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

Percentage Accurate: 99.9% → 100.0%

Time: 8.1s

Alternatives: 11

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

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. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+r+ 99.9%

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

   8. *-lft-identity 99.9%

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

   9. metadata-eval 99.9%

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

   10. count-2 99.9%

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

   11. distribute-rgt-out 99.9%

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

   12. fma-define 99.9%

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

   13. metadata-eval 99.9%

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

   14. metadata-eval 99.9%

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

   15. count-2 99.9%

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

   16. *-commutative 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+86}:\\ \;\;\;\;\left(z + x\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 + x \cdot \frac{3}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+86)
   (+ (+ z x) (* x 2.0))
   (if (<= z 3.9e-14) (+ x (* 2.0 (+ x y))) (* z (+ 1.0 (* x (/ 3.0 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+86) {
		tmp = (z + x) + (x * 2.0);
	} else if (z <= 3.9e-14) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z * (1.0 + (x * (3.0 / 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 <= (-2.5d+86)) then
        tmp = (z + x) + (x * 2.0d0)
    else if (z <= 3.9d-14) then
        tmp = x + (2.0d0 * (x + y))
    else
        tmp = z * (1.0d0 + (x * (3.0d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+86) {
		tmp = (z + x) + (x * 2.0);
	} else if (z <= 3.9e-14) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z * (1.0 + (x * (3.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+86:
		tmp = (z + x) + (x * 2.0)
	elif z <= 3.9e-14:
		tmp = x + (2.0 * (x + y))
	else:
		tmp = z * (1.0 + (x * (3.0 / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+86)
		tmp = Float64(Float64(z + x) + Float64(x * 2.0));
	elseif (z <= 3.9e-14)
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	else
		tmp = Float64(z * Float64(1.0 + Float64(x * Float64(3.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e+86)
		tmp = (z + x) + (x * 2.0);
	elseif (z <= 3.9e-14)
		tmp = x + (2.0 * (x + y));
	else
		tmp = z * (1.0 + (x * (3.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+86], N[(N[(z + x), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-14], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 + N[(x * N[(3.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e86

   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 89.7%

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

   if -2.4999999999999999e86 < z < 3.8999999999999998e-14

   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 0 92.1%

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

   if 3.8999999999999998e-14 < 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+ 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 x around inf 87.1%

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

   6. Taylor expanded in z around -inf 87.1%

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

   7. Taylor expanded in z around inf 87.1%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(2 \cdot \frac{x}{z} + \frac{x}{z}\right)\right)} \]
   8. Step-by-step derivation

      1. distribute-lft1-in 87.1%

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

      2. metadata-eval 87.1%

         \[\leadsto z \cdot \left(1 + \color{blue}{3} \cdot \frac{x}{z}\right) \]

      3. associate-*r/ 87.1%

         \[\leadsto z \cdot \left(1 + \color{blue}{\frac{3 \cdot x}{z}}\right) \]

      4. *-commutative 87.1%

         \[\leadsto z \cdot \left(1 + \frac{\color{blue}{x \cdot 3}}{z}\right) \]

      5. associate-*r/ 87.2%

         \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{3}{z}}\right) \]

   9. Simplified 87.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + x \cdot \frac{3}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+86}:\\ \;\;\;\;\left(z + x\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-14}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 + x \cdot \frac{3}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6500:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-66}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+44}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6500.0)
   (* x 3.0)
   (if (<= x 1.02e-66) z (if (<= x 5.2e+44) (* y 2.0) (* x 3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6500.0) {
		tmp = x * 3.0;
	} else if (x <= 1.02e-66) {
		tmp = z;
	} else if (x <= 5.2e+44) {
		tmp = y * 2.0;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6500.0d0)) then
        tmp = x * 3.0d0
    else if (x <= 1.02d-66) then
        tmp = z
    else if (x <= 5.2d+44) then
        tmp = y * 2.0d0
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6500.0) {
		tmp = x * 3.0;
	} else if (x <= 1.02e-66) {
		tmp = z;
	} else if (x <= 5.2e+44) {
		tmp = y * 2.0;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6500.0:
		tmp = x * 3.0
	elif x <= 1.02e-66:
		tmp = z
	elif x <= 5.2e+44:
		tmp = y * 2.0
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6500.0)
		tmp = Float64(x * 3.0);
	elseif (x <= 1.02e-66)
		tmp = z;
	elseif (x <= 5.2e+44)
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6500.0)
		tmp = x * 3.0;
	elseif (x <= 1.02e-66)
		tmp = z;
	elseif (x <= 5.2e+44)
		tmp = y * 2.0;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6500.0], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 1.02e-66], z, If[LessEqual[x, 5.2e+44], N[(y * 2.0), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6500 or 5.1999999999999998e44 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. *-lft-identity 99.8%

