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

Percentage Accurate: 99.9% → 99.0%

Time: 6.1s

Alternatives: 9

Speedup: 1.0×

• 20.7% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x * y + N[(z * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. distribute-rgt-in 99.2%

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

   2. associate-+l+ 99.2%

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

   3. *-commutative 99.2%

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

   4. fma-define 99.9%

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

   5. distribute-lft-out 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 62.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+221}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+173}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-9} \lor \neg \left(x \leq 4.8 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.2e+221)
   (* x y)
   (if (<= x -2.4e+173)
     (* x z)
     (if (<= x -1.1e+125)
       (* x y)
       (if (<= x -6.5e+68)
         (* x z)
         (if (or (<= x -3.2e-9) (not (<= x 4.8e-61))) (* x y) (* z 5.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.2e+221) {
		tmp = x * y;
	} else if (x <= -2.4e+173) {
		tmp = x * z;
	} else if (x <= -1.1e+125) {
		tmp = x * y;
	} else if (x <= -6.5e+68) {
		tmp = x * z;
	} else if ((x <= -3.2e-9) || !(x <= 4.8e-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 <= (-3.2d+221)) then
        tmp = x * y
    else if (x <= (-2.4d+173)) then
        tmp = x * z
    else if (x <= (-1.1d+125)) then
        tmp = x * y
    else if (x <= (-6.5d+68)) then
        tmp = x * z
    else if ((x <= (-3.2d-9)) .or. (.not. (x <= 4.8d-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 <= -3.2e+221) {
		tmp = x * y;
	} else if (x <= -2.4e+173) {
		tmp = x * z;
	} else if (x <= -1.1e+125) {
		tmp = x * y;
	} else if (x <= -6.5e+68) {
		tmp = x * z;
	} else if ((x <= -3.2e-9) || !(x <= 4.8e-61)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.2e+221:
		tmp = x * y
	elif x <= -2.4e+173:
		tmp = x * z
	elif x <= -1.1e+125:
		tmp = x * y
	elif x <= -6.5e+68:
		tmp = x * z
	elif (x <= -3.2e-9) or not (x <= 4.8e-61):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.2e+221)
		tmp = Float64(x * y);
	elseif (x <= -2.4e+173)
		tmp = Float64(x * z);
	elseif (x <= -1.1e+125)
		tmp = Float64(x * y);
	elseif (x <= -6.5e+68)
		tmp = Float64(x * z);
	elseif ((x <= -3.2e-9) || !(x <= 4.8e-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 <= -3.2e+221)
		tmp = x * y;
	elseif (x <= -2.4e+173)
		tmp = x * z;
	elseif (x <= -1.1e+125)
		tmp = x * y;
	elseif (x <= -6.5e+68)
		tmp = x * z;
	elseif ((x <= -3.2e-9) || ~((x <= 4.8e-61)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.2e+221], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.4e+173], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.1e+125], N[(x * y), $MachinePrecision], If[LessEqual[x, -6.5e+68], N[(x * z), $MachinePrecision], If[Or[LessEqual[x, -3.2e-9], N[Not[LessEqual[x, 4.8e-61]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2e221 or -2.3999999999999999e173 < x < -1.09999999999999995e125 or -6.5000000000000005e68 < x < -3.20000000000000012e-9 or 4.8000000000000002e-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 65.8%

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

   if -3.2e221 < x < -2.3999999999999999e173 or -1.09999999999999995e125 < x < -6.5000000000000005e68

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 88.0%

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

      1. *-commutative 88.0%

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

   8. Simplified 88.0%

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

   if -3.20000000000000012e-9 < x < 4.8000000000000002e-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 77.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+221}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+173}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-9} \lor \neg \left(x \leq 4.8 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -410000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -410000.0) (not (<= x 5.0)))
   (* x (+ y z))
   (+ (* x y) (* z 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -410000.0) || !(x <= 5.0)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * y) + (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 <= (-410000.0d0)) .or. (.not. (x <= 5.0d0))) then
        tmp = x * (y + z)
    else
        tmp = (x * y) + (z * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -410000.0) || !(x <= 5.0)) {
		tmp = x * (y + z);
	} else {
		tmp = (x * y) + (z * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -410000.0) or not (x <= 5.0):
		tmp = x * (y + z)
	else:
		tmp = (x * y) + (z * 5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -410000.0) || !(x <= 5.0))
		tmp = Float64(x * Float64(y + z));
	else
		tmp = Float64(Float64(x * y) + Float64(z * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -410000.0) || ~((x <= 5.0)))
		tmp = x * (y + z);
	else
		tmp = (x * y) + (z * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -410000.0], N[Not[LessEqual[x, 5.0]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1e5 or 5 < 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 98.3%

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

      1. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   if -4.1e5 < x < 5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 87.2%

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

      1. associate-/l* 87.0%

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

      2. distribute-rgt-out 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in x around 0 86.9%

