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

Percentage Accurate: 99.9% → 100.0%

Time: 8.6s

Alternatives: 11

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: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-165}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-37}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+94)
   (* y 2.0)
   (if (<= y -1.15e-134)
     z
     (if (<= y 5.5e-165) (* x 3.0) (if (<= y 3.7e-37) z (* y 2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+94) {
		tmp = y * 2.0;
	} else if (y <= -1.15e-134) {
		tmp = z;
	} else if (y <= 5.5e-165) {
		tmp = x * 3.0;
	} else if (y <= 3.7e-37) {
		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 <= (-4.2d+94)) then
        tmp = y * 2.0d0
    else if (y <= (-1.15d-134)) then
        tmp = z
    else if (y <= 5.5d-165) then
        tmp = x * 3.0d0
    else if (y <= 3.7d-37) 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 <= -4.2e+94) {
		tmp = y * 2.0;
	} else if (y <= -1.15e-134) {
		tmp = z;
	} else if (y <= 5.5e-165) {
		tmp = x * 3.0;
	} else if (y <= 3.7e-37) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+94:
		tmp = y * 2.0
	elif y <= -1.15e-134:
		tmp = z
	elif y <= 5.5e-165:
		tmp = x * 3.0
	elif y <= 3.7e-37:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+94)
		tmp = Float64(y * 2.0);
	elseif (y <= -1.15e-134)
		tmp = z;
	elseif (y <= 5.5e-165)
		tmp = Float64(x * 3.0);
	elseif (y <= 3.7e-37)
		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 <= -4.2e+94)
		tmp = y * 2.0;
	elseif (y <= -1.15e-134)
		tmp = z;
	elseif (y <= 5.5e-165)
		tmp = x * 3.0;
	elseif (y <= 3.7e-37)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+94], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, -1.15e-134], z, If[LessEqual[y, 5.5e-165], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 3.7e-37], z, N[(y * 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999979e94 or 3.7e-37 < 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 70.7%

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

   7. Simplified 70.7%

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

   if -4.19999999999999979e94 < y < -1.15e-134 or 5.49999999999999969e-165 < y < 3.7e-37

   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 60.6%

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

   if -1.15e-134 < y < 5.49999999999999969e-165

   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 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-134}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-165}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-37}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot 2 + x \cdot 3\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* y 2.0) (* x 3.0))))
   (if (<= x -9.8e+109) t_0 (if (<= x 1.45e+31) (+ z (* y 2.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y * 2.0) + (x * 3.0);
	double tmp;
	if (x <= -9.8e+109) {
		tmp = t_0;
	} else if (x <= 1.45e+31) {
		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 = (y * 2.0d0) + (x * 3.0d0)
    if (x <= (-9.8d+109)) then
        tmp = t_0
    else if (x <= 1.45d+31) 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 = (y * 2.0) + (x * 3.0);
	double tmp;
	if (x <= -9.8e+109) {
		tmp = t_0;
	} else if (x <= 1.45e+31) {
		tmp = z + (y * 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * 2.0) + (x * 3.0)
	tmp = 0
	if x <= -9.8e+109:
		tmp = t_0
	elif x <= 1.45e+31:
		tmp = z + (y * 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * 2.0) + Float64(x * 3.0))
	tmp = 0.0
	if (x <= -9.8e+109)
		tmp = t_0;
	elseif (x <= 1.45e+31)
		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 = (y * 2.0) + (x * 3.0);
	tmp = 0.0;
	if (x <= -9.8e+109)
		tmp = t_0;
	elseif (x <= 1.45e+31)
		tmp = z + (y * 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 2.0), $MachinePrecision] + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.8e+109], t$95$0, If[LessEqual[x, 1.45e+31], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.8000000000000007e109 or 1.45e31 < 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+ 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 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0

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

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

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

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

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

      3. *-lowering-*.f64 93.3%

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

   7. Simplified 93.3%

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

   if -9.8000000000000007e109 < x < 1.45e31

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 92.0%

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

   7. Simplified 92.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+109}:\\ \;\;\;\;y \cdot 2 + x \cdot 3\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+31}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2 + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + x \cdot 3\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+21}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* x 3.0))))
   (if (<= x -3.9e+91) t_0 (if (<= x 9e+21) (+ 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 <= -3.9e+91) {
		tmp = t_0;
	} else if (x <= 9e+21) {
		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 <= (-3.9d+91)) then
        tmp = t_0
    else if (x <= 9d+21) 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 <= -3.9e+91) {
		tmp = t_0;
	} else if (x <= 9e+21) {
		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 <= -3.9e+91:
		tmp = t_0
	elif x <= 9e+21:
		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 <= -3.9e+91)
		tmp = t_0;
	elseif (x <= 9e+21)
		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 <= -3.9e+91)
		tmp = t_0;
	elseif (x <= 9e+21)
		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, -3.9e+91], t$95$0, If[LessEqual[x, 9e+21], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.89999999999999968e91 or 9e21 < 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+ 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 82.6%

