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

Percentage Accurate: 99.9% → 100.0%

Time: 8.0s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z - N[(x * -3.0 + 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. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. remove-double-neg 99.9%

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

   4. unsub-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+r+ 99.9%

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

   9. associate-+r+ 99.9%

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

   10. distribute-neg-in 99.9%

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

   11. distribute-neg-out 99.9%

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

   12. neg-mul-1 99.9%

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

   13. count-2 99.9%

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

   14. distribute-lft-neg-in 99.9%

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

   15. metadata-eval 99.9%

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

   16. metadata-eval 99.9%

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

   17. distribute-rgt-out 99.9%

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

   18. distribute-neg-out 99.9%

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

   19. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto z - \mathsf{fma}\left(x, -3, y \cdot -2\right) \]
6. Add Preprocessing

Alternative 2: 78.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+195} \lor \neg \left(y \leq -3.1 \cdot 10^{+131}\right) \land \left(y \leq -1.25 \cdot 10^{+72} \lor \neg \left(y \leq 1.72 \cdot 10^{+145}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e+195)
         (and (not (<= y -3.1e+131))
              (or (<= y -1.25e+72) (not (<= y 1.72e+145)))))
   (* y 2.0)
   (- z (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+195) || (!(y <= -3.1e+131) && ((y <= -1.25e+72) || !(y <= 1.72e+145)))) {
		tmp = y * 2.0;
	} else {
		tmp = z - (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 ((y <= (-1.5d+195)) .or. (.not. (y <= (-3.1d+131))) .and. (y <= (-1.25d+72)) .or. (.not. (y <= 1.72d+145))) then
        tmp = y * 2.0d0
    else
        tmp = z - (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+195) || (!(y <= -3.1e+131) && ((y <= -1.25e+72) || !(y <= 1.72e+145)))) {
		tmp = y * 2.0;
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e+195) or (not (y <= -3.1e+131) and ((y <= -1.25e+72) or not (y <= 1.72e+145))):
		tmp = y * 2.0
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e+195) || (!(y <= -3.1e+131) && ((y <= -1.25e+72) || !(y <= 1.72e+145))))
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(z - Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.5e+195) || (~((y <= -3.1e+131)) && ((y <= -1.25e+72) || ~((y <= 1.72e+145)))))
		tmp = y * 2.0;
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e+195], And[N[Not[LessEqual[y, -3.1e+131]], $MachinePrecision], Or[LessEqual[y, -1.25e+72], N[Not[LessEqual[y, 1.72e+145]], $MachinePrecision]]]], N[(y * 2.0), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e195 or -3.10000000000000016e131 < y < -1.24999999999999998e72 or 1.71999999999999994e145 < 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+ 99.9%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 77.5%

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

   if -1.5e195 < y < -3.10000000000000016e131 or -1.24999999999999998e72 < y < 1.71999999999999994e145

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+r+ 99.9%

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

      9. associate-+r+ 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. distribute-neg-out 99.9%

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

      12. neg-mul-1 99.9%

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

      13. count-2 99.9%

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

      14. distribute-lft-neg-in 99.9%

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

      15. metadata-eval 99.9%

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

      16. metadata-eval 99.9%

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

      17. distribute-rgt-out 99.9%

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

      18. distribute-neg-out 99.9%

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

      19. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 86.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+195} \lor \neg \left(y \leq -3.1 \cdot 10^{+131}\right) \land \left(y \leq -1.25 \cdot 10^{+72} \lor \neg \left(y \leq 1.72 \cdot 10^{+145}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -64000000000000 \lor \neg \left(y \leq 0.0095 \lor \neg \left(y \leq 1.2 \cdot 10^{+19}\right) \land y \leq 8.8 \cdot 10^{+43}\right):\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -64000000000000.0)
         (not (or (<= y 0.0095) (and (not (<= y 1.2e+19)) (<= y 8.8e+43)))))
   (- z (* y -2.0))
   (- z (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -64000000000000.0) || !((y <= 0.0095) || (!(y <= 1.2e+19) && (y <= 8.8e+43)))) {
		tmp = z - (y * -2.0);
	} else {
		tmp = z - (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 ((y <= (-64000000000000.0d0)) .or. (.not. (y <= 0.0095d0) .or. (.not. (y <= 1.2d+19)) .and. (y <= 8.8d+43))) then
        tmp = z - (y * (-2.0d0))
    else
        tmp = z - (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -64000000000000.0) || !((y <= 0.0095) || (!(y <= 1.2e+19) && (y <= 8.8e+43)))) {
		tmp = z - (y * -2.0);
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -64000000000000.0) or not ((y <= 0.0095) or (not (y <= 1.2e+19) and (y <= 8.8e+43))):
		tmp = z - (y * -2.0)
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -64000000000000.0) || !((y <= 0.0095) || (!(y <= 1.2e+19) && (y <= 8.8e+43))))
		tmp = Float64(z - Float64(y * -2.0));
	else
		tmp = Float64(z - Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -64000000000000.0) || ~(((y <= 0.0095) || (~((y <= 1.2e+19)) && (y <= 8.8e+43)))))
		tmp = z - (y * -2.0);
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -64000000000000.0], N[Not[Or[LessEqual[y, 0.0095], And[N[Not[LessEqual[y, 1.2e+19]], $MachinePrecision], LessEqual[y, 8.8e+43]]]], $MachinePrecision]], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e13 or 0.00949999999999999976 < y < 1.2e19 or 8.80000000000000002e43 < 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+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 82.0%

