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

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 7

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, 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. Add Preprocessing

Alternative 2: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+195}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e+39)
   (* x z)
   (if (<= x -8e-36)
     (* x y)
     (if (<= x 3.5e-38) (* z 5.0) (if (<= x 3.6e+195) (* x y) (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e+39) {
		tmp = x * z;
	} else if (x <= -8e-36) {
		tmp = x * y;
	} else if (x <= 3.5e-38) {
		tmp = z * 5.0;
	} else if (x <= 3.6e+195) {
		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 <= (-2.6d+39)) then
        tmp = x * z
    else if (x <= (-8d-36)) then
        tmp = x * y
    else if (x <= 3.5d-38) then
        tmp = z * 5.0d0
    else if (x <= 3.6d+195) 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 <= -2.6e+39) {
		tmp = x * z;
	} else if (x <= -8e-36) {
		tmp = x * y;
	} else if (x <= 3.5e-38) {
		tmp = z * 5.0;
	} else if (x <= 3.6e+195) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e+39:
		tmp = x * z
	elif x <= -8e-36:
		tmp = x * y
	elif x <= 3.5e-38:
		tmp = z * 5.0
	elif x <= 3.6e+195:
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e+39)
		tmp = Float64(x * z);
	elseif (x <= -8e-36)
		tmp = Float64(x * y);
	elseif (x <= 3.5e-38)
		tmp = Float64(z * 5.0);
	elseif (x <= 3.6e+195)
		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 <= -2.6e+39)
		tmp = x * z;
	elseif (x <= -8e-36)
		tmp = x * y;
	elseif (x <= 3.5e-38)
		tmp = z * 5.0;
	elseif (x <= 3.6e+195)
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e+39], N[(x * z), $MachinePrecision], If[LessEqual[x, -8e-36], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.5e-38], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 3.6e+195], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6e39 or 3.5999999999999999e195 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. distribute-rgt-in 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in x around inf 67.5%

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

   if -2.6e39 < x < -7.9999999999999995e-36 or 3.5000000000000001e-38 < x < 3.5999999999999999e195

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto x \cdot \left(y + z\right) + \color{blue}{\left(\sqrt[3]{z \cdot 5} \cdot \sqrt[3]{z \cdot 5}\right) \cdot \sqrt[3]{z \cdot 5}} \]

      2. pow3 99.8%

         \[\leadsto x \cdot \left(y + z\right) + \color{blue}{{\left(\sqrt[3]{z \cdot 5}\right)}^{3}} \]

   4. Applied egg-rr 99.8%

      \[\leadsto x \cdot \left(y + z\right) + \color{blue}{{\left(\sqrt[3]{z \cdot 5}\right)}^{3}} \]

   5. Taylor expanded in y around inf 60.6%

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

   if -7.9999999999999995e-36 < x < 3.5000000000000001e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. distribute-rgt-in 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around 0 75.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+195}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -30.5 \lor \neg \left(x \leq 5.1\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -30.5) (not (<= x 5.1))) (* x (+ y z)) (+ (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -30.5) || !(x <= 5.1)) {
		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 <= (-30.5d0)) .or. (.not. (x <= 5.1d0))) 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 <= -30.5) || !(x <= 5.1)) {
		tmp = x * (y + z);
	} else {
		tmp = (z * 5.0) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -30.5) or not (x <= 5.1):
		tmp = x * (y + z)
	else:
		tmp = (z * 5.0) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -30.5) || !(x <= 5.1))
		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 <= -30.5) || ~((x <= 5.1)))
		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, -30.5], N[Not[LessEqual[x, 5.1]], $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 < -30.5 or 5.0999999999999996 < 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 99.1%

