.5e-236)
         (+ y y)
         (if (<= x 5.4e-176) (+ y z) (if (<= x 1.1e+42) (+ y y) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (3.0 * x);
	double tmp;
	if (x <= -3.8e+38) {
		tmp = t_0;
	} else if (x <= -1.05e-193) {
		tmp = y + z;
	} else if (x <= -8.5e-236) {
		tmp = y + y;
	} else if (x <= 5.4e-176) {
		tmp = y + z;
	} else if (x <= 1.1e+42) {
		tmp = y + y;
	} 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 = y + (3.0d0 * x)
    if (x <= (-3.8d+38)) then
        tmp = t_0
    else if (x <= (-1.05d-193)) then
        tmp = y + z
    else if (x <= (-8.5d-236)) then
        tmp = y + y
    else if (x <= 5.4d-176) then
        tmp = y + z
    else if (x <= 1.1d+42) then
        tmp = y + y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (3.0 * x);
	double tmp;
	if (x <= -3.8e+38) {
		tmp = t_0;
	} else if (x <= -1.05e-193) {
		tmp = y + z;
	} else if (x <= -8.5e-236) {
		tmp = y + y;
	} else if (x <= 5.4e-176) {
		tmp = y + z;
	} else if (x <= 1.1e+42) {
		tmp = y + y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (3.0 * x)
	tmp = 0
	if x <= -3.8e+38:
		tmp = t_0
	elif x <= -1.05e-193:
		tmp = y + z
	elif x <= -8.5e-236:
		tmp = y + y
	elif x <= 5.4e-176:
		tmp = y + z
	elif x <= 1.1e+42:
		tmp = y + y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(3.0 * x))
	tmp = 0.0
	if (x <= -3.8e+38)
		tmp = t_0;
	elseif (x <= -1.05e-193)
		tmp = Float64(y + z);
	elseif (x <= -8.5e-236)
		tmp = Float64(y + y);
	elseif (x <= 5.4e-176)
		tmp = Float64(y + z);
	elseif (x <= 1.1e+42)
		tmp = Float64(y + y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (3.0 * x);
	tmp = 0.0;
	if (x <= -3.8e+38)
		tmp = t_0;
	elseif (x <= -1.05e-193)
		tmp = y + z;
	elseif (x <= -8.5e-236)
		tmp = y + y;
	elseif (x <= 5.4e-176)
		tmp = y + z;
	elseif (x <= 1.1e+42)
		tmp = y + y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(3.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8e+38], t$95$0, If[LessEqual[x, -1.05e-193], N[(y + z), $MachinePrecision], If[LessEqual[x, -8.5e-236], N[(y + y), $MachinePrecision], If[LessEqual[x, 5.4e-176], N[(y + z), $MachinePrecision], If[LessEqual[x, 1.1e+42], N[(y + y), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998e38 or 1.1000000000000001e42 < 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+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+r+ 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

      13. associate-+r+ 99.8%

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

      14. count-2 99.8%

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

      15. distribute-rgt1-in 99.8%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 81.7%

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

      1. +-commutative 81.7%

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

      2. fma-def 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in z around 0 65.8%

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

   if -3.7999999999999998e38 < x < -1.05e-193 or -8.49999999999999929e-236 < x < 5.3999999999999997e-176

   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+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-+l+ 100.0%

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

      12. +-commutative 100.0%

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

      13. associate-+r+ 100.0%

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

      14. count-2 100.0%

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

      15. distribute-rgt1-in 100.0%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 68.8%

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

      1. +-commutative 68.8%

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

      2. fma-def 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. +-commutative 64.3%

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

   9. Simplified 64.3%

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

   if -1.05e-193 < x < -8.49999999999999929e-236 or 5.3999999999999997e-176 < x < 1.1000000000000001e42

   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+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 99.9%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-+l+ 100.0%

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

      12. +-commutative 100.0%

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

      13. associate-+r+ 100.0%

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

      14. count-2 100.0%

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

      15. distribute-rgt1-in 100.0%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 63.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;y + 3 \cdot x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-193}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-236}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-176}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;y + 3 \cdot x\\ \end{array} \]