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

      1. metadata-eval 82.0%

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

      2. cancel-sign-sub-inv 82.0%

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

      3. *-commutative 82.0%

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

   7. Simplified 82.0%

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

   if -6.4e13 < y < 0.00949999999999999976 or 1.2e19 < y < 8.80000000000000002e43

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.8%

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

      3. remove-double-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+r+ 99.8%

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

      9. associate-+r+ 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. distribute-neg-out 99.8%

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

      12. neg-mul-1 99.8%

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

      13. count-2 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-rgt-out 99.8%

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

      18. distribute-neg-out 99.8%

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

      19. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 96.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -64000000000000 \lor \neg \left(y \leq 0.0095 \lor \neg \left(y \leq 1.2 \cdot 10^{+19}\right) \land y \leq 8.8 \cdot 10^{+43}\right):\\ \;\;\;\;z - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.052:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-186}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-226}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+131}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.052)
   (* y 2.0)
   (if (<= y -5.1e-186)
     z
     (if (<= y -2.4e-226) (* x 3.0) (if (<= y 2.2e+131) z (* y 2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.052) {
		tmp = y * 2.0;
	} else if (y <= -5.1e-186) {
		tmp = z;
	} else if (y <= -2.4e-226) {
		tmp = x * 3.0;
	} else if (y <= 2.2e+131) {
		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 <= (-0.052d0)) then
        tmp = y * 2.0d0
    else if (y <= (-5.1d-186)) then
        tmp = z
    else if (y <= (-2.4d-226)) then
        tmp = x * 3.0d0
    else if (y <= 2.2d+131) 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 <= -0.052) {
		tmp = y * 2.0;
	} else if (y <= -5.1e-186) {
		tmp = z;
	} else if (y <= -2.4e-226) {
		tmp = x * 3.0;
	} else if (y <= 2.2e+131) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.052:
		tmp = y * 2.0
	elif y <= -5.1e-186:
		tmp = z
	elif y <= -2.4e-226:
		tmp = x * 3.0
	elif y <= 2.2e+131:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.052)
		tmp = Float64(y * 2.0);
	elseif (y <= -5.1e-186)
		tmp = z;
	elseif (y <= -2.4e-226)
		tmp = Float64(x * 3.0);
	elseif (y <= 2.2e+131)
		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 <= -0.052)
		tmp = y * 2.0;
	elseif (y <= -5.1e-186)
		tmp = z;
	elseif (y <= -2.4e-226)
		tmp = x * 3.0;
	elseif (y <= 2.2e+131)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.052], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, -5.1e-186], z, If[LessEqual[y, -2.4e-226], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 2.2e+131], z, N[(y * 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0519999999999999976 or 2.1999999999999999e131 < 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+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.5%

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

   if -0.0519999999999999976 < y < -5.1000000000000003e-186 or -2.4e-226 < y < 2.1999999999999999e131

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 53.0%

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

   if -5.1000000000000003e-186 < y < -2.4e-226

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.052:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-186}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-226}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+131}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-13}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{elif}\;z \leq 21.5:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.52e-13)
   (- z (* y -2.0))
   (if (<= z 21.5) (+ x (* 2.0 (+ x y))) (- z (* x -3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.52e-13) {
		tmp = z - (y * -2.0);
	} else if (z <= 21.5) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z - (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 (z <= (-1.52d-13)) then
        tmp = z - (y * (-2.0d0))
    else if (z <= 21.5d0) then
        tmp = x + (2.0d0 * (x + y))
    else
        tmp = z - (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.52e-13) {
		tmp = z - (y * -2.0);
	} else if (z <= 21.5) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.52e-13:
		tmp = z - (y * -2.0)
	elif z <= 21.5:
		tmp = x + (2.0 * (x + y))
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.52e-13)
		tmp = Float64(z - Float64(y * -2.0));
	elseif (z <= 21.5)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	else
		tmp = Float64(z - Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.52e-13)
		tmp = z - (y * -2.0);
	elseif (z <= 21.5)
		tmp = x + (2.0 * (x + y));
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.52e-13], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 21.5], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5200000000000001e-13

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 87.5%

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

      1. metadata-eval 87.5%

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

      2. cancel-sign-sub-inv 87.5%

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

      3. *-commutative 87.5%

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

   7. Simplified 87.5%

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

   if -1.5200000000000001e-13 < z < 21.5

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 95.8%

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

   if 21.5 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+r+ 100.0%

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

      9. associate-+r+ 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. neg-mul-1 100.0%

