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

Percentage Accurate: 99.9% → 100.0%

Time: 5.9s

Alternatives: 7

Speedup: 1.0×

• 21.0% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z * 5.0 + N[(x * N[(z + y), $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. +-commutative 99.9%

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

   2. fma-define 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -0.0037:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-96}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -0.0037)
     t_0
     (if (<= x -5.8e-93)
       (* z (+ 5.0 x))
       (if (<= x -1.15e-154) (* x y) (if (<= x 2.8e-96) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.0037) {
		tmp = t_0;
	} else if (x <= -5.8e-93) {
		tmp = z * (5.0 + x);
	} else if (x <= -1.15e-154) {
		tmp = x * y;
	} else if (x <= 2.8e-96) {
		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 * (z + y)
    if (x <= (-0.0037d0)) then
        tmp = t_0
    else if (x <= (-5.8d-93)) then
        tmp = z * (5.0d0 + x)
    else if (x <= (-1.15d-154)) then
        tmp = x * y
    else if (x <= 2.8d-96) 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 * (z + y);
	double tmp;
	if (x <= -0.0037) {
		tmp = t_0;
	} else if (x <= -5.8e-93) {
		tmp = z * (5.0 + x);
	} else if (x <= -1.15e-154) {
		tmp = x * y;
	} else if (x <= 2.8e-96) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -0.0037:
		tmp = t_0
	elif x <= -5.8e-93:
		tmp = z * (5.0 + x)
	elif x <= -1.15e-154:
		tmp = x * y
	elif x <= 2.8e-96:
		tmp = z * 5.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -0.0037)
		tmp = t_0;
	elseif (x <= -5.8e-93)
		tmp = Float64(z * Float64(5.0 + x));
	elseif (x <= -1.15e-154)
		tmp = Float64(x * y);
	elseif (x <= 2.8e-96)
		tmp = Float64(z * 5.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -0.0037)
		tmp = t_0;
	elseif (x <= -5.8e-93)
		tmp = z * (5.0 + x);
	elseif (x <= -1.15e-154)
		tmp = x * y;
	elseif (x <= 2.8e-96)
		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[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0037], t$95$0, If[LessEqual[x, -5.8e-93], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-154], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.8e-96], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.0037000000000000002 or 2.80000000000000015e-96 < 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 94.9%

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

      1. +-commutative 94.9%

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

   5. Simplified 94.9%

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

   if -0.0037000000000000002 < x < -5.7999999999999997e-93

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 70.9%

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

      1. distribute-rgt-in 70.9%

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

   5. Simplified 70.9%

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

   if -5.7999999999999997e-93 < x < -1.15e-154

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 59.7%

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

   if -1.15e-154 < x < 2.80000000000000015e-96

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.8%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0037:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-96}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -14500000 \lor \neg \left(x \leq 0.29\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -14500000.0) (not (<= x 0.29)))
   (* x (+ z y))
   (+ (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -14500000.0) || !(x <= 0.29)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (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 <= (-14500000.0d0)) .or. (.not. (x <= 0.29d0))) then
        tmp = x * (z + y)
    else
        tmp = (z * 5.0d0) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -14500000.0) || !(x <= 0.29)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -14500000.0) or not (x <= 0.29):
		tmp = x * (z + y)
	else:
		tmp = (z * 5.0) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -14500000.0) || !(x <= 0.29))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(z * 5.0) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -14500000.0) || ~((x <= 0.29)))
		tmp = x * (z + y);
	else
		tmp = (z * 5.0) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -14500000.0], N[Not[LessEqual[x, 0.29]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(z * 5.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e7 or 0.28999999999999998 < 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 99.3%

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

      1. +-commutative 99.3%

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

   5. Simplified 99.3%

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

   if -1.45e7 < x < 0.28999999999999998

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 96.2%

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

      1. associate-+r+ 96.2%

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

      2. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around inf 87.8%

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

      1. associate-/l* 87.6%

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

   8. Simplified 87.6%

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

   9. Taylor expanded in x around 0 86.7%

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

       1. associate-*r/ 86.9%

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

       2. *-commutative 86.9%

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

       3. associate-*r/ 86.8%

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

   11. Simplified 86.8%

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

   12. Taylor expanded in y around 0 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14500000 \lor \neg \left(x \leq 0.29\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-154} \lor \neg \left(x \leq 5.7 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-154) (not (<= x 5.7e-95))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-154) || !(x <= 5.7e-95)) {
		tmp = x * (z + 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 <= (-1.15d-154)) .or. (.not. (x <= 5.7d-95))) then
        tmp = x * (z + 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 <= -1.15e-154) || !(x <= 5.7e-95)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e-154) or not (x <= 5.7e-95):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-154) || !(x <= 5.7e-95))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.15e-154) || ~((x <= 5.7e-95)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-154], N[Not[LessEqual[x, 5.7e-95]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-154 or 5.7e-95 < 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 87.1%

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

      1. +-commutative 87.1%

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

   5. Simplified 87.1%

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

   if -1.15e-154 < x < 5.7e-95

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.8%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-154} \lor \neg \left(x \leq 5.7 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-154} \lor \neg \left(x \leq 3.8 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-154) (not (<= x 3.8e-81))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-154) || !(x <= 3.8e-81)) {
		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 <= (-1.15d-154)) .or. (.not. (x <= 3.8d-81))) 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 <= -1.15e-154) || !(x <= 3.8e-81)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e-154) or not (x <= 3.8e-81):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-154) || !(x <= 3.8e-81))
		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 <= -1.15e-154) || ~((x <= 3.8e-81)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-154], N[Not[LessEqual[x, 3.8e-81]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-154 or 3.7999999999999999e-81 < 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 52.2%

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

   if -1.15e-154 < x < 3.7999999999999999e-81

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-154} \lor \neg \left(x \leq 3.8 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(z + y), $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. Final simplification 99.9%

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

Alternative 7: 36.4% 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. Add Preprocessing

3. Taylor expanded in x around 0 36.7%

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

4. Final simplification 36.7%

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

Developer target: 97.6% 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 2024077 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

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

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