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

      9. metadata-eval 99.8%

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

      10. count-2 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

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

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 85.1%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. *-commutative 70.2%

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

   8. Simplified 70.2%

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

   if -6500 < x < 1.01999999999999996e-66

   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. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. count-2 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

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

      14. metadata-eval 100.0%

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

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 52.2%

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

   if 1.01999999999999996e-66 < x < 5.1999999999999998e44

   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 100.0%

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

   6. Taylor expanded in z around 0 77.6%

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

   7. Taylor expanded in x around 0 68.1%

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

   8. Taylor expanded in y around inf 66.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6500:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-66}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+44}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+88}:\\ \;\;\;\;\left(z + x\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-22}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.4e+88)
   (+ (+ z x) (* x 2.0))
   (if (<= z 3e-22) (+ x (* 2.0 (+ x y))) (+ z (* x 3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e+88) {
		tmp = (z + x) + (x * 2.0);
	} else if (z <= 3e-22) {
		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 <= (-4.4d+88)) then
        tmp = (z + x) + (x * 2.0d0)
    else if (z <= 3d-22) 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 <= -4.4e+88) {
		tmp = (z + x) + (x * 2.0);
	} else if (z <= 3e-22) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z + (x * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.4e+88:
		tmp = (z + x) + (x * 2.0)
	elif z <= 3e-22:
		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 <= -4.4e+88)
		tmp = Float64(Float64(z + x) + Float64(x * 2.0));
	elseif (z <= 3e-22)
		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 <= -4.4e+88)
		tmp = (z + x) + (x * 2.0);
	elseif (z <= 3e-22)
		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, -4.4e+88], N[(N[(z + x), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-22], 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 < -4.40000000000000017e88

   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 89.7%

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

   if -4.40000000000000017e88 < z < 2.9999999999999999e-22

   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 0 92.0%

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

   if 2.9999999999999999e-22 < 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. +-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. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. *-lft-identity 99.8%

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

      9. metadata-eval 99.8%

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

      10. count-2 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

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

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 87.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+88}:\\ \;\;\;\;\left(z + x\right) + x \cdot 2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-22}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+85}:\\ \;\;\;\;z + \frac{x}{0.3333333333333333}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+85)
   (+ z (/ x 0.3333333333333333))
   (if (<= z 3.4e-22) (+ x (* 2.0 (+ x y))) (+ z (* x 3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+85) {
		tmp = z + (x / 0.3333333333333333);
	} else if (z <= 3.4e-22) {
		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 <= (-2d+85)) then
        tmp = z + (x / 0.3333333333333333d0)
    else if (z <= 3.4d-22) 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 <= -2e+85) {
		tmp = z + (x / 0.3333333333333333);
	} else if (z <= 3.4e-22) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z + (x * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+85:
		tmp = z + (x / 0.3333333333333333)
	elif z <= 3.4e-22:
		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 <= -2e+85)
		tmp = Float64(z + Float64(x / 0.3333333333333333));
	elseif (z <= 3.4e-22)
		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 <= -2e+85)
		tmp = z + (x / 0.3333333333333333);
	elseif (z <= 3.4e-22)
		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, -2e+85], N[(z + N[(x / 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-22], 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 < -2e85

   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. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. *-lft-identity 99.9%

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

      9. metadata-eval 99.9%

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

      10. count-2 99.9%

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

      11. distribute-rgt-out 99.9%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

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

      14. metadata-eval 100.0%

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

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 inf 79.8%

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

   6. Taylor expanded in x around inf 69.6%

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

      1. associate-*r/ 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/l* 69.7%

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

   8. Simplified 69.7%

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

      1. associate-*r* 77.4%

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

      2. clear-num 77.4%

         \[\leadsto z + \left(y \cdot x\right) \cdot \color{blue}{\frac{1}{\frac{y}{3}}} \]

      3. un-div-inv 77.4%

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

      4. div-inv 77.3%

         \[\leadsto z + \frac{y \cdot x}{\color{blue}{y \cdot \frac{1}{3}}} \]

      5. metadata-eval 77.3%

         \[\leadsto z + \frac{y \cdot x}{y \cdot \color{blue}{0.3333333333333333}} \]

   10. Applied egg-rr 77.3%

       \[\leadsto z + \color{blue}{\frac{y \cdot x}{y \cdot 0.3333333333333333}} \]
   11. Step-by-step derivation

       1. times-frac 89.7%

          \[\leadsto z + \color{blue}{\frac{y}{y} \cdot \frac{x}{0.3333333333333333}} \]

       2. *-inverses 89.7%

          \[\leadsto z + \color{blue}{1} \cdot \frac{x}{0.3333333333333333} \]

