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

Percentage Accurate: 99.9% → 100.0%

Time: 10.4s

Alternatives: 8

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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. associate-+l+ N/A

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. associate-+l+ N/A

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

   8. +-commutative N/A

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

   9. lift-+.f64 N/A

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

   10. associate-+l+ N/A

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

   11. lift-+.f64 N/A

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

   12. flip-+ N/A

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

   13. div-inv N/A

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

   14. +-commutative N/A

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

   15. lower-fma.f64 N/A

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

   16. difference-of-squares N/A

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

   17. lift-+.f64 N/A

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

   18. lower-*.f64 N/A

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

   19. lower--.f64 N/A

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

   20. lower-/.f64 N/A

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

   21. lower--.f64 N/A

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

4. Applied egg-rr 57.1%

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

5. Taylor expanded in x around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{2}}, \frac{1}{x - y}, \left(x + y\right) + \left(x + z\right)\right) \]
6. Step-by-step derivation

   1. unpow2 N/A

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

   2. lower-*.f64 50.9

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

7. Simplified 50.9%

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

8. Taylor expanded in y around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-+l+ N/A

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

   4. associate-+r+ N/A

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

   5. distribute-rgt1-in N/A

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

   6. metadata-eval N/A

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

   7. lower-fma.f64 N/A

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

   8. +-commutative N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 100.0

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

10. Simplified 100.0%

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

Alternative 2: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+83}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-196}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-296}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-116}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+115}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e+83)
   (* 3.0 x)
   (if (<= x -7.4e-196)
     (* y 2.0)
     (if (<= x -1.25e-296)
       (+ y z)
       (if (<= x 3.2e-116)
         (* y 2.0)
         (if (<= x 3.1e+115) (+ y z) (* 3.0 x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+83) {
		tmp = 3.0 * x;
	} else if (x <= -7.4e-196) {
		tmp = y * 2.0;
	} else if (x <= -1.25e-296) {
		tmp = y + z;
	} else if (x <= 3.2e-116) {
		tmp = y * 2.0;
	} else if (x <= 3.1e+115) {
		tmp = y + z;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.8d+83)) then
        tmp = 3.0d0 * x
    else if (x <= (-7.4d-196)) then
        tmp = y * 2.0d0
    else if (x <= (-1.25d-296)) then
        tmp = y + z
    else if (x <= 3.2d-116) then
        tmp = y * 2.0d0
    else if (x <= 3.1d+115) then
        tmp = y + z
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+83) {
		tmp = 3.0 * x;
	} else if (x <= -7.4e-196) {
		tmp = y * 2.0;
	} else if (x <= -1.25e-296) {
		tmp = y + z;
	} else if (x <= 3.2e-116) {
		tmp = y * 2.0;
	} else if (x <= 3.1e+115) {
		tmp = y + z;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e+83:
		tmp = 3.0 * x
	elif x <= -7.4e-196:
		tmp = y * 2.0
	elif x <= -1.25e-296:
		tmp = y + z
	elif x <= 3.2e-116:
		tmp = y * 2.0
	elif x <= 3.1e+115:
		tmp = y + z
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e+83)
		tmp = Float64(3.0 * x);
	elseif (x <= -7.4e-196)
		tmp = Float64(y * 2.0);
	elseif (x <= -1.25e-296)
		tmp = Float64(y + z);
	elseif (x <= 3.2e-116)
		tmp = Float64(y * 2.0);
	elseif (x <= 3.1e+115)
		tmp = Float64(y + z);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e+83)
		tmp = 3.0 * x;
	elseif (x <= -7.4e-196)
		tmp = y * 2.0;
	elseif (x <= -1.25e-296)
		tmp = y + z;
	elseif (x <= 3.2e-116)
		tmp = y * 2.0;
	elseif (x <= 3.1e+115)
		tmp = y + z;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e+83], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, -7.4e-196], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, -1.25e-296], N[(y + z), $MachinePrecision], If[LessEqual[x, 3.2e-116], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 3.1e+115], N[(y + z), $MachinePrecision], N[(3.0 * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.79999999999999982e83 or 3.10000000000000005e115 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.1

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

   5. Simplified 70.1%

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

   if -4.79999999999999982e83 < x < -7.4000000000000002e-196 or -1.25000000000000008e-296 < x < 3.20000000000000009e-116

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 57.6

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

   5. Simplified 57.6%

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

   if -7.4000000000000002e-196 < x < -1.25000000000000008e-296 or 3.20000000000000009e-116 < x < 3.10000000000000005e115

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+l+ N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. associate-+l+ N/A

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

      11. lift-+.f64 N/A

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

      12. flip-+ N/A

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

      13. div-inv N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. difference-of-squares N/A

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

      17. lift-+.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 N/A

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

      21. lower--.f64 N/A

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

   4. Applied egg-rr 75.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{2}}, \frac{1}{x - y}, \left(x + y\right) + \left(x + z\right)\right) \]
   6. Step-by-step derivation

      1. unpow2 N/A

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

      2. lower-*.f64 74.9

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

   7. Simplified 74.9%

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

   8. Taylor expanded in x around 0

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

      1. lower-+.f64 67.8

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

   10. Simplified 67.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+83}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-196}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-296}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-116}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+115}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{elif}\;y \leq 3.5:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e+59)
   (fma 2.0 y z)
   (if (<= y 3.5) (fma x 3.0 z) (fma 2.0 (+ x y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+59) {
		tmp = fma(2.0, y, z);
	} else if (y <= 3.5) {
		tmp = fma(x, 3.0, z);
	} else {
		tmp = fma(2.0, (x + y), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e+59)
		tmp = fma(2.0, y, z);
	elseif (y <= 3.5)
		tmp = fma(x, 3.0, z);
	else
		tmp = fma(2.0, Float64(x + y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.3e+59], N[(2.0 * y + z), $MachinePrecision], If[LessEqual[y, 3.5], N[(x * 3.0 + z), $MachinePrecision], N[(2.0 * N[(x + y), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2999999999999999e59

