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

Percentage Accurate: 99.9% → 100.0%

Time: 4.0s

Alternatives: 8

Speedup: 1.0×

• 20.1% 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: 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: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+190}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-99}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+20} \lor \neg \left(x \leq 2.2 \cdot 10^{+87}\right) \land x \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+190)
   (* z x)
   (if (<= x -2.2e+128)
     (* x y)
     (if (<= x -5.4e+57)
       (* z x)
       (if (<= x -5.8e-14)
         (* x y)
         (if (<= x 8e-99)
           (* z 5.0)
           (if (or (<= x 1.25e+20) (and (not (<= x 2.2e+87)) (<= x 4.8e+141)))
             (* x y)
             (* z x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+190) {
		tmp = z * x;
	} else if (x <= -2.2e+128) {
		tmp = x * y;
	} else if (x <= -5.4e+57) {
		tmp = z * x;
	} else if (x <= -5.8e-14) {
		tmp = x * y;
	} else if (x <= 8e-99) {
		tmp = z * 5.0;
	} else if ((x <= 1.25e+20) || (!(x <= 2.2e+87) && (x <= 4.8e+141))) {
		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 <= (-7.5d+190)) then
        tmp = z * x
    else if (x <= (-2.2d+128)) then
        tmp = x * y
    else if (x <= (-5.4d+57)) then
        tmp = z * x
    else if (x <= (-5.8d-14)) then
        tmp = x * y
    else if (x <= 8d-99) then
        tmp = z * 5.0d0
    else if ((x <= 1.25d+20) .or. (.not. (x <= 2.2d+87)) .and. (x <= 4.8d+141)) 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 <= -7.5e+190) {
		tmp = z * x;
	} else if (x <= -2.2e+128) {
		tmp = x * y;
	} else if (x <= -5.4e+57) {
		tmp = z * x;
	} else if (x <= -5.8e-14) {
		tmp = x * y;
	} else if (x <= 8e-99) {
		tmp = z * 5.0;
	} else if ((x <= 1.25e+20) || (!(x <= 2.2e+87) && (x <= 4.8e+141))) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+190:
		tmp = z * x
	elif x <= -2.2e+128:
		tmp = x * y
	elif x <= -5.4e+57:
		tmp = z * x
	elif x <= -5.8e-14:
		tmp = x * y
	elif x <= 8e-99:
		tmp = z * 5.0
	elif (x <= 1.25e+20) or (not (x <= 2.2e+87) and (x <= 4.8e+141)):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+190)
		tmp = Float64(z * x);
	elseif (x <= -2.2e+128)
		tmp = Float64(x * y);
	elseif (x <= -5.4e+57)
		tmp = Float64(z * x);
	elseif (x <= -5.8e-14)
		tmp = Float64(x * y);
	elseif (x <= 8e-99)
		tmp = Float64(z * 5.0);
	elseif ((x <= 1.25e+20) || (!(x <= 2.2e+87) && (x <= 4.8e+141)))
		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 <= -7.5e+190)
		tmp = z * x;
	elseif (x <= -2.2e+128)
		tmp = x * y;
	elseif (x <= -5.4e+57)
		tmp = z * x;
	elseif (x <= -5.8e-14)
		tmp = x * y;
	elseif (x <= 8e-99)
		tmp = z * 5.0;
	elseif ((x <= 1.25e+20) || (~((x <= 2.2e+87)) && (x <= 4.8e+141)))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+190], N[(z * x), $MachinePrecision], If[LessEqual[x, -2.2e+128], N[(x * y), $MachinePrecision], If[LessEqual[x, -5.4e+57], N[(z * x), $MachinePrecision], If[LessEqual[x, -5.8e-14], N[(x * y), $MachinePrecision], If[LessEqual[x, 8e-99], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.25e+20], And[N[Not[LessEqual[x, 2.2e+87]], $MachinePrecision], LessEqual[x, 4.8e+141]]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.4999999999999994e190 or -2.20000000000000017e128 < x < -5.3999999999999997e57 or 1.25e20 < x < 2.2000000000000001e87 or 4.79999999999999995e141 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 73.3%

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

   if -7.4999999999999994e190 < x < -2.20000000000000017e128 or -5.3999999999999997e57 < x < -5.8000000000000005e-14 or 8.0000000000000002e-99 < x < 1.25e20 or 2.2000000000000001e87 < x < 4.79999999999999995e141

