Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C

Percentage Accurate: 99.9% → 100.0%

Time: 5.6s

Alternatives: 9

Speedup: 1.1×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, 5, x \cdot \left(y + z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma z 5.0 (* x (+ y z))))

C

double code(double x, double y, double z) {
	return fma(z, 5.0, (x * (y + z)));
}

Julia

function code(x, y, z)
	return fma(z, 5.0, Float64(x * Float64(y + z)))
end

Wolfram

code[x_, y_, z_] := N[(z * 5.0 + N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{z \cdot 5 + x \cdot \left(y + z\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{z \cdot 5} + x \cdot \left(y + z\right) \]

   4. lower-fma.f64 100.0

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 100.0

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+48}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-13}:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+228}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e+176)
   (* x y)
   (if (<= x -4.3e+48)
     (* x z)
     (if (<= x -1.55e-18)
       (* x y)
       (if (<= x 3.3e-13)
         (* 5.0 z)
         (if (<= x 1.08e+38)
           (* x y)
           (if (<= x 7.5e+158)
             (* x z)
             (if (<= x 1.3e+228) (* x y) (* x z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+176) {
		tmp = x * y;
	} else if (x <= -4.3e+48) {
		tmp = x * z;
	} else if (x <= -1.55e-18) {
		tmp = x * y;
	} else if (x <= 3.3e-13) {
		tmp = 5.0 * z;
	} else if (x <= 1.08e+38) {
		tmp = x * y;
	} else if (x <= 7.5e+158) {
		tmp = x * z;
	} else if (x <= 1.3e+228) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.8d+176)) then
        tmp = x * y
    else if (x <= (-4.3d+48)) then
        tmp = x * z
    else if (x <= (-1.55d-18)) then
        tmp = x * y
    else if (x <= 3.3d-13) then
        tmp = 5.0d0 * z
    else if (x <= 1.08d+38) then
        tmp = x * y
    else if (x <= 7.5d+158) then
        tmp = x * z
    else if (x <= 1.3d+228) then
        tmp = x * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+176) {
		tmp = x * y;
	} else if (x <= -4.3e+48) {
		tmp = x * z;
	} else if (x <= -1.55e-18) {
		tmp = x * y;
	} else if (x <= 3.3e-13) {
		tmp = 5.0 * z;
	} else if (x <= 1.08e+38) {
		tmp = x * y;
	} else if (x <= 7.5e+158) {
		tmp = x * z;
	} else if (x <= 1.3e+228) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e+176:
		tmp = x * y
	elif x <= -4.3e+48:
		tmp = x * z
	elif x <= -1.55e-18:
		tmp = x * y
	elif x <= 3.3e-13:
		tmp = 5.0 * z
	elif x <= 1.08e+38:
		tmp = x * y
	elif x <= 7.5e+158:
		tmp = x * z
	elif x <= 1.3e+228:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e+176)
		tmp = Float64(x * y);
	elseif (x <= -4.3e+48)
		tmp = Float64(x * z);
	elseif (x <= -1.55e-18)
		tmp = Float64(x * y);
	elseif (x <= 3.3e-13)
		tmp = Float64(5.0 * z);
	elseif (x <= 1.08e+38)
		tmp = Float64(x * y);
	elseif (x <= 7.5e+158)
		tmp = Float64(x * z);
	elseif (x <= 1.3e+228)
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e+176)
		tmp = x * y;
	elseif (x <= -4.3e+48)
		tmp = x * z;
	elseif (x <= -1.55e-18)
		tmp = x * y;
	elseif (x <= 3.3e-13)
		tmp = 5.0 * z;
	elseif (x <= 1.08e+38)
		tmp = x * y;
	elseif (x <= 7.5e+158)
		tmp = x * z;
	elseif (x <= 1.3e+228)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e+176], N[(x * y), $MachinePrecision], If[LessEqual[x, -4.3e+48], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.55e-18], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.3e-13], N[(5.0 * z), $MachinePrecision], If[LessEqual[x, 1.08e+38], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.5e+158], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.3e+228], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8000000000000003e176 or -4.29999999999999978e48 < x < -1.55000000000000003e-18 or 3.3000000000000001e-13 < x < 1.07999999999999995e38 or 7.5000000000000004e158 < x < 1.30000000000000004e228

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 77.2

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

   5. Applied rewrites 77.2%

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

   if -4.8000000000000003e176 < x < -4.29999999999999978e48 or 1.07999999999999995e38 < x < 7.5000000000000004e158 or 1.30000000000000004e228 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 69.9%