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 95.7

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

   5. Simplified 95.7%

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

   if -3.2999999999999999e59 < y < 3.5

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 90.7

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

   5. Simplified 90.7%

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

   if 3.5 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 84.6

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

   5. Simplified 84.6%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{elif}\;y \leq 3.5:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+60}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.1e+60)
   (fma 2.0 y z)
   (if (<= y 1.95e+163) (fma x 3.0 z) (fma 2.0 y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e+60) {
		tmp = fma(2.0, y, z);
	} else if (y <= 1.95e+163) {
		tmp = fma(x, 3.0, z);
	} else {
		tmp = fma(2.0, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.1e+60)
		tmp = fma(2.0, y, z);
	elseif (y <= 1.95e+163)
		tmp = fma(x, 3.0, z);
	else
		tmp = fma(2.0, y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.1e+60], N[(2.0 * y + z), $MachinePrecision], If[LessEqual[y, 1.95e+163], N[(x * 3.0 + z), $MachinePrecision], N[(2.0 * y + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.09999999999999996e60 or 1.95000000000000012e163 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 95.2

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

   5. Simplified 95.2%

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

   if -5.09999999999999996e60 < y < 1.95000000000000012e163

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 85.3

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

   5. Simplified 85.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 3, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e+135) (* 3.0 x) (if (<= x 2.7e+115) (fma 2.0 y z) (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e+135) {
		tmp = 3.0 * x;
	} else if (x <= 2.7e+115) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e+135)
		tmp = Float64(3.0 * x);
	elseif (x <= 2.7e+115)
		tmp = fma(2.0, y, z);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e+135], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, 2.7e+115], N[(2.0 * y + z), $MachinePrecision], N[(3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000036e135 or 2.70000000000000004e115 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 73.1

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

   5. Simplified 73.1%

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

   if -9.50000000000000036e135 < x < 2.70000000000000004e115

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 87.5

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

   5. Simplified 87.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, y, z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+135}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+26}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+37}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7e+26) (+ y z) (if (<= z 1.26e+37) (* y 2.0) (+ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e+26) {
		tmp = y + z;
	} else if (z <= 1.26e+37) {
		tmp = y * 2.0;
	} else {
		tmp = y + 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 <= (-7d+26)) then
        tmp = y + z
    else if (z <= 1.26d+37) then
        tmp = y * 2.0d0
    else
        tmp = y + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e+26) {
		tmp = y + z;
	} else if (z <= 1.26e+37) {
		tmp = y * 2.0;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7e+26:
		tmp = y + z
	elif z <= 1.26e+37:
		tmp = y * 2.0
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7e+26)
		tmp = Float64(y + z);
	elseif (z <= 1.26e+37)
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7e+26)
		tmp = y + z;
	elseif (z <= 1.26e+37)
		tmp = y * 2.0;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7e+26], N[(y + z), $MachinePrecision], If[LessEqual[z, 1.26e+37], N[(y * 2.0), $MachinePrecision], N[(y + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.9999999999999998e26 or 1.26e37 < z

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+l+ N/A

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. +-commutative N/A

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

      9. lift-+.f64 N/A

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

      10. associate-+l+ N/A

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

      11. lift-+.f64 N/A

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

      12. flip-+ N/A

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

      13. div-inv N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. difference-of-squares N/A

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

      17. lift-+.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 N/A

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

      21. lower--.f64 N/A

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

   4. Applied egg-rr 56.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{2}}, \frac{1}{x - y}, \left(x + y\right) + \left(x + z\right)\right) \]
   6. Step-by-step derivation

      1. unpow2 N/A

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

      2. lower-*.f64 63.0

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

   7. Simplified 63.0%

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

   8. Taylor expanded in x around 0

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

      1. lower-+.f64 65.5

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

   10. Simplified 65.5%

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

   if -6.9999999999999998e26 < z < 1.26e37

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 53.0

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

   5. Simplified 53.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+26}:\\ \;\;\;\;y + z\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+37}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. associate-+l+ N/A

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. associate-+l+ N/A

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

   8. +-commutative N/A

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

   9. lift-+.f64 N/A

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

   10. count-2 N/A

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

   11. +-commutative N/A

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

   12. lower-fma.f64 N/A

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

   13. lower-+.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 8: 39.2% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. associate-+l+ N/A

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. associate-+l+ N/A

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

   8. +-commutative N/A

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

   9. lift-+.f64 N/A

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

   10. associate-+l+ N/A

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

   11. lift-+.f64 N/A

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

   12. flip-+ N/A

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

   13. div-inv N/A

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

   14. +-commutative N/A

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

   15. lower-fma.f64 N/A

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

   16. difference-of-squares N/A

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

   17. lift-+.f64 N/A

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

   18. lower-*.f64 N/A

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

   19. lower--.f64 N/A

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

   20. lower-/.f64 N/A

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

   21. lower--.f64 N/A

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

4. Applied egg-rr 57.1%

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

5. Taylor expanded in x around inf

   \[\leadsto \mathsf{fma}\left(\color{blue}{{x}^{2}}, \frac{1}{x - y}, \left(x + y\right) + \left(x + z\right)\right) \]
6. Step-by-step derivation

   1. unpow2 N/A

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

   2. lower-*.f64 50.9

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

7. Simplified 50.9%

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

8. Taylor expanded in x around 0

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

   1. lower-+.f64 40.3

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

10. Simplified 40.3%

    \[\leadsto \color{blue}{y + z} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024212 
(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))