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

   if -30.5 < x < 5.0999999999999996

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.2%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -30.5 \lor \neg \left(x \leq 5.1\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-37} \lor \neg \left(x \leq 7.8 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e-37) (not (<= x 7.8e-39))) (* x (+ y z)) (* z (+ x 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-37) || !(x <= 7.8e-39)) {
		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 <= (-9d-37)) .or. (.not. (x <= 7.8d-39))) 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 <= -9e-37) || !(x <= 7.8e-39)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + 5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e-37) or not (x <= 7.8e-39):
		tmp = x * (y + z)
	else:
		tmp = z * (x + 5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e-37) || !(x <= 7.8e-39))
		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 <= -9e-37) || ~((x <= 7.8e-39)))
		tmp = x * (y + z);
	else
		tmp = z * (x + 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e-37], N[Not[LessEqual[x, 7.8e-39]], $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 < -9.00000000000000081e-37 or 7.80000000000000059e-39 < 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 92.7%

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

   if -9.00000000000000081e-37 < x < 7.80000000000000059e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. distribute-rgt-in 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-37} \lor \neg \left(x \leq 7.8 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-36} \lor \neg \left(x \leq 5 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e-36) (not (<= x 5e-39))) (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e-36) || !(x <= 5e-39)) {
		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 <= (-7.2d-36)) .or. (.not. (x <= 5d-39))) 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 <= -7.2e-36) || !(x <= 5e-39)) {
		tmp = x * (y + z);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e-36) or not (x <= 5e-39):
		tmp = x * (y + z)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e-36) || !(x <= 5e-39))
		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 <= -7.2e-36) || ~((x <= 5e-39)))
		tmp = x * (y + z);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e-36], N[Not[LessEqual[x, 5e-39]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000064e-36 or 4.9999999999999998e-39 < 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 92.7%

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

   if -7.20000000000000064e-36 < x < 4.9999999999999998e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. distribute-rgt-in 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around 0 75.6%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-36} \lor \neg \left(x \leq 5 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-36} \lor \neg \left(x \leq 1.85 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.6e-36) (not (<= x 1.85e-38))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.6e-36) || !(x <= 1.85e-38)) {
		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 <= (-3.6d-36)) .or. (.not. (x <= 1.85d-38))) 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 <= -3.6e-36) || !(x <= 1.85e-38)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.6e-36) or not (x <= 1.85e-38):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.6e-36) || !(x <= 1.85e-38))
		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 <= -3.6e-36) || ~((x <= 1.85e-38)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.6e-36], N[Not[LessEqual[x, 1.85e-38]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.60000000000000032e-36 or 1.85e-38 < x

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.9%

         \[\leadsto x \cdot \left(y + z\right) + \color{blue}{\left(\sqrt[3]{z \cdot 5} \cdot \sqrt[3]{z \cdot 5}\right) \cdot \sqrt[3]{z \cdot 5}} \]

      2. pow3 99.9%

         \[\leadsto x \cdot \left(y + z\right) + \color{blue}{{\left(\sqrt[3]{z \cdot 5}\right)}^{3}} \]

   4. Applied egg-rr 99.9%

      \[\leadsto x \cdot \left(y + z\right) + \color{blue}{{\left(\sqrt[3]{z \cdot 5}\right)}^{3}} \]

   5. Taylor expanded in y around inf 48.9%

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

   if -3.60000000000000032e-36 < x < 1.85e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. distribute-rgt-in 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around 0 75.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-36} \lor \neg \left(x \leq 1.85 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.0% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x * y), $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. add-cube-cbrt 99.3%

      \[\leadsto x \cdot \left(y + z\right) + \color{blue}{\left(\sqrt[3]{z \cdot 5} \cdot \sqrt[3]{z \cdot 5}\right) \cdot \sqrt[3]{z \cdot 5}} \]

   2. pow3 99.3%

      \[\leadsto x \cdot \left(y + z\right) + \color{blue}{{\left(\sqrt[3]{z \cdot 5}\right)}^{3}} \]

4. Applied egg-rr 99.3%

   \[\leadsto x \cdot \left(y + z\right) + \color{blue}{{\left(\sqrt[3]{z \cdot 5}\right)}^{3}} \]

5. Taylor expanded in y around inf 40.1%

   \[\leadsto \color{blue}{x \cdot y} \]
6. Add Preprocessing

Developer Target 1: 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 2024186 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (+ x 5) z) (* x y)))

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