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

   7. Taylor expanded in y around 0 98.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -410000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -410000:\\ \;\;\;\;x \cdot y + x \cdot z\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -410000.0)
   (+ (* x y) (* x z))
   (if (<= x 5.0) (+ (* x y) (* z 5.0)) (* x (+ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -410000.0) {
		tmp = (x * y) + (x * z);
	} else if (x <= 5.0) {
		tmp = (x * y) + (z * 5.0);
	} else {
		tmp = x * (y + 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 <= (-410000.0d0)) then
        tmp = (x * y) + (x * z)
    else if (x <= 5.0d0) then
        tmp = (x * y) + (z * 5.0d0)
    else
        tmp = x * (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -410000.0) {
		tmp = (x * y) + (x * z);
	} else if (x <= 5.0) {
		tmp = (x * y) + (z * 5.0);
	} else {
		tmp = x * (y + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -410000.0:
		tmp = (x * y) + (x * z)
	elif x <= 5.0:
		tmp = (x * y) + (z * 5.0)
	else:
		tmp = x * (y + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -410000.0)
		tmp = Float64(Float64(x * y) + Float64(x * z));
	elseif (x <= 5.0)
		tmp = Float64(Float64(x * y) + Float64(z * 5.0));
	else
		tmp = Float64(x * Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -410000.0)
		tmp = (x * y) + (x * z);
	elseif (x <= 5.0)
		tmp = (x * y) + (z * 5.0);
	else
		tmp = x * (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -410000.0], N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.0], N[(N[(x * y), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1e5

   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%

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

      1. +-commutative 99.1%

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

   5. Simplified 99.1%

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

      1. distribute-lft-in 99.2%

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

   7. Applied egg-rr 99.2%

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

   if -4.1e5 < x < 5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 87.2%

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

      1. associate-/l* 87.0%

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

      2. distribute-rgt-out 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in x around 0 86.9%

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

   7. Taylor expanded in y around 0 98.7%

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

   if 5 < 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 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -410000:\\ \;\;\;\;x \cdot y + x \cdot z\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{-6} \lor \neg \left(x \leq 2.5 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.1e-6) (not (<= x 2.5e-60))) (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.1e-6) || !(x <= 2.5e-60)) {
		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 <= (-7.1d-6)) .or. (.not. (x <= 2.5d-60))) 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 <= -7.1e-6) || !(x <= 2.5e-60)) {
		tmp = x * (y + z);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.1e-6) or not (x <= 2.5e-60):
		tmp = x * (y + z)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.1e-6) || !(x <= 2.5e-60))
		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 <= -7.1e-6) || ~((x <= 2.5e-60)))
		tmp = x * (y + z);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.1e-6], N[Not[LessEqual[x, 2.5e-60]], $MachinePrecision]], N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0999999999999998e-6 or 2.5000000000000001e-60 < 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 95.5%

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

      1. +-commutative 95.5%

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

   5. Simplified 95.5%

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

   if -7.0999999999999998e-6 < x < 2.5000000000000001e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{-6} \lor \neg \left(x \leq 2.5 \cdot 10^{-60}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11.5 \lor \neg \left(x \leq 1.6 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -11.5) (not (<= x 1.6e-58))) (* x (+ y z)) (* z (+ x 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -11.5) || !(x <= 1.6e-58)) {
		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 <= (-11.5d0)) .or. (.not. (x <= 1.6d-58))) 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 <= -11.5) || !(x <= 1.6e-58)) {
		tmp = x * (y + z);
	} else {
		tmp = z * (x + 5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -11.5) or not (x <= 1.6e-58):
		tmp = x * (y + z)
	else:
		tmp = z * (x + 5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -11.5) || !(x <= 1.6e-58))
		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 <= -11.5) || ~((x <= 1.6e-58)))
		tmp = x * (y + z);
	else
		tmp = z * (x + 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -11.5], N[Not[LessEqual[x, 1.6e-58]], $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 < -11.5 or 1.6e-58 < 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 95.5%

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

      1. +-commutative 95.5%

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

   5. Simplified 95.5%

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

   if -11.5 < x < 1.6e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.5%

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

      1. distribute-rgt-in 77.5%

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

   5. Simplified 77.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11.5 \lor \neg \left(x \leq 1.6 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-9} \lor \neg \left(x \leq 4.2 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9e-9) (not (<= x 4.2e-59))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9e-9) || !(x <= 4.2e-59)) {
		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 <= (-9d-9)) .or. (.not. (x <= 4.2d-59))) 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 <= -9e-9) || !(x <= 4.2e-59)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9e-9) or not (x <= 4.2e-59):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9e-9) || !(x <= 4.2e-59))
		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 <= -9e-9) || ~((x <= 4.2e-59)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9e-9], N[Not[LessEqual[x, 4.2e-59]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999953e-9 or 4.19999999999999993e-59 < 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 59.9%

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

   if -8.99999999999999953e-9 < x < 4.19999999999999993e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 77.1%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-9} \lor \neg \left(x \leq 4.2 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (x * (y + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 9: 36.5% 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 41.7%

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

4. Final simplification 41.7%

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

Developer target: 98.1% 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 2024130 
(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)))