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

   if -1.55000000000000003e-18 < x < 3.3000000000000001e-13

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 77.3

         \[\leadsto \color{blue}{5 \cdot z} \]

   5. Applied rewrites 77.3%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+48}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-13}:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+38}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+228}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 0.00215:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+28)
   (* x (+ y z))
   (if (<= x 0.00215) (fma z 5.0 (* x y)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+28) {
		tmp = x * (y + z);
	} else if (x <= 0.00215) {
		tmp = fma(z, 5.0, (x * y));
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+28)
		tmp = Float64(x * Float64(y + z));
	elseif (x <= 0.00215)
		tmp = fma(z, 5.0, Float64(x * y));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+28], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00215], N[(z * 5.0 + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.04999999999999995e28

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -1.04999999999999995e28 < x < 0.00215

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. lift-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right)} + z \cdot 5 \]

      3. lift-+.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(y + z\right)} + z \cdot 5 \]

      4. distribute-rgt-in N/A

         \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

      6. +-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot x + z \cdot 5\right) + y \cdot x} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(z \cdot x + \color{blue}{z \cdot 5}\right) + y \cdot x \]

      8. distribute-lft-out N/A

         \[\leadsto \color{blue}{z \cdot \left(x + 5\right)} + y \cdot x \]

      9. lower-fma.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{5}, y \cdot x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 99.1%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{5}, y \cdot x\right) \]

   if 0.00215 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.9

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

   5. Applied rewrites 98.9%

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

   7. Applied rewrites 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 0.00215:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e-18)
   (* x (+ y z))
   (if (<= x 1.7e-7) (fma z 5.0 (* x z)) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e-18) {
		tmp = x * (y + z);
	} else if (x <= 1.7e-7) {
		tmp = fma(z, 5.0, (x * z));
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e-18)
		tmp = Float64(x * Float64(y + z));
	elseif (x <= 1.7e-7)
		tmp = fma(z, 5.0, Float64(x * z));
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e-18], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-7], N[(z * 5.0 + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000003e-18

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -1.55000000000000003e-18 < x < 1.69999999999999987e-7

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(y + z\right) + z \cdot 5} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{z \cdot 5 + x \cdot \left(y + z\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot 5} + x \cdot \left(y + z\right) \]

      4. lower-fma.f64 100.0

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 100.0

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{x \cdot z}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{z \cdot x}\right) \]

      2. lower-*.f64 77.6

         \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{z \cdot x}\right) \]

   7. Applied rewrites 77.6%

      \[\leadsto \mathsf{fma}\left(z, 5, \color{blue}{z \cdot x}\right) \]

   if 1.69999999999999987e-7 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.9

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

   5. Applied rewrites 98.9%

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

   7. Applied rewrites 98.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.55e-18)
   (* x (+ y z))
   (if (<= x 1.7e-7) (* (- x -5.0) z) (fma z x (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.55e-18) {
		tmp = x * (y + z);
	} else if (x <= 1.7e-7) {
		tmp = (x - -5.0) * z;
	} else {
		tmp = fma(z, x, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.55e-18)
		tmp = Float64(x * Float64(y + z));
	elseif (x <= 1.7e-7)
		tmp = Float64(Float64(x - -5.0) * z);
	else
		tmp = fma(z, x, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.55e-18], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-7], N[(N[(x - -5.0), $MachinePrecision] * z), $MachinePrecision], N[(z * x + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000003e-18

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -1.55000000000000003e-18 < x < 1.69999999999999987e-7

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + 5\right)} \cdot z \]

      4. metadata-eval N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(-5\right)\right)}\right) \cdot z \]

      5. sub-neg N/A

         \[\leadsto \color{blue}{\left(x - -5\right)} \cdot z \]

      6. lower--.f64 77.5

         \[\leadsto \color{blue}{\left(x - -5\right)} \cdot z \]

   5. Applied rewrites 77.5%

      \[\leadsto \color{blue}{\left(x - -5\right) \cdot z} \]

   if 1.69999999999999987e-7 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.9

