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

Percentage Accurate: 99.9% → 100.0%

Time: 7.8s

Alternatives: 10

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

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

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. associate-+r+ N/A

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

   8. associate-+r+ N/A

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

   9. +-commutative N/A

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

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

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

   11. count-2 N/A

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

   12. *-commutative N/A

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

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

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

   14. count-2 N/A

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

   15. distribute-rgt1-in N/A

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

   16. *-commutative N/A

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

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

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

   18. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. fma-define N/A

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

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

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

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

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

   6. *-lowering-*.f64 100.0%

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

6. Applied egg-rr 100.0%

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

Alternative 2: 54.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+107}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-222}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-250}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-104}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+90}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.28e+107)
   (* y 2.0)
   (if (<= y -1.9e-46)
     (+ x z)
     (if (<= y -2.7e-222)
       (* x 3.0)
       (if (<= y 3.2e-250)
         (+ x z)
         (if (<= y 7.2e-104)
           (* x 3.0)
           (if (<= y 6.4e+90) (+ x z) (* y 2.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.28e+107) {
		tmp = y * 2.0;
	} else if (y <= -1.9e-46) {
		tmp = x + z;
	} else if (y <= -2.7e-222) {
		tmp = x * 3.0;
	} else if (y <= 3.2e-250) {
		tmp = x + z;
	} else if (y <= 7.2e-104) {
		tmp = x * 3.0;
	} else if (y <= 6.4e+90) {
		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 <= (-1.28d+107)) then
        tmp = y * 2.0d0
    else if (y <= (-1.9d-46)) then
        tmp = x + z
    else if (y <= (-2.7d-222)) then
        tmp = x * 3.0d0
    else if (y <= 3.2d-250) then
        tmp = x + z
    else if (y <= 7.2d-104) then
        tmp = x * 3.0d0
    else if (y <= 6.4d+90) 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 <= -1.28e+107) {
		tmp = y * 2.0;
	} else if (y <= -1.9e-46) {
		tmp = x + z;
	} else if (y <= -2.7e-222) {
		tmp = x * 3.0;
	} else if (y <= 3.2e-250) {
		tmp = x + z;
	} else if (y <= 7.2e-104) {
		tmp = x * 3.0;
	} else if (y <= 6.4e+90) {
		tmp = x + z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.28e+107:
		tmp = y * 2.0
	elif y <= -1.9e-46:
		tmp = x + z
	elif y <= -2.7e-222:
		tmp = x * 3.0
	elif y <= 3.2e-250:
		tmp = x + z
	elif y <= 7.2e-104:
		tmp = x * 3.0
	elif y <= 6.4e+90:
		tmp = x + z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.28e+107)
		tmp = Float64(y * 2.0);
	elseif (y <= -1.9e-46)
		tmp = Float64(x + z);
	elseif (y <= -2.7e-222)
		tmp = Float64(x * 3.0);
	elseif (y <= 3.2e-250)
		tmp = Float64(x + z);
	elseif (y <= 7.2e-104)
		tmp = Float64(x * 3.0);
	elseif (y <= 6.4e+90)
		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 <= -1.28e+107)
		tmp = y * 2.0;
	elseif (y <= -1.9e-46)
		tmp = x + z;
	elseif (y <= -2.7e-222)
		tmp = x * 3.0;
	elseif (y <= 3.2e-250)
		tmp = x + z;
	elseif (y <= 7.2e-104)
		tmp = x * 3.0;
	elseif (y <= 6.4e+90)
		tmp = x + z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.28e+107], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, -1.9e-46], N[(x + z), $MachinePrecision], If[LessEqual[y, -2.7e-222], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 3.2e-250], N[(x + z), $MachinePrecision], If[LessEqual[y, 7.2e-104], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 6.4e+90], N[(x + z), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2799999999999999e107 or 6.39999999999999997e90 < 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 72.9%

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

   7. Simplified 72.9%

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

   if -1.2799999999999999e107 < y < -1.8999999999999998e-46 or -2.7e-222 < y < 3.20000000000000005e-250 or 7.1999999999999996e-104 < y < 6.39999999999999997e90

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 60.6%

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

   if -1.8999999999999998e-46 < y < -2.7e-222 or 3.20000000000000005e-250 < y < 7.1999999999999996e-104

