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

Percentage Accurate: 99.9% → 99.9%

Time: 5.3s

Alternatives: 7

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 2.5287982891879715e-63
  2. y = 9.050861586043441e+73
  3. z = 3.2774792587131747e+246

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-def 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 59.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+90}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4500:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+82} \lor \neg \left(x \leq 6.5 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+182)
   (* x y)
   (if (<= x -5.6e+90)
     (* x z)
     (if (<= x -3.8e+53)
       (* x y)
       (if (<= x -4500.0)
         (* x z)
         (if (<= x 2.1e-78)
           (* z 5.0)
           (if (or (<= x 5.2e+82) (not (<= x 6.5e+225))) (* x y) (* x z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+182) {
		tmp = x * y;
	} else if (x <= -5.6e+90) {
		tmp = x * z;
	} else if (x <= -3.8e+53) {
		tmp = x * y;
	} else if (x <= -4500.0) {
		tmp = x * z;
	} else if (x <= 2.1e-78) {
		tmp = z * 5.0;
	} else if ((x <= 5.2e+82) || !(x <= 6.5e+225)) {
		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 <= (-1.3d+182)) then
        tmp = x * y
    else if (x <= (-5.6d+90)) then
        tmp = x * z
    else if (x <= (-3.8d+53)) then
        tmp = x * y
    else if (x <= (-4500.0d0)) then
        tmp = x * z
    else if (x <= 2.1d-78) then
        tmp = z * 5.0d0
    else if ((x <= 5.2d+82) .or. (.not. (x <= 6.5d+225))) 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 <= -1.3e+182) {
		tmp = x * y;
	} else if (x <= -5.6e+90) {
		tmp = x * z;
	} else if (x <= -3.8e+53) {
		tmp = x * y;
	} else if (x <= -4500.0) {
		tmp = x * z;
	} else if (x <= 2.1e-78) {
		tmp = z * 5.0;
	} else if ((x <= 5.2e+82) || !(x <= 6.5e+225)) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+182:
		tmp = x * y
	elif x <= -5.6e+90:
		tmp = x * z
	elif x <= -3.8e+53:
		tmp = x * y
	elif x <= -4500.0:
		tmp = x * z
	elif x <= 2.1e-78:
		tmp = z * 5.0
	elif (x <= 5.2e+82) or not (x <= 6.5e+225):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+182)
		tmp = Float64(x * y);
	elseif (x <= -5.6e+90)
		tmp = Float64(x * z);
	elseif (x <= -3.8e+53)
		tmp = Float64(x * y);
	elseif (x <= -4500.0)
		tmp = Float64(x * z);
	elseif (x <= 2.1e-78)
		tmp = Float64(z * 5.0);
	elseif ((x <= 5.2e+82) || !(x <= 6.5e+225))
		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 <= -1.3e+182)
		tmp = x * y;
	elseif (x <= -5.6e+90)
		tmp = x * z;
	elseif (x <= -3.8e+53)
		tmp = x * y;
	elseif (x <= -4500.0)
		tmp = x * z;
	elseif (x <= 2.1e-78)
		tmp = z * 5.0;
	elseif ((x <= 5.2e+82) || ~((x <= 6.5e+225)))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+182], N[(x * y), $MachinePrecision], If[LessEqual[x, -5.6e+90], N[(x * z), $MachinePrecision], If[LessEqual[x, -3.8e+53], N[(x * y), $MachinePrecision], If[LessEqual[x, -4500.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 2.1e-78], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 5.2e+82], N[Not[LessEqual[x, 6.5e+225]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e182 or -5.6000000000000001e90 < x < -3.79999999999999997e53 or 2.1000000000000001e-78 < x < 5.1999999999999997e82 or 6.5000000000000006e225 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 68.2%

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

   if -1.3e182 < x < -5.6000000000000001e90 or -3.79999999999999997e53 < x < -4500 or 5.1999999999999997e82 < x < 6.5000000000000006e225

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 71.9%

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

   if -4500 < x < 2.1000000000000001e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.9%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{+90}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4500:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+82} \lor \neg \left(x \leq 6.5 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-15} \lor \neg \left(x \leq 1.8 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-15) (not (<= x 1.8e-90))) (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-15) || !(x <= 1.8e-90)) {
		tmp = x * (y + z);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1d-15)) .or. (.not. (x <= 1.8d-90))) then
        tmp = x * (y + z)
    else
        tmp = z * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-15) || !(x <= 1.8e-90)) {
		tmp = x * (y + z);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-15) or not (x <= 1.8e-90):
		tmp = x * (y + z)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-15) || !(x <= 1.8e-90))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e-15) || ~((x <= 1.8e-90)))
		tmp = x * (y + z);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-15], N[Not[LessEqual[x, 1.8e-90]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0000000000000001e-15 or 1.7999999999999999e-90 < 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 91.7%

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

      1. +-commutative 91.7%

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

   5. Simplified 91.7%

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

   if -1.0000000000000001e-15 < x < 1.7999999999999999e-90

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-15} \lor \neg \left(x \leq 1.8 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-13} \lor \neg \left(x \leq 1.8 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.2e-13) (not (<= x 1.8e-90))) (* x (+ y z)) (* z (+ x 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e-13) || !(x <= 1.8e-90)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6.2d-13)) .or. (.not. (x <= 1.8d-90))) then
        tmp = x * (y + z)
    else
        tmp = z * (x + 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e-13) || !(x <= 1.8e-90)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + 5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.2e-13) or not (x <= 1.8e-90):
		tmp = x * (y + z)
	else:
		tmp = z * (x + 5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.2e-13) || !(x <= 1.8e-90))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(z * Float64(x + 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.2e-13) || ~((x <= 1.8e-90)))
		tmp = x * (y + z);
	else
		tmp = z * (x + 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e-13], N[Not[LessEqual[x, 1.8e-90]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999998e-13 or 1.7999999999999999e-90 < 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 91.7%

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

      1. +-commutative 91.7%

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

   5. Simplified 91.7%

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

   if -6.1999999999999998e-13 < x < 1.7999999999999999e-90

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.1%

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

      1. distribute-rgt-in 73.1%

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

   5. Simplified 73.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-13} \lor \neg \left(x \leq 1.8 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-14} \lor \neg \left(x \leq 2.6 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-14) (not (<= x 2.6e-77))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-14) || !(x <= 2.6e-77)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.5d-14)) .or. (.not. (x <= 2.6d-77))) then
        tmp = x * y
    else
        tmp = z * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-14) || !(x <= 2.6e-77)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e-14) or not (x <= 2.6e-77):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-14) || !(x <= 2.6e-77))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.5e-14) || ~((x <= 2.6e-77)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-14], N[Not[LessEqual[x, 2.6e-77]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.49999999999999991e-14 or 2.6000000000000001e-77 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 53.6%

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

   if -5.49999999999999991e-14 < x < 2.6000000000000001e-77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.3%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-14} \lor \neg \left(x \leq 2.6 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 100.0%

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

3. Final simplification 100.0%

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

Alternative 7: 34.6% 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 100.0%

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

3. Taylor expanded in x around 0 36.8%

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

4. Final simplification 36.8%

   \[\leadsto z \cdot 5 \]
5. Add Preprocessing

Developer target: 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 2024031 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

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