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

   5. Applied rewrites 98.9%

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

   7. Applied rewrites 98.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1.55e-18) t_0 (if (<= x 1.7e-7) (* (- x -5.0) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.55e-18) {
		tmp = t_0;
	} else if (x <= 1.7e-7) {
		tmp = (x - -5.0) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-1.55d-18)) then
        tmp = t_0
    else if (x <= 1.7d-7) then
        tmp = (x - (-5.0d0)) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.55e-18) {
		tmp = t_0;
	} else if (x <= 1.7e-7) {
		tmp = (x - -5.0) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -1.55e-18:
		tmp = t_0
	elif x <= 1.7e-7:
		tmp = (x - -5.0) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1.55e-18)
		tmp = t_0;
	elseif (x <= 1.7e-7)
		tmp = Float64(Float64(x - -5.0) * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -1.55e-18)
		tmp = t_0;
	elseif (x <= 1.7e-7)
		tmp = (x - -5.0) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e-18], t$95$0, If[LessEqual[x, 1.7e-7], N[(N[(x - -5.0), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000003e-18 or 1.69999999999999987e-7 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -1.55000000000000003e-18 < x < 1.69999999999999987e-7

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(5 + x\right) \cdot z} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(x + 5\right)} \cdot z \]

      4. metadata-eval N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(-5\right)\right)}\right) \cdot z \]

      5. sub-neg N/A

         \[\leadsto \color{blue}{\left(x - -5\right)} \cdot z \]

      6. lower--.f64 77.5

         \[\leadsto \color{blue}{\left(x - -5\right)} \cdot z \]

   5. Applied rewrites 77.5%

      \[\leadsto \color{blue}{\left(x - -5\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\left(x - -5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-13}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -1.55e-18) t_0 (if (<= x 3.3e-13) (* 5.0 z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.55e-18) {
		tmp = t_0;
	} else if (x <= 3.3e-13) {
		tmp = 5.0 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-1.55d-18)) then
        tmp = t_0
    else if (x <= 3.3d-13) then
        tmp = 5.0d0 * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -1.55e-18) {
		tmp = t_0;
	} else if (x <= 3.3e-13) {
		tmp = 5.0 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -1.55e-18:
		tmp = t_0
	elif x <= 3.3e-13:
		tmp = 5.0 * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -1.55e-18)
		tmp = t_0;
	elseif (x <= 3.3e-13)
		tmp = Float64(5.0 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + z);
	tmp = 0.0;
	if (x <= -1.55e-18)
		tmp = t_0;
	elseif (x <= 3.3e-13)
		tmp = 5.0 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e-18], t$95$0, If[LessEqual[x, 3.3e-13], N[(5.0 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000003e-18 or 3.3000000000000001e-13 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 98.0

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

   5. Applied rewrites 98.0%

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

   if -1.55000000000000003e-18 < x < 3.3000000000000001e-13

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 77.3

         \[\leadsto \color{blue}{5 \cdot z} \]

   5. Applied rewrites 77.3%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-13}:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+28) (* x z) (if (<= x 5.0) (* 5.0 z) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+28) {
		tmp = x * z;
	} else if (x <= 5.0) {
		tmp = 5.0 * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.05d+28)) then
        tmp = x * z
    else if (x <= 5.0d0) then
        tmp = 5.0d0 * z
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+28) {
		tmp = x * z;
	} else if (x <= 5.0) {
		tmp = 5.0 * z;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e+28:
		tmp = x * z
	elif x <= 5.0:
		tmp = 5.0 * z
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+28)
		tmp = Float64(x * z);
	elseif (x <= 5.0)
		tmp = Float64(5.0 * z);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e+28)
		tmp = x * z;
	elseif (x <= 5.0)
		tmp = 5.0 * z;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+28], N[(x * z), $MachinePrecision], If[LessEqual[x, 5.0], N[(5.0 * z), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04999999999999995e28 or 5 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.4%

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

   if -1.04999999999999995e28 < x < 5

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{5 \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 72.4

         \[\leadsto \color{blue}{5 \cdot z} \]

   5. Applied rewrites 72.4%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;5 \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. lower-+.f64 64.8

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

5. Applied rewrites 64.8%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 29.1%

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

9. Final simplification 29.1%

   \[\leadsto x \cdot z \]
10. Add Preprocessing

Developer Target 1: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 5\right) \cdot z + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (+ x 5.0) z) (* x y)))

C

double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

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 + 5.0d0) * z) + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

Python

def code(x, y, z):
	return ((x + 5.0) * z) + (x * y)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + 5.0) * z) + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + 5.0) * z) + (x * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024259 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (+ x 5) z) (* x y)))

  (+ (* x (+ y z)) (* z 5.0)))