Alternative 3: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-190}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-238}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-177}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e+38)
   (* 3.0 x)
   (if (<= x -1.6e-190)
     (+ y z)
     (if (<= x -9.5e-238)
       (+ y y)
       (if (<= x 1.8e-177) (+ y z) (if (<= x 1.75e+109) (+ y y) (* 3.0 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+38) {
		tmp = 3.0 * x;
	} else if (x <= -1.6e-190) {
		tmp = y + z;
	} else if (x <= -9.5e-238) {
		tmp = y + y;
	} else if (x <= 1.8e-177) {
		tmp = y + z;
	} else if (x <= 1.75e+109) {
		tmp = y + y;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.25d+38)) then
        tmp = 3.0d0 * x
    else if (x <= (-1.6d-190)) then
        tmp = y + z
    else if (x <= (-9.5d-238)) then
        tmp = y + y
    else if (x <= 1.8d-177) then
        tmp = y + z
    else if (x <= 1.75d+109) then
        tmp = y + y
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+38) {
		tmp = 3.0 * x;
	} else if (x <= -1.6e-190) {
		tmp = y + z;
	} else if (x <= -9.5e-238) {
		tmp = y + y;
	} else if (x <= 1.8e-177) {
		tmp = y + z;
	} else if (x <= 1.75e+109) {
		tmp = y + y;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e+38:
		tmp = 3.0 * x
	elif x <= -1.6e-190:
		tmp = y + z
	elif x <= -9.5e-238:
		tmp = y + y
	elif x <= 1.8e-177:
		tmp = y + z
	elif x <= 1.75e+109:
		tmp = y + y
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e+38)
		tmp = Float64(3.0 * x);
	elseif (x <= -1.6e-190)
		tmp = Float64(y + z);
	elseif (x <= -9.5e-238)
		tmp = Float64(y + y);
	elseif (x <= 1.8e-177)
		tmp = Float64(y + z);
	elseif (x <= 1.75e+109)
		tmp = Float64(y + y);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.25e+38)
		tmp = 3.0 * x;
	elseif (x <= -1.6e-190)
		tmp = y + z;
	elseif (x <= -9.5e-238)
		tmp = y + y;
	elseif (x <= 1.8e-177)
		tmp = y + z;
	elseif (x <= 1.75e+109)
		tmp = y + y;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e+38], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, -1.6e-190], N[(y + z), $MachinePrecision], If[LessEqual[x, -9.5e-238], N[(y + y), $MachinePrecision], If[LessEqual[x, 1.8e-177], N[(y + z), $MachinePrecision], If[LessEqual[x, 1.75e+109], N[(y + y), $MachinePrecision], N[(3.0 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.24999999999999992e38 or 1.74999999999999992e109 < 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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 67.1%

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

   if -1.24999999999999992e38 < x < -1.6e-190 or -9.50000000000000059e-238 < x < 1.79999999999999991e-177

   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+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. +-commutative 100.0%

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

      10. +-commutative 100.0%

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

      11. associate-+l+ 100.0%

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

      12. +-commutative 100.0%

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

      13. associate-+r+ 100.0%

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

      14. count-2 100.0%

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

      15. distribute-rgt1-in 100.0%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 68.8%

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

      1. +-commutative 68.8%

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

      2. fma-def 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. +-commutative 64.3%

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

   9. Simplified 64.3%

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

   if -1.6e-190 < x < -9.50000000000000059e-238 or 1.79999999999999991e-177 < x < 1.74999999999999992e109

   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+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      10. +-commutative 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. associate-+r+ 99.9%

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

      14. count-2 99.9%

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

      15. distribute-rgt1-in 99.9%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 56.1%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+38}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-190}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-238}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-177}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \]

Alternative 4: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+71}:\\ \;\;\;\;z + 3 \cdot x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+39}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e+71)
   (+ z (* 3.0 x))
   (if (<= x 5e+39) (+ z (* y 2.0)) (+ x (* 2.0 (+ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+71) {
		tmp = z + (3.0 * x);
	} else if (x <= 5e+39) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (2.0 * (y + x));
	}
	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 <= (-2d+71)) then
        tmp = z + (3.0d0 * x)
    else if (x <= 5d+39) then
        tmp = z + (y * 2.0d0)
    else
        tmp = x + (2.0d0 * (y + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+71) {
		tmp = z + (3.0 * x);
	} else if (x <= 5e+39) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (2.0 * (y + x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e+71:
		tmp = z + (3.0 * x)
	elif x <= 5e+39:
		tmp = z + (y * 2.0)
	else:
		tmp = x + (2.0 * (y + x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e+71)
		tmp = Float64(z + Float64(3.0 * x));
	elseif (x <= 5e+39)
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(x + Float64(2.0 * Float64(y + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e+71)
		tmp = z + (3.0 * x);
	elseif (x <= 5e+39)
		tmp = z + (y * 2.0);
	else
		tmp = x + (2.0 * (y + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e+71], N[(z + N[(3.0 * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+39], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(2.0 * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0000000000000001e71

   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+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+r+ 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

      13. associate-+r+ 99.8%

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

      14. count-2 99.8%

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

      15. distribute-rgt1-in 99.8%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. fma-def 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in y around 0 87.9%

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

   if -2.0000000000000001e71 < x < 5.00000000000000015e39

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.5%

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

   if 5.00000000000000015e39 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 85.3%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+71}:\\ \;\;\;\;z + 3 \cdot x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+39}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \]