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

      13. count-2 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. distribute-rgt-out 100.0%

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

      18. distribute-neg-out 100.0%

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

      19. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 83.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{-13}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{elif}\;z \leq 21.5:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{elif}\;z \leq 0.29:\\ \;\;\;\;x \cdot 3 - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e-13)
   (- z (* y -2.0))
   (if (<= z 0.29) (- (* x 3.0) (* y -2.0)) (- z (* x -3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e-13) {
		tmp = z - (y * -2.0);
	} else if (z <= 0.29) {
		tmp = (x * 3.0) - (y * -2.0);
	} else {
		tmp = z - (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 (z <= (-1.55d-13)) then
        tmp = z - (y * (-2.0d0))
    else if (z <= 0.29d0) then
        tmp = (x * 3.0d0) - (y * (-2.0d0))
    else
        tmp = z - (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e-13) {
		tmp = z - (y * -2.0);
	} else if (z <= 0.29) {
		tmp = (x * 3.0) - (y * -2.0);
	} else {
		tmp = z - (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e-13:
		tmp = z - (y * -2.0)
	elif z <= 0.29:
		tmp = (x * 3.0) - (y * -2.0)
	else:
		tmp = z - (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e-13)
		tmp = Float64(z - Float64(y * -2.0));
	elseif (z <= 0.29)
		tmp = Float64(Float64(x * 3.0) - Float64(y * -2.0));
	else
		tmp = Float64(z - Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e-13)
		tmp = z - (y * -2.0);
	elseif (z <= 0.29)
		tmp = (x * 3.0) - (y * -2.0);
	else
		tmp = z - (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e-13], N[(z - N[(y * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.29], N[(N[(x * 3.0), $MachinePrecision] - N[(y * -2.0), $MachinePrecision]), $MachinePrecision], N[(z - N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e-13

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 87.5%

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

      1. metadata-eval 87.5%

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

      2. cancel-sign-sub-inv 87.5%

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

      3. *-commutative 87.5%

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

   7. Simplified 87.5%

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

   if -1.55e-13 < z < 0.28999999999999998

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. remove-double-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+r+ 99.8%

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

      9. associate-+r+ 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. distribute-neg-out 99.8%

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

      12. neg-mul-1 99.8%

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

      13. count-2 99.8%

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

      14. distribute-lft-neg-in 99.8%

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

      15. metadata-eval 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-rgt-out 99.8%

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

      18. distribute-neg-out 99.8%

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

      19. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.8%

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

   6. Taylor expanded in z around 0 95.8%

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

   if 0.28999999999999998 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. remove-double-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+r+ 100.0%

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

      9. associate-+r+ 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. distribute-neg-out 100.0%

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

      12. neg-mul-1 100.0%

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

      13. count-2 100.0%

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

      14. distribute-lft-neg-in 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. distribute-rgt-out 100.0%

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

      18. distribute-neg-out 100.0%

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

      19. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 83.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;z - y \cdot -2\\ \mathbf{elif}\;z \leq 0.29:\\ \;\;\;\;x \cdot 3 - y \cdot -2\\ \mathbf{else}:\\ \;\;\;\;z - x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+36}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 28.5:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.85e+36) z (if (<= z 28.5) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+36) {
		tmp = z;
	} else if (z <= 28.5) {
		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 <= (-1.85d+36)) then
        tmp = z
    else if (z <= 28.5d0) 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 <= -1.85e+36) {
		tmp = z;
	} else if (z <= 28.5) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.85e+36:
		tmp = z
	elif z <= 28.5:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.85e+36)
		tmp = z;
	elseif (z <= 28.5)
		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 <= -1.85e+36)
		tmp = z;
	elseif (z <= 28.5)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.85e+36], z, If[LessEqual[z, 28.5], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000014e36 or 28.5 < z

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 67.8%

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

   if -1.85000000000000014e36 < z < 28.5

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 47.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+36}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 28.5:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 9: 99.9% accurate, 1.2× speedup

Math

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

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(Float64(z + 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[(N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision] - N[(y * -2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. remove-double-neg 99.9%

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

   4. unsub-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+r+ 99.9%

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

   9. associate-+r+ 99.9%

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

   10. distribute-neg-in 99.9%

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

   11. distribute-neg-out 99.9%

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

   12. neg-mul-1 99.9%

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

   13. count-2 99.9%

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

   14. distribute-lft-neg-in 99.9%

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

   15. metadata-eval 99.9%

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

   16. metadata-eval 99.9%

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

   17. distribute-rgt-out 99.9%

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

   18. distribute-neg-out 99.9%

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

   19. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around 0 99.9%

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

6. Final simplification 99.9%

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

Alternative 10: 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+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 34.6%

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

6. Final simplification 34.6%

   \[\leadsto z \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(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))