   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 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+107}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-46}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-222}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-250}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-104}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+90}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+107}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-230}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-245}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-103}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e+107)
   (* y 2.0)
   (if (<= y -2.1e-46)
     z
     (if (<= y -6.8e-230)
       (* x 3.0)
       (if (<= y 7.8e-245)
         z
         (if (<= y 3.3e-103) (* x 3.0) (if (<= y 1.6e+90) z (* y 2.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e+107) {
		tmp = y * 2.0;
	} else if (y <= -2.1e-46) {
		tmp = z;
	} else if (y <= -6.8e-230) {
		tmp = x * 3.0;
	} else if (y <= 7.8e-245) {
		tmp = z;
	} else if (y <= 3.3e-103) {
		tmp = x * 3.0;
	} else if (y <= 1.6e+90) {
		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 <= (-9.8d+107)) then
        tmp = y * 2.0d0
    else if (y <= (-2.1d-46)) then
        tmp = z
    else if (y <= (-6.8d-230)) then
        tmp = x * 3.0d0
    else if (y <= 7.8d-245) then
        tmp = z
    else if (y <= 3.3d-103) then
        tmp = x * 3.0d0
    else if (y <= 1.6d+90) 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 <= -9.8e+107) {
		tmp = y * 2.0;
	} else if (y <= -2.1e-46) {
		tmp = z;
	} else if (y <= -6.8e-230) {
		tmp = x * 3.0;
	} else if (y <= 7.8e-245) {
		tmp = z;
	} else if (y <= 3.3e-103) {
		tmp = x * 3.0;
	} else if (y <= 1.6e+90) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.8e+107:
		tmp = y * 2.0
	elif y <= -2.1e-46:
		tmp = z
	elif y <= -6.8e-230:
		tmp = x * 3.0
	elif y <= 7.8e-245:
		tmp = z
	elif y <= 3.3e-103:
		tmp = x * 3.0
	elif y <= 1.6e+90:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e+107)
		tmp = Float64(y * 2.0);
	elseif (y <= -2.1e-46)
		tmp = z;
	elseif (y <= -6.8e-230)
		tmp = Float64(x * 3.0);
	elseif (y <= 7.8e-245)
		tmp = z;
	elseif (y <= 3.3e-103)
		tmp = Float64(x * 3.0);
	elseif (y <= 1.6e+90)
		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 <= -9.8e+107)
		tmp = y * 2.0;
	elseif (y <= -2.1e-46)
		tmp = z;
	elseif (y <= -6.8e-230)
		tmp = x * 3.0;
	elseif (y <= 7.8e-245)
		tmp = z;
	elseif (y <= 3.3e-103)
		tmp = x * 3.0;
	elseif (y <= 1.6e+90)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.8e+107], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, -2.1e-46], z, If[LessEqual[y, -6.8e-230], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 7.8e-245], z, If[LessEqual[y, 3.3e-103], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 1.6e+90], z, N[(y * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.8000000000000003e107 or 1.59999999999999999e90 < 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 72.9%

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

   7. Simplified 72.9%

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

   if -9.8000000000000003e107 < y < -2.09999999999999987e-46 or -6.8e-230 < y < 7.7999999999999998e-245 or 3.2999999999999999e-103 < y < 1.59999999999999999e90

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 56.6%

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

   if -2.09999999999999987e-46 < y < -6.8e-230 or 7.7999999999999998e-245 < y < 3.2999999999999999e-103

   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 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+107}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-230}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-245}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-103}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+90}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z + x \cdot 3\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ z (* x 3.0))))
   (if (<= x -1.2e+27) t_0 (if (<= x 2.15e-10) (+ 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 <= -1.2e+27) {
		tmp = t_0;
	} else if (x <= 2.15e-10) {
		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 <= (-1.2d+27)) then
        tmp = t_0
    else if (x <= 2.15d-10) 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 <= -1.2e+27) {
		tmp = t_0;
	} else if (x <= 2.15e-10) {
		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 <= -1.2e+27:
		tmp = t_0
	elif x <= 2.15e-10:
		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 <= -1.2e+27)
		tmp = t_0;
	elseif (x <= 2.15e-10)
		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 <= -1.2e+27)
		tmp = t_0;
	elseif (x <= 2.15e-10)
		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, -1.2e+27], t$95$0, If[LessEqual[x, 2.15e-10], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999999e27 or 2.15000000000000007e-10 < x