Alternative 5: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+71}:\\ \;\;\;\;y + \left(z + 3 \cdot x\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.1e+71)
   (+ y (+ z (* 3.0 x)))
   (if (<= x 3.8e+39) (+ z (* y 2.0)) (+ x (* 2.0 (+ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e+71) {
		tmp = y + (z + (3.0 * x));
	} else if (x <= 3.8e+39) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (2.0 * (y + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.1d+71)) then
        tmp = y + (z + (3.0d0 * x))
    else if (x <= 3.8d+39) then
        tmp = z + (y * 2.0d0)
    else
        tmp = x + (2.0d0 * (y + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e+71) {
		tmp = y + (z + (3.0 * x));
	} else if (x <= 3.8e+39) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x + (2.0 * (y + x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.1e+71:
		tmp = y + (z + (3.0 * x))
	elif x <= 3.8e+39:
		tmp = z + (y * 2.0)
	else:
		tmp = x + (2.0 * (y + x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.1e+71)
		tmp = Float64(y + Float64(z + Float64(3.0 * x)));
	elseif (x <= 3.8e+39)
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(x + Float64(2.0 * Float64(y + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.1e+71)
		tmp = y + (z + (3.0 * x));
	elseif (x <= 3.8e+39)
		tmp = z + (y * 2.0);
	else
		tmp = x + (2.0 * (y + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.1e+71], N[(y + N[(z + N[(3.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+39], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(2.0 * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.09999999999999997e71

   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+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+r+ 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

      13. associate-+r+ 99.8%

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

      14. count-2 99.8%

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

      15. distribute-rgt1-in 99.8%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 89.6%

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

   if -1.09999999999999997e71 < x < 3.7999999999999998e39

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.5%

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

   if 3.7999999999999998e39 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 85.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+71}:\\ \;\;\;\;y + \left(z + 3 \cdot x\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(y + x\right)\\ \end{array} \]

Alternative 6: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+36}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-191}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+109}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.7e+36)
   (* 3.0 x)
   (if (<= x -5.2e-191) z (if (<= x 2.2e+109) (+ y y) (* 3.0 x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e+36) {
		tmp = 3.0 * x;
	} else if (x <= -5.2e-191) {
		tmp = z;
	} else if (x <= 2.2e+109) {
		tmp = y + y;
	} else {
		tmp = 3.0 * x;
	}
	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 <= (-3.7d+36)) then
        tmp = 3.0d0 * x
    else if (x <= (-5.2d-191)) then
        tmp = z
    else if (x <= 2.2d+109) then
        tmp = y + y
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e+36) {
		tmp = 3.0 * x;
	} else if (x <= -5.2e-191) {
		tmp = z;
	} else if (x <= 2.2e+109) {
		tmp = y + y;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.7e+36:
		tmp = 3.0 * x
	elif x <= -5.2e-191:
		tmp = z
	elif x <= 2.2e+109:
		tmp = y + y
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.7e+36)
		tmp = Float64(3.0 * x);
	elseif (x <= -5.2e-191)
		tmp = z;
	elseif (x <= 2.2e+109)
		tmp = Float64(y + y);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.7e+36)
		tmp = 3.0 * x;
	elseif (x <= -5.2e-191)
		tmp = z;
	elseif (x <= 2.2e+109)
		tmp = y + y;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.7e+36], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, -5.2e-191], z, If[LessEqual[x, 2.2e+109], N[(y + y), $MachinePrecision], N[(3.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.70000000000000029e36 or 2.1999999999999999e109 < 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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 66.5%

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

   if -3.70000000000000029e36 < x < -5.19999999999999972e-191

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 61.9%

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

   if -5.19999999999999972e-191 < x < 2.1999999999999999e109

   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+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      10. +-commutative 99.9%

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

      11. associate-+l+ 99.9%

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

      12. +-commutative 99.9%

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

      13. associate-+r+ 99.9%

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

      14. count-2 99.9%

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

      15. distribute-rgt1-in 99.9%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 53.4%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+36}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-191}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+109}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \]

Alternative 7: 80.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+72} \lor \neg \left(x \leq 7.3 \cdot 10^{+146}\right):\\ \;\;\;\;y + 3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e+72) (not (<= x 7.3e+146)))
   (+ y (* 3.0 x))
   (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+72) || !(x <= 7.3e+146)) {
		tmp = y + (3.0 * x);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8.2d+72)) .or. (.not. (x <= 7.3d+146))) then
        tmp = y + (3.0d0 * x)
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+72) || !(x <= 7.3e+146)) {
		tmp = y + (3.0 * x);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e+72) or not (x <= 7.3e+146):
		tmp = y + (3.0 * x)
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e+72) || !(x <= 7.3e+146))
		tmp = Float64(y + Float64(3.0 * x));
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.2e+72) || ~((x <= 7.3e+146)))
		tmp = y + (3.0 * x);
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e+72], N[Not[LessEqual[x, 7.3e+146]], $MachinePrecision]], N[(y + N[(3.0 * x), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.19999999999999926e72 or 7.30000000000000034e146 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.7%