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.4%

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

   if -5.8000000000000005e-14 < x < 8.0000000000000002e-99

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+190}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-99}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+20} \lor \neg \left(x \leq 2.2 \cdot 10^{+87}\right) \land x \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-14} \lor \neg \left(x \leq 6.5 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.5e-14) (not (<= x 6.5e-97)))
   (* x (+ z y))
   (+ (* z 5.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-14) || !(x <= 6.5e-97)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (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 <= (-3.5d-14)) .or. (.not. (x <= 6.5d-97))) then
        tmp = x * (z + y)
    else
        tmp = (z * 5.0d0) + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-14) || !(x <= 6.5e-97)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.5e-14) or not (x <= 6.5e-97):
		tmp = x * (z + y)
	else:
		tmp = (z * 5.0) + (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.5e-14) || !(x <= 6.5e-97))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(z * 5.0) + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.5e-14) || ~((x <= 6.5e-97)))
		tmp = x * (z + y);
	else
		tmp = (z * 5.0) + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-14], N[Not[LessEqual[x, 6.5e-97]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(z * 5.0), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5000000000000002e-14 or 6.5000000000000004e-97 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.4%

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

      1. +-commutative 95.4%

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

   4. Simplified 95.4%

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

   if -3.5000000000000002e-14 < x < 6.5000000000000004e-97

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 78.6%

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

      1. *-commutative 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-14} \lor \neg \left(x \leq 6.5 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + z \cdot x\\ \end{array} \]

Alternative 4: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-14} \lor \neg \left(x \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e-14) (not (<= x 8e-99))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e-14) || !(x <= 8e-99)) {
		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 <= (-6d-14)) .or. (.not. (x <= 8d-99))) 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 <= -6e-14) || !(x <= 8e-99)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e-14) or not (x <= 8e-99):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e-14) || !(x <= 8e-99))
		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 <= -6e-14) || ~((x <= 8e-99)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e-14], N[Not[LessEqual[x, 8e-99]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999997e-14 or 8.0000000000000002e-99 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.4%

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

      1. +-commutative 95.4%

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

   4. Simplified 95.4%

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

   if -5.9999999999999997e-14 < x < 8.0000000000000002e-99

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-14} \lor \neg \left(x \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]

Alternative 5: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-14} \lor \neg \left(x \leq 1.45 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5e-14) (not (<= x 1.45e-95))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e-14) || !(x <= 1.45e-95)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + 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 <= (-5d-14)) .or. (.not. (x <= 1.45d-95))) then
        tmp = x * (z + y)
    else
        tmp = z * (5.0d0 + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e-14) || !(x <= 1.45e-95)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5e-14) or not (x <= 1.45e-95):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5e-14) || !(x <= 1.45e-95))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * Float64(5.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5e-14) || ~((x <= 1.45e-95)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5e-14], N[Not[LessEqual[x, 1.45e-95]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000002e-14 or 1.45000000000000001e-95 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 95.4%

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

      1. +-commutative 95.4%

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

   4. Simplified 95.4%

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

   if -5.0000000000000002e-14 < x < 1.45000000000000001e-95

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 78.6%

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

      1. distribute-rgt-in 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-14} \lor \neg \left(x \leq 1.45 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]

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. Final simplification 99.9%

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

Alternative 7: 60.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-14} \lor \neg \left(x \leq 4 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e-14) (not (<= x 4e-90))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e-14) || !(x <= 4e-90)) {
		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 <= (-4.8d-14)) .or. (.not. (x <= 4d-90))) 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 <= -4.8e-14) || !(x <= 4e-90)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e-14) or not (x <= 4e-90):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e-14) || !(x <= 4e-90))
		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 <= -4.8e-14) || ~((x <= 4e-90)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e-14], N[Not[LessEqual[x, 4e-90]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e-14 or 3.99999999999999998e-90 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 51.9%

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

   if -4.8e-14 < x < 3.99999999999999998e-90

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-14} \lor \neg \left(x \leq 4 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]

Alternative 8: 36.9% 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 39.9%

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

3. Final simplification 39.9%

   \[\leadsto z \cdot 5 \]

Developer target: 98.3% 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 2023322 
(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)))