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

Percentage Accurate: 99.9% → 99.9%

Time: 6.6s

Alternatives: 8

Speedup: 1.0×

• 21.1% 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: 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]

Derivation

1. Initial program 99.9%

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

Alternative 2: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -130000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -130000.0) t_0 (if (<= x 5.0) (+ (* x y) (* z 5.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -130000.0) {
		tmp = t_0;
	} else if (x <= 5.0) {
		tmp = (x * y) + (z * 5.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-130000.0d0)) then
        tmp = t_0
    else if (x <= 5.0d0) then
        tmp = (x * y) + (z * 5.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -130000.0) {
		tmp = t_0;
	} else if (x <= 5.0) {
		tmp = (x * y) + (z * 5.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -130000.0:
		tmp = t_0
	elif x <= 5.0:
		tmp = (x * y) + (z * 5.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -130000.0)
		tmp = t_0;
	elseif (x <= 5.0)
		tmp = Float64(Float64(x * y) + Float64(z * 5.0));
	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 <= -130000.0)
		tmp = t_0;
	elseif (x <= 5.0)
		tmp = (x * y) + (z * 5.0);
	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, -130000.0], t$95$0, If[LessEqual[x, 5.0], N[(N[(x * y), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e5 or 5 < x

   1. Initial program 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 97.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 98.8%

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

   7. Simplified 98.8%

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

   if -1.3e5 < x < 5

   1. Initial program 99.9%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{5}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 99.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -130000:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-113}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -4.2e-8) t_0 (if (<= x 4e-113) (* z (+ x 5.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -4.2e-8) {
		tmp = t_0;
	} else if (x <= 4e-113) {
		tmp = z * (x + 5.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-4.2d-8)) then
        tmp = t_0
    else if (x <= 4d-113) then
        tmp = z * (x + 5.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -4.2e-8) {
		tmp = t_0;
	} else if (x <= 4e-113) {
		tmp = z * (x + 5.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -4.2e-8:
		tmp = t_0
	elif x <= 4e-113:
		tmp = z * (x + 5.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -4.2e-8)
		tmp = t_0;
	elseif (x <= 4e-113)
		tmp = Float64(z * Float64(x + 5.0));
	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 <= -4.2e-8)
		tmp = t_0;
	elseif (x <= 4e-113)
		tmp = z * (x + 5.0);
	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, -4.2e-8], t$95$0, If[LessEqual[x, 4e-113], N[(z * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999989e-8 or 3.99999999999999991e-113 < x

   1. Initial program 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 97.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 93.8%

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

   7. Simplified 93.8%

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

   if -4.19999999999999989e-8 < x < 3.99999999999999991e-113

   1. Initial program 99.8%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0

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

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

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(5 + x\right)}\right) \]

      2. +-lowering-+.f64 79.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(5, \color{blue}{x}\right)\right) \]

   7. Simplified 79.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-113}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + z\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y z))))
   (if (<= x -4.2e-33) t_0 (if (<= x 3.4e-113) (* z 5.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -4.2e-33) {
		tmp = t_0;
	} else if (x <= 3.4e-113) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y + z)
    if (x <= (-4.2d-33)) then
        tmp = t_0
    else if (x <= 3.4d-113) then
        tmp = z * 5.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + z);
	double tmp;
	if (x <= -4.2e-33) {
		tmp = t_0;
	} else if (x <= 3.4e-113) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + z)
	tmp = 0
	if x <= -4.2e-33:
		tmp = t_0
	elif x <= 3.4e-113:
		tmp = z * 5.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (x <= -4.2e-33)
		tmp = t_0;
	elseif (x <= 3.4e-113)
		tmp = Float64(z * 5.0);
	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 <= -4.2e-33)
		tmp = t_0;
	elseif (x <= 3.4e-113)
		tmp = z * 5.0;
	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, -4.2e-33], t$95$0, If[LessEqual[x, 3.4e-113], N[(z * 5.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e-33 or 3.4000000000000002e-113 < x

   1. Initial program 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 97.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 92.7%

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

   7. Simplified 92.7%

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

   if -4.2e-33 < x < 3.4000000000000002e-113

   1. Initial program 99.8%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 80.8%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

   7. Simplified 80.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-53}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0) (* x z) (if (<= x 1.45e-53) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = x * z;
	} else if (x <= 1.45e-53) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	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 <= (-5.0d0)) then
        tmp = x * z
    else if (x <= 1.45d-53) then
        tmp = z * 5.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = x * z;
	} else if (x <= 1.45e-53) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.0:
		tmp = x * z
	elif x <= 1.45e-53:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(x * z);
	elseif (x <= 1.45e-53)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.0)
		tmp = x * z;
	elseif (x <= 1.45e-53)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 1.45e-53], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5

   1. Initial program 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 96.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 96.7%

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

   5. Taylor expanded in x around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 60.4%

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

   10. Simplified 60.4%

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

   if -5 < x < 1.4499999999999999e-53

   1. Initial program 99.9%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

   7. Simplified 75.6%

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

   if 1.4499999999999999e-53 < x

   1. Initial program 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 97.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-53}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-53}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e-34) (* x y) (if (<= x 1.75e-53) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-34) {
		tmp = x * y;
	} else if (x <= 1.75e-53) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	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 <= (-1.75d-34)) then
        tmp = x * y
    else if (x <= 1.75d-53) then
        tmp = z * 5.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-34) {
		tmp = x * y;
	} else if (x <= 1.75e-53) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e-34:
		tmp = x * y
	elif x <= 1.75e-53:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e-34)
		tmp = Float64(x * y);
	elseif (x <= 1.75e-53)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e-34)
		tmp = x * y;
	elseif (x <= 1.75e-53)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e-34], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.75e-53], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e-34 or 1.74999999999999997e-53 < x

   1. Initial program 100.0%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 97.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 97.3%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 54.6%

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

   7. Simplified 54.6%

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

   if -1.75e-34 < x < 1.74999999999999997e-53

   1. Initial program 99.9%

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

      1. distribute-rgt-in N/A

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

      2. associate-+l+ N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

      6. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

      8. +-lowering-+.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

   7. Simplified 78.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-53}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + (z * (x + 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 * (x + 5.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. distribute-rgt-in N/A

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

   2. associate-+l+ N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

   6. distribute-lft-out N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

   8. +-lowering-+.f64 98.4%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

3. Simplified 98.4%

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

Alternative 8: 36.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ z \cdot 5 \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z * 5.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. distribute-rgt-in N/A

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

   2. associate-+l+ N/A

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

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

      \[\leadsto \mathsf{+.f64}\left(\left(y \cdot x\right), \color{blue}{\left(z \cdot x + z \cdot 5\right)}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z \cdot x} + z \cdot 5\right)\right) \]

   6. distribute-lft-out N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(x + 5\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{\left(x + 5\right)}\right)\right) \]

   8. +-lowering-+.f64 98.4%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, \color{blue}{5}\right)\right)\right) \]

3. Simplified 98.4%

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

5. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 35.0%

      \[\leadsto \mathsf{*.f64}\left(5, \color{blue}{z}\right) \]

7. Simplified 35.0%

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

8. Final simplification 35.0%

   \[\leadsto z \cdot 5 \]
9. 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 2024155 
(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)))