       3. associate-*r/ 89.7%

          \[\leadsto z + \color{blue}{\frac{1 \cdot x}{0.3333333333333333}} \]

       4. *-lft-identity 89.7%

          \[\leadsto z + \frac{\color{blue}{x}}{0.3333333333333333} \]

   12. Simplified 89.7%

       \[\leadsto z + \color{blue}{\frac{x}{0.3333333333333333}} \]

   if -2e85 < z < 3.3999999999999998e-22

   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 0 92.0%

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

   if 3.3999999999999998e-22 < 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. +-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. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. *-lft-identity 99.8%

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

      9. metadata-eval 99.8%

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

      10. count-2 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

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

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 87.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+85}:\\ \;\;\;\;z + \frac{x}{0.3333333333333333}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+39} \lor \neg \left(x \leq 2.05 \cdot 10^{+45}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e+39) (not (<= x 2.05e+45)))
   (+ z (* x 3.0))
   (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e+39) || !(x <= 2.05e+45)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.7d+39)) .or. (.not. (x <= 2.05d+45))) then
        tmp = z + (x * 3.0d0)
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e+39) || !(x <= 2.05e+45)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e+39) or not (x <= 2.05e+45):
		tmp = z + (x * 3.0)
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e+39) || !(x <= 2.05e+45))
		tmp = Float64(z + Float64(x * 3.0));
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.7e+39) || ~((x <= 2.05e+45)))
		tmp = z + (x * 3.0);
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e+39], N[Not[LessEqual[x, 2.05e+45]], $MachinePrecision]], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.70000000000000003e39 or 2.05000000000000006e45 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. associate-+r+ 99.7%

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

      7. associate-+r+ 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. count-2 99.7%

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

      11. distribute-rgt-out 99.7%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

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

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.4%

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

   if -2.70000000000000003e39 < x < 2.05000000000000006e45

   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. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. count-2 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

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

      14. metadata-eval 100.0%

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

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 90.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+39} \lor \neg \left(x \leq 2.05 \cdot 10^{+45}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+111} \lor \neg \left(x \leq 2 \cdot 10^{+151}\right):\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.15e+111) (not (<= x 2e+151))) (* x 3.0) (+ z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.15e+111) || !(x <= 2e+151)) {
		tmp = x * 3.0;
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.15d+111)) .or. (.not. (x <= 2d+151))) then
        tmp = x * 3.0d0
    else
        tmp = z + (y * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.15e+111) || !(x <= 2e+151)) {
		tmp = x * 3.0;
	} else {
		tmp = z + (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.15e+111) or not (x <= 2e+151):
		tmp = x * 3.0
	else:
		tmp = z + (y * 2.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.15e+111) || !(x <= 2e+151))
		tmp = Float64(x * 3.0);
	else
		tmp = Float64(z + Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.15e+111) || ~((x <= 2e+151)))
		tmp = x * 3.0;
	else
		tmp = z + (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.15e+111], N[Not[LessEqual[x, 2e+151]], $MachinePrecision]], N[(x * 3.0), $MachinePrecision], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999997e111 or 2.00000000000000003e151 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. associate-+r+ 99.7%

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

      7. associate-+r+ 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. count-2 99.7%

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

      11. distribute-rgt-out 99.7%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

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

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 93.1%

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

   6. Taylor expanded in z around 0 85.3%

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

      1. *-commutative 85.3%

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

   8. Simplified 85.3%

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

   if -2.14999999999999997e111 < x < 2.00000000000000003e151

   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. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. count-2 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

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

      14. metadata-eval 100.0%

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

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 84.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+111} \lor \neg \left(x \leq 2 \cdot 10^{+151}\right):\\ \;\;\;\;x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;z + \frac{x}{0.3333333333333333}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+46}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+38)
   (+ z (/ x 0.3333333333333333))
   (if (<= x 2e+46) (+ z (* y 2.0)) (+ z (* x 3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+38) {
		tmp = z + (x / 0.3333333333333333);
	} else if (x <= 2e+46) {
		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 (x <= (-1.3d+38)) then
        tmp = z + (x / 0.3333333333333333d0)
    else if (x <= 2d+46) 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 (x <= -1.3e+38) {
		tmp = z + (x / 0.3333333333333333);
	} else if (x <= 2e+46) {
		tmp = z + (y * 2.0);
	} else {
		tmp = z + (x * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+38:
		tmp = z + (x / 0.3333333333333333)
	elif x <= 2e+46:
		tmp = z + (y * 2.0)
	else:
		tmp = z + (x * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+38)
		tmp = Float64(z + Float64(x / 0.3333333333333333));
	elseif (x <= 2e+46)
		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 (x <= -1.3e+38)
		tmp = z + (x / 0.3333333333333333);
	elseif (x <= 2e+46)
		tmp = z + (y * 2.0);
	else
		tmp = z + (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+38], N[(z + N[(x / 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+46], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e38

