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

Percentage Accurate: 99.9% → 99.9%

Time: 5.9s

Alternatives: 8

Speedup: 1.0×

• 20.9% 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, 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 99.9%

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

   1. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+57}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-65}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.45e+57)
   (* x z)
   (if (<= x -6.7e-12)
     (* x y)
     (if (<= x 1.66e-65) (* z 5.0) (if (<= x 1.2e+132) (* x y) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.45e+57) {
		tmp = x * z;
	} else if (x <= -6.7e-12) {
		tmp = x * y;
	} else if (x <= 1.66e-65) {
		tmp = z * 5.0;
	} else if (x <= 1.2e+132) {
		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 <= (-2.45d+57)) then
        tmp = x * z
    else if (x <= (-6.7d-12)) then
        tmp = x * y
    else if (x <= 1.66d-65) then
        tmp = z * 5.0d0
    else if (x <= 1.2d+132) 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 <= -2.45e+57) {
		tmp = x * z;
	} else if (x <= -6.7e-12) {
		tmp = x * y;
	} else if (x <= 1.66e-65) {
		tmp = z * 5.0;
	} else if (x <= 1.2e+132) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.45e+57:
		tmp = x * z
	elif x <= -6.7e-12:
		tmp = x * y
	elif x <= 1.66e-65:
		tmp = z * 5.0
	elif x <= 1.2e+132:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.45e+57)
		tmp = Float64(x * z);
	elseif (x <= -6.7e-12)
		tmp = Float64(x * y);
	elseif (x <= 1.66e-65)
		tmp = Float64(z * 5.0);
	elseif (x <= 1.2e+132)
		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 <= -2.45e+57)
		tmp = x * z;
	elseif (x <= -6.7e-12)
		tmp = x * y;
	elseif (x <= 1.66e-65)
		tmp = z * 5.0;
	elseif (x <= 1.2e+132)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.45e+57], N[(x * z), $MachinePrecision], If[LessEqual[x, -6.7e-12], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.66e-65], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 1.2e+132], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.45e57 or 1.2000000000000001e132 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. distribute-lft-in 95.3%

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

      2. *-commutative 95.3%

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

      3. +-commutative 95.3%

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

      4. associate-+r+ 95.3%

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

      5. *-commutative 95.3%

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

      6. distribute-lft-in 95.3%

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

      7. fma-define 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in z around inf 65.5%

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

      1. +-commutative 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in x around inf 65.5%

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

   if -2.45e57 < x < -6.7000000000000001e-12 or 1.6599999999999999e-65 < x < 1.2000000000000001e132

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -6.7000000000000001e-12 < x < 1.6599999999999999e-65

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+57}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -6.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{-65}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.0) (not (<= x 2e-14))) (* x (+ y z)) (+ (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 2e-14)) {
		tmp = x * (y + z);
	} 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 <= (-5.0d0)) .or. (.not. (x <= 2d-14))) then
        tmp = x * (y + z)
    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 <= -5.0) || !(x <= 2e-14)) {
		tmp = x * (y + z);
	} else {
		tmp = (z * 5.0) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.0) or not (x <= 2e-14):
		tmp = x * (y + z)
	else:
		tmp = (z * 5.0) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.0) || !(x <= 2e-14))
		tmp = Float64(x * Float64(y + z));
	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 <= -5.0) || ~((x <= 2e-14)))
		tmp = x * (y + z);
	else
		tmp = (z * 5.0) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.0], N[Not[LessEqual[x, 2e-14]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(z * 5.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5 or 2e-14 < 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 99.0%

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

      1. +-commutative 99.0%

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

   5. Simplified 99.0%

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

   if -5 < x < 2e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.7%

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

   4. Taylor expanded in x around 0 75.7%

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

   5. Taylor expanded in x around 0 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-11} \lor \neg \left(x \leq 5.8 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.9e-11) (not (<= x 5.8e-61))) (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.9e-11) || !(x <= 5.8e-61)) {
		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 <= (-2.9d-11)) .or. (.not. (x <= 5.8d-61))) 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 <= -2.9e-11) || !(x <= 5.8e-61)) {
		tmp = x * (y + z);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.9e-11) or not (x <= 5.8e-61):
		tmp = x * (y + z)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.9e-11) || !(x <= 5.8e-61))
		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 <= -2.9e-11) || ~((x <= 5.8e-61)))
		tmp = x * (y + z);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.9e-11], N[Not[LessEqual[x, 5.8e-61]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e-11 or 5.7999999999999999e-61 < 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 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

   if -2.9e-11 < x < 5.7999999999999999e-61

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-11} \lor \neg \left(x \leq 5.8 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420000000 \lor \neg \left(x \leq 7 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -420000000.0) (not (<= x 7e-64)))
   (* x (+ y z))
   (* z (+ x 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -420000000.0) || !(x <= 7e-64)) {
		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 <= (-420000000.0d0)) .or. (.not. (x <= 7d-64))) 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 <= -420000000.0) || !(x <= 7e-64)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + 5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -420000000.0) or not (x <= 7e-64):
		tmp = x * (y + z)
	else:
		tmp = z * (x + 5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -420000000.0) || !(x <= 7e-64))
		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 <= -420000000.0) || ~((x <= 7e-64)))
		tmp = x * (y + z);
	else
		tmp = z * (x + 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -420000000.0], N[Not[LessEqual[x, 7e-64]], $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 < -4.2e8 or 7.0000000000000006e-64 < 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 96.0%

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

      1. +-commutative 96.0%

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

   5. Simplified 96.0%

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

   if -4.2e8 < x < 7.0000000000000006e-64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 73.8%

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

      1. distribute-rgt-in 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000000 \lor \neg \left(x \leq 7 \cdot 10^{-64}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-16} \lor \neg \left(x \leq 4.4 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e-16) (not (<= x 4.4e-61))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-16) || !(x <= 4.4e-61)) {
		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 <= (-1.5d-16)) .or. (.not. (x <= 4.4d-61))) 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 <= -1.5e-16) || !(x <= 4.4e-61)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e-16) or not (x <= 4.4e-61):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e-16) || !(x <= 4.4e-61))
		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 <= -1.5e-16) || ~((x <= 4.4e-61)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e-16], N[Not[LessEqual[x, 4.4e-61]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999997e-16 or 4.40000000000000017e-61 < 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 50.4%

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

   if -1.49999999999999997e-16 < x < 4.40000000000000017e-61

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.0%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-16} \lor \neg \left(x \leq 4.4 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Final simplification 99.9%

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

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. Add Preprocessing

3. Taylor expanded in x around 0 37.1%

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

4. Final simplification 37.1%

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

Developer target: 97.7% 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 2024066 
(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)))