   1. Initial program 99.8%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 83.6%

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

   7. Simplified 83.6%

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

   if -1.19999999999999999e27 < x < 2.15000000000000007e-10

   1. Initial program 100.0%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 94.1%

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

   7. Simplified 94.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+27}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+156}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.3e+28)
   (* x 3.0)
   (if (<= x 1.45e+156) (+ z (* y 2.0)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+28) {
		tmp = x * 3.0;
	} else if (x <= 1.45e+156) {
		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 <= (-2.3d+28)) then
        tmp = x * 3.0d0
    else if (x <= 1.45d+156) 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 <= -2.3e+28) {
		tmp = x * 3.0;
	} else if (x <= 1.45e+156) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.3e+28:
		tmp = x * 3.0
	elif x <= 1.45e+156:
		tmp = z + (y * 2.0)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.3e+28)
		tmp = Float64(x * 3.0);
	elseif (x <= 1.45e+156)
		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 <= -2.3e+28)
		tmp = x * 3.0;
	elseif (x <= 1.45e+156)
		tmp = z + (y * 2.0);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.3e+28], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 1.45e+156], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999984e28 or 1.45000000000000005e156 < x

   1. Initial program 99.8%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 71.2%

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

   7. Simplified 71.2%

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

   if -2.29999999999999984e28 < x < 1.45000000000000005e156

   1. Initial program 99.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

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

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

      3. *-lowering-*.f64 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+28}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+156}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+80}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+93}:\\ \;\;\;\;x + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.16e+80) (+ x z) (if (<= z 8.1e+93) (+ x (* y 2.0)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+80) {
		tmp = x + z;
	} else if (z <= 8.1e+93) {
		tmp = x + (y * 2.0);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.16d+80)) then
        tmp = x + z
    else if (z <= 8.1d+93) then
        tmp = x + (y * 2.0d0)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+80) {
		tmp = x + z;
	} else if (z <= 8.1e+93) {
		tmp = x + (y * 2.0);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.16e+80:
		tmp = x + z
	elif z <= 8.1e+93:
		tmp = x + (y * 2.0)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.16e+80)
		tmp = Float64(x + z);
	elseif (z <= 8.1e+93)
		tmp = Float64(x + Float64(y * 2.0));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.16e+80)
		tmp = x + z;
	elseif (z <= 8.1e+93)
		tmp = x + (y * 2.0);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.16e+80], N[(x + z), $MachinePrecision], If[LessEqual[z, 8.1e+93], N[(x + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15999999999999997e80 or 8.09999999999999983e93 < z

   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 72.8%

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

   if -1.15999999999999997e80 < z < 8.09999999999999983e93

   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 54.6%

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

   5. Simplified 54.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+80}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+93}:\\ \;\;\;\;x + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+70}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.3e+70) z (if (<= z 7.6e+93) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+70) {
		tmp = z;
	} else if (z <= 7.6e+93) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.3d+70)) then
        tmp = z
    else if (z <= 7.6d+93) then
        tmp = y * 2.0d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+70) {
		tmp = z;
	} else if (z <= 7.6e+93) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.3e+70:
		tmp = z
	elif z <= 7.6e+93:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.3e+70)
		tmp = z;
	elseif (z <= 7.6e+93)
		tmp = Float64(y * 2.0);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.3e+70)
		tmp = z;
	elseif (z <= 7.6e+93)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.3e+70], z, If[LessEqual[z, 7.6e+93], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.30000000000000016e70 or 7.5999999999999996e93 < z

   1. Initial program 99.9%

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

      1. associate-+l+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

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

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. associate-+r+ N/A

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

      8. associate-+r+ N/A

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

      9. +-commutative N/A

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

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

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

      11. count-2 N/A

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

      12. *-commutative N/A

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

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

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

      14. count-2 N/A

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

      15. distribute-rgt1-in N/A

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

      16. *-commutative N/A

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

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

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

      18. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 69.9%

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

   if -3.30000000000000016e70 < z < 7.5999999999999996e93

   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 48.6%

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

   7. Simplified 48.6%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+70}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

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

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. associate-+r+ N/A

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

   8. associate-+r+ N/A

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

   9. +-commutative N/A

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

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

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

   11. count-2 N/A

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

   12. *-commutative N/A

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

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

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

   14. count-2 N/A

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

   15. distribute-rgt1-in N/A

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

   16. *-commutative N/A

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

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

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

   18. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 9: 34.4% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

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

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. associate-+r+ N/A

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

   8. associate-+r+ N/A

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

   9. +-commutative N/A

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

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

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

   11. count-2 N/A

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

   12. *-commutative N/A

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

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

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

   14. count-2 N/A

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

   15. distribute-rgt1-in N/A

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

   16. *-commutative N/A

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

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

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

   18. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf

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

7. Simplified 34.1%

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

Alternative 10: 7.8% 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 39.1%

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

6. Taylor expanded in z around 0

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

8. Simplified 7.8%

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

Reproduce

herbie shell --seed 2024158 
(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))