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. associate-+r+ 99.7%

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

      7. associate-+r+ 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. count-2 99.7%

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

      11. distribute-rgt-out 99.7%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

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

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   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 inf 67.3%

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

   6. Taylor expanded in x around inf 51.8%

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

      1. associate-*r/ 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-/l* 51.8%

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

   8. Simplified 51.8%

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

      1. associate-*r* 60.2%

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

      2. clear-num 60.2%

         \[\leadsto z + \left(y \cdot x\right) \cdot \color{blue}{\frac{1}{\frac{y}{3}}} \]

      3. un-div-inv 60.3%

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

      4. div-inv 60.3%

         \[\leadsto z + \frac{y \cdot x}{\color{blue}{y \cdot \frac{1}{3}}} \]

      5. metadata-eval 60.3%

         \[\leadsto z + \frac{y \cdot x}{y \cdot \color{blue}{0.3333333333333333}} \]

   10. Applied egg-rr 60.3%

       \[\leadsto z + \color{blue}{\frac{y \cdot x}{y \cdot 0.3333333333333333}} \]
   11. Step-by-step derivation

       1. times-frac 84.1%

          \[\leadsto z + \color{blue}{\frac{y}{y} \cdot \frac{x}{0.3333333333333333}} \]

       2. *-inverses 84.1%

          \[\leadsto z + \color{blue}{1} \cdot \frac{x}{0.3333333333333333} \]

       3. associate-*r/ 84.1%

          \[\leadsto z + \color{blue}{\frac{1 \cdot x}{0.3333333333333333}} \]

       4. *-lft-identity 84.1%

          \[\leadsto z + \frac{\color{blue}{x}}{0.3333333333333333} \]

   12. Simplified 84.1%

       \[\leadsto z + \color{blue}{\frac{x}{0.3333333333333333}} \]

   if -1.3e38 < x < 2e46

   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. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. *-lft-identity 100.0%

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

      9. metadata-eval 100.0%

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

      10. count-2 100.0%

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

      11. distribute-rgt-out 100.0%

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

      12. fma-define 100.0%

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

      13. metadata-eval 100.0%

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

      14. metadata-eval 100.0%

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

      15. count-2 100.0%

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

      16. *-commutative 100.0%

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

   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 90.9%

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

   if 2e46 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. *-lft-identity 99.8%

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

      9. metadata-eval 99.8%

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

      10. count-2 99.8%

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

      11. distribute-rgt-out 99.8%

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

      12. fma-define 99.8%

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

      13. metadata-eval 99.8%

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

      14. metadata-eval 99.8%

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

      15. count-2 99.8%

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

      16. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+38}:\\ \;\;\;\;z + \frac{x}{0.3333333333333333}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+46}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+39}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-10}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e+39) z (if (<= z 1.26e-10) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+39) {
		tmp = z;
	} else if (z <= 1.26e-10) {
		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 <= (-9.5d+39)) then
        tmp = z
    else if (z <= 1.26d-10) 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 <= -9.5e+39) {
		tmp = z;
	} else if (z <= 1.26e-10) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e+39:
		tmp = z
	elif z <= 1.26e-10:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e+39)
		tmp = z;
	elseif (z <= 1.26e-10)
		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 <= -9.5e+39)
		tmp = z;
	elseif (z <= 1.26e-10)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e+39], z, If[LessEqual[z, 1.26e-10], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000011e39 or 1.26000000000000004e-10 < 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. +-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. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. *-lft-identity 99.9%

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

      9. metadata-eval 99.9%

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

      10. count-2 99.9%

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

      11. distribute-rgt-out 99.9%

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

      12. fma-define 99.9%

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

      13. metadata-eval 99.9%

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

      14. metadata-eval 99.9%

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

      15. count-2 99.9%

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

      16. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.4%

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

   if -9.50000000000000011e39 < z < 1.26000000000000004e-10

   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 76.5%

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

   6. Taylor expanded in z around 0 93.7%

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

   7. Taylor expanded in x around 0 55.3%

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

   8. Taylor expanded in y around inf 48.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+39}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-10}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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 11: 34.3% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+r+ 99.9%

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

   8. *-lft-identity 99.9%

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

   9. metadata-eval 99.9%

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

   10. count-2 99.9%

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

   11. distribute-rgt-out 99.9%

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

   12. fma-define 99.9%

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

   13. metadata-eval 99.9%

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

   14. metadata-eval 99.9%

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

   15. count-2 99.9%

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

   16. *-commutative 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 33.5%

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

Reproduce

herbie shell --seed 2024180 
(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))