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

Percentage Accurate: 99.9% → 100.0%

Time: 5.3s

Alternatives: 7

Speedup: 1.0×

• 21.4% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+203}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+27}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+118}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.3e+203)
   (* z x)
   (if (<= x -3.5e+112)
     (* x y)
     (if (<= x -1e+27)
       (* z x)
       (if (<= x -6.4e-68)
         (* x y)
         (if (<= x 1.1e-15)
           (* z 5.0)
           (if (<= x 1.3e+118) (* x y) (* z x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+203) {
		tmp = z * x;
	} else if (x <= -3.5e+112) {
		tmp = x * y;
	} else if (x <= -1e+27) {
		tmp = z * x;
	} else if (x <= -6.4e-68) {
		tmp = x * y;
	} else if (x <= 1.1e-15) {
		tmp = z * 5.0;
	} else if (x <= 1.3e+118) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.3d+203)) then
        tmp = z * x
    else if (x <= (-3.5d+112)) then
        tmp = x * y
    else if (x <= (-1d+27)) then
        tmp = z * x
    else if (x <= (-6.4d-68)) then
        tmp = x * y
    else if (x <= 1.1d-15) then
        tmp = z * 5.0d0
    else if (x <= 1.3d+118) then
        tmp = x * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.3e+203) {
		tmp = z * x;
	} else if (x <= -3.5e+112) {
		tmp = x * y;
	} else if (x <= -1e+27) {
		tmp = z * x;
	} else if (x <= -6.4e-68) {
		tmp = x * y;
	} else if (x <= 1.1e-15) {
		tmp = z * 5.0;
	} else if (x <= 1.3e+118) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.3e+203:
		tmp = z * x
	elif x <= -3.5e+112:
		tmp = x * y
	elif x <= -1e+27:
		tmp = z * x
	elif x <= -6.4e-68:
		tmp = x * y
	elif x <= 1.1e-15:
		tmp = z * 5.0
	elif x <= 1.3e+118:
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.3e+203)
		tmp = Float64(z * x);
	elseif (x <= -3.5e+112)
		tmp = Float64(x * y);
	elseif (x <= -1e+27)
		tmp = Float64(z * x);
	elseif (x <= -6.4e-68)
		tmp = Float64(x * y);
	elseif (x <= 1.1e-15)
		tmp = Float64(z * 5.0);
	elseif (x <= 1.3e+118)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.3e+203)
		tmp = z * x;
	elseif (x <= -3.5e+112)
		tmp = x * y;
	elseif (x <= -1e+27)
		tmp = z * x;
	elseif (x <= -6.4e-68)
		tmp = x * y;
	elseif (x <= 1.1e-15)
		tmp = z * 5.0;
	elseif (x <= 1.3e+118)
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.3e+203], N[(z * x), $MachinePrecision], If[LessEqual[x, -3.5e+112], N[(x * y), $MachinePrecision], If[LessEqual[x, -1e+27], N[(z * x), $MachinePrecision], If[LessEqual[x, -6.4e-68], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.1e-15], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 1.3e+118], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999999e203 or -3.49999999999999997e112 < x < -1e27 or 1.30000000000000008e118 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 67.3%

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

   if -2.2999999999999999e203 < x < -3.49999999999999997e112 or -1e27 < x < -6.3999999999999998e-68 or 1.09999999999999993e-15 < x < 1.30000000000000008e118

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 63.2%

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

   if -6.3999999999999998e-68 < x < 1.09999999999999993e-15

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 76.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+203}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+27}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+118}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -54 \lor \neg \left(x \leq 1.15 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -54.0) (not (<= x 1.15e-6)))
   (* x (+ z y))
   (+ (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -54.0) || !(x <= 1.15e-6)) {
		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 <= (-54.0d0)) .or. (.not. (x <= 1.15d-6))) 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 <= -54.0) || !(x <= 1.15e-6)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -54.0) or not (x <= 1.15e-6):
		tmp = x * (z + y)
	else:
		tmp = (z * 5.0) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -54.0) || !(x <= 1.15e-6))
		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 <= -54.0) || ~((x <= 1.15e-6)))
		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, -54.0], N[Not[LessEqual[x, 1.15e-6]], $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 < -54 or 1.15e-6 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around inf 98.4%

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

      1. +-commutative 98.4%

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

   4. Simplified 98.4%

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

   if -54 < x < 1.15e-6

   1. Initial program 99.8%

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

      1. flip-+ 58.3%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot y - z \cdot z}{y - z}} + z \cdot 5 \]

      2. associate-*r/ 58.2%

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

   3. Applied egg-rr 58.2%

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

      1. associate-/l* 58.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{y - z}{y \cdot y - z \cdot z}}} + z \cdot 5 \]

   5. Simplified 58.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{y - z}{y \cdot y - z \cdot z}}} + z \cdot 5 \]

   6. Taylor expanded in y around inf 98.8%

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

      1. *-commutative 98.8%

         \[\leadsto \color{blue}{y \cdot x} + z \cdot 5 \]

   8. Simplified 98.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -54 \lor \neg \left(x \leq 1.15 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \]

Alternative 4: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-67} \lor \neg \left(x \leq 1.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e-67) (not (<= x 1.2e-15))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e-67) || !(x <= 1.2e-15)) {
		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 <= (-3.3d-67)) .or. (.not. (x <= 1.2d-15))) 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 <= -3.3e-67) || !(x <= 1.2e-15)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e-67) or not (x <= 1.2e-15):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e-67) || !(x <= 1.2e-15))
		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 <= -3.3e-67) || ~((x <= 1.2e-15)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e-67], N[Not[LessEqual[x, 1.2e-15]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000002e-67 or 1.19999999999999997e-15 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around inf 93.4%

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

      1. +-commutative 93.4%

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

   4. Simplified 93.4%

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

   if -3.3000000000000002e-67 < x < 1.19999999999999997e-15

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 76.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-67} \lor \neg \left(x \leq 1.2 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]

Alternative 5: 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. Final simplification 99.9%

   \[\leadsto x \cdot \left(z + y\right) + z \cdot 5 \]

Alternative 6: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.16e-66) (* x y) (if (<= x 1.15e-15) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.16e-66) {
		tmp = x * y;
	} else if (x <= 1.15e-15) {
		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 <= (-1.16d-66)) then
        tmp = x * y
    else if (x <= 1.15d-15) 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 <= -1.16e-66) {
		tmp = x * y;
	} else if (x <= 1.15e-15) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.16e-66:
		tmp = x * y
	elif x <= 1.15e-15:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.16e-66)
		tmp = Float64(x * y);
	elseif (x <= 1.15e-15)
		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 <= -1.16e-66)
		tmp = x * y;
	elseif (x <= 1.15e-15)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.16e-66], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.15e-15], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.16000000000000002e-66 or 1.14999999999999995e-15 < x

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 50.5%

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

   if -1.16000000000000002e-66 < x < 1.14999999999999995e-15

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 76.7%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-15}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

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. Taylor expanded in x around 0 33.1%

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

3. Final simplification 33.1%

   \[\leadsto z \cdot 5 \]

Developer target: 98.0% 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 2023293 
(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)))