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

      6. associate-+l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+r+ 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. associate-+l+ 99.7%

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

      12. +-commutative 99.7%

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

      13. associate-+r+ 99.7%

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

      14. count-2 99.7%

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

      15. distribute-rgt1-in 99.7%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. +-commutative 87.3%

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

      2. fma-def 87.5%

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

   6. Simplified 87.5%

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

   7. Taylor expanded in z around 0 74.1%

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

   if -8.19999999999999926e72 < x < 7.30000000000000034e146

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 88.6%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+72} \lor \neg \left(x \leq 7.3 \cdot 10^{+146}\right):\\ \;\;\;\;y + 3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]

Alternative 8: 84.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+71} \lor \neg \left(x \leq 4.8 \cdot 10^{+109}\right):\\ \;\;\;\;z + 3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.3e+71) (not (<= x 4.8e+109)))
   (+ z (* 3.0 x))
   (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e+71) || !(x <= 4.8e+109)) {
		tmp = z + (3.0 * x);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.3d+71)) .or. (.not. (x <= 4.8d+109))) then
        tmp = z + (3.0d0 * x)
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e+71) || !(x <= 4.8e+109)) {
		tmp = z + (3.0 * x);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.3e+71) or not (x <= 4.8e+109):
		tmp = z + (3.0 * x)
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.3e+71) || !(x <= 4.8e+109))
		tmp = Float64(z + Float64(3.0 * x));
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.3e+71) || ~((x <= 4.8e+109)))
		tmp = z + (3.0 * x);
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.3e+71], N[Not[LessEqual[x, 4.8e+109]], $MachinePrecision]], N[(z + N[(3.0 * x), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000002e71 or 4.79999999999999975e109 < 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+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+r+ 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. associate-+l+ 99.8%

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

      12. +-commutative 99.8%

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

      13. associate-+r+ 99.8%

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

      14. count-2 99.8%

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

      15. distribute-rgt1-in 99.8%

          \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

      16. fma-def 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. fma-def 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around 0 84.6%

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

   if -2.3000000000000002e71 < x < 4.79999999999999975e109

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 90.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+71} \lor \neg \left(x \leq 4.8 \cdot 10^{+109}\right):\\ \;\;\;\;z + 3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]

Alternative 9: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (z + (2.0 * (y + 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 + (z + (2.0d0 * (y + x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(z + N[(2.0 * N[(y + x), $MachinePrecision]), $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. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto x + \left(z + 2 \cdot \left(y + x\right)\right) \]

Alternative 10: 52.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+36}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+38}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.6e+36) (* 3.0 x) (if (<= x 4.6e+38) z (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e+36) {
		tmp = 3.0 * x;
	} else if (x <= 4.6e+38) {
		tmp = z;
	} else {
		tmp = 3.0 * x;
	}
	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 <= (-3.6d+36)) then
        tmp = 3.0d0 * x
    else if (x <= 4.6d+38) then
        tmp = z
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e+36) {
		tmp = 3.0 * x;
	} else if (x <= 4.6e+38) {
		tmp = z;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.6e+36:
		tmp = 3.0 * x
	elif x <= 4.6e+38:
		tmp = z
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.6e+36)
		tmp = Float64(3.0 * x);
	elseif (x <= 4.6e+38)
		tmp = z;
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.6e+36)
		tmp = 3.0 * x;
	elseif (x <= 4.6e+38)
		tmp = z;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.6e+36], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, 4.6e+38], z, N[(3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5999999999999997e36 or 4.6000000000000002e38 < 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. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 61.5%

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

   if -3.5999999999999997e36 < x < 4.6000000000000002e38

   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. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 50.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+36}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+38}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \]

Alternative 11: 8.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

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+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+r+ 99.9%

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

   9. +-commutative 99.9%

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

   10. +-commutative 99.9%

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

   11. associate-+l+ 99.9%

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

   12. +-commutative 99.9%

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

   13. associate-+r+ 99.9%

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

   14. count-2 99.9%

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

   15. distribute-rgt1-in 99.9%

       \[\leadsto y + \left(z + \left(\color{blue}{\left(2 + 1\right) \cdot x} + y\right)\right) \]

   16. fma-def 99.9%

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

   17. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 71.8%

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

   1. +-commutative 71.8%

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

   2. fma-def 71.9%

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

6. Simplified 71.9%

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

7. Taylor expanded in y around inf 8.4%

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

8. Final simplification 8.4%

   \[\leadsto y \]

Alternative 12: 34.9% 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. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around inf 34.0%

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

5. Final simplification 34.0%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023297 
(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))