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

   7. Simplified 82.6%

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

   if -3.89999999999999968e91 < x < 9e21

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 92.9%

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

   7. Simplified 92.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+91}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+21}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+31}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.2e+132) (* x 3.0) (if (<= x 1.6e+31) (+ z (* y 2.0)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e+132) {
		tmp = x * 3.0;
	} else if (x <= 1.6e+31) {
		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 <= (-6.2d+132)) then
        tmp = x * 3.0d0
    else if (x <= 1.6d+31) 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 <= -6.2e+132) {
		tmp = x * 3.0;
	} else if (x <= 1.6e+31) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.2e+132:
		tmp = x * 3.0
	elif x <= 1.6e+31:
		tmp = z + (y * 2.0)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.2e+132)
		tmp = Float64(x * 3.0);
	elseif (x <= 1.6e+31)
		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 <= -6.2e+132)
		tmp = x * 3.0;
	elseif (x <= 1.6e+31)
		tmp = z + (y * 2.0);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.2e+132], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 1.6e+31], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999995e132 or 1.6e31 < 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+ 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 77.5%

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

   7. Simplified 77.5%

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

   if -6.1999999999999995e132 < x < 1.6e31

   1. Initial program 99.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+31}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 2\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 10^{-18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 2.0))))
   (if (<= y -4.8e+100) t_0 (if (<= y 1e-18) (+ x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 2.0);
	double tmp;
	if (y <= -4.8e+100) {
		tmp = t_0;
	} else if (y <= 1e-18) {
		tmp = x + z;
	} 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 = x + (y * 2.0d0)
    if (y <= (-4.8d+100)) then
        tmp = t_0
    else if (y <= 1d-18) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 2.0);
	double tmp;
	if (y <= -4.8e+100) {
		tmp = t_0;
	} else if (y <= 1e-18) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 2.0)
	tmp = 0
	if y <= -4.8e+100:
		tmp = t_0
	elif y <= 1e-18:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 2.0))
	tmp = 0.0
	if (y <= -4.8e+100)
		tmp = t_0;
	elseif (y <= 1e-18)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 2.0);
	tmp = 0.0;
	if (y <= -4.8e+100)
		tmp = t_0;
	elseif (y <= 1e-18)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+100], t$95$0, If[LessEqual[y, 1e-18], N[(x + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000023e100 or 1.0000000000000001e-18 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 75.0%

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

   5. Simplified 75.0%

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

   if -4.80000000000000023e100 < y < 1.0000000000000001e-18

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 56.1%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;x + y \cdot 2\\ \mathbf{elif}\;y \leq 10^{-18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+100}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-20}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+100) (* y 2.0) (if (<= y 2.35e-20) (+ x z) (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+100) {
		tmp = y * 2.0;
	} else if (y <= 2.35e-20) {
		tmp = x + z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.2d+100)) then
        tmp = y * 2.0d0
    else if (y <= 2.35d-20) then
        tmp = x + z
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+100) {
		tmp = y * 2.0;
	} else if (y <= 2.35e-20) {
		tmp = x + z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+100:
		tmp = y * 2.0
	elif y <= 2.35e-20:
		tmp = x + z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+100)
		tmp = Float64(y * 2.0);
	elseif (y <= 2.35e-20)
		tmp = Float64(x + z);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e+100)
		tmp = y * 2.0;
	elseif (y <= 2.35e-20)
		tmp = x + z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+100], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 2.35e-20], N[(x + z), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999997e100 or 2.35000000000000007e-20 < 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 72.8%

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

   7. Simplified 72.8%

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

   if -4.1999999999999997e100 < y < 2.35000000000000007e-20

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 56.1%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+100}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-20}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-37}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e+94) (* y 2.0) (if (<= y 4.2e-37) z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+94) {
		tmp = y * 2.0;
	} else if (y <= 4.2e-37) {
		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 <= (-2.5d+94)) then
        tmp = y * 2.0d0
    else if (y <= 4.2d-37) 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 <= -2.5e+94) {
		tmp = y * 2.0;
	} else if (y <= 4.2e-37) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e+94:
		tmp = y * 2.0
	elif y <= 4.2e-37:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e+94)
		tmp = Float64(y * 2.0);
	elseif (y <= 4.2e-37)
		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 <= -2.5e+94)
		tmp = y * 2.0;
	elseif (y <= 4.2e-37)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e+94], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 4.2e-37], z, N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000005e94 or 4.2000000000000002e-37 < 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 70.7%

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

   7. Simplified 70.7%

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

   if -2.50000000000000005e94 < y < 4.2000000000000002e-37

   1. Initial program 99.8%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 50.9%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-37}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

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

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. associate-+r+ N/A

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

   8. associate-+r+ N/A

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

   9. +-commutative N/A

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

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

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

   11. count-2 N/A

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

   12. *-commutative N/A

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

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

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

   14. count-2 N/A

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

   15. distribute-rgt1-in N/A

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

   16. *-commutative N/A

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

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

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

   18. metadata-eval 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. Add Preprocessing

Alternative 10: 34.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 3.5e+122) z x))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.5e+122) {
		tmp = z;
	} else {
		tmp = 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 <= 3.5d+122) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.5e+122) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 3.5e+122:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.5e+122)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.5e+122)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.5e+122], z, x]

Derivation

1. Split input into 2 regimes

2. if x < 3.50000000000000014e122

   1. Initial program 99.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 38.7%

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

   if 3.50000000000000014e122 < x

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   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 16.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 16.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 7.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around inf

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

5. Simplified 38.4%

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

6. Taylor expanded in z around 0

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

8. Simplified 7.5%

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

Reproduce

herbie shell --seed 2024152 
(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))