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

Percentage Accurate: 99.9% → 100.0%

Time: 5.8s

Alternatives: 9

Speedup: 1.0×

• 20.3% 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. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-define 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+256}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+194}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3e+256)
   (* x y)
   (if (<= x -3.8e+194)
     (* z x)
     (if (<= x -1.4e-11) (* x y) (if (<= x 5.0) (* z 5.0) (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3e+256) {
		tmp = x * y;
	} else if (x <= -3.8e+194) {
		tmp = z * x;
	} else if (x <= -1.4e-11) {
		tmp = x * y;
	} else if (x <= 5.0) {
		tmp = z * 5.0;
	} 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 <= (-3d+256)) then
        tmp = x * y
    else if (x <= (-3.8d+194)) then
        tmp = z * x
    else if (x <= (-1.4d-11)) then
        tmp = x * y
    else if (x <= 5.0d0) then
        tmp = z * 5.0d0
    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 <= -3e+256) {
		tmp = x * y;
	} else if (x <= -3.8e+194) {
		tmp = z * x;
	} else if (x <= -1.4e-11) {
		tmp = x * y;
	} else if (x <= 5.0) {
		tmp = z * 5.0;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3e+256:
		tmp = x * y
	elif x <= -3.8e+194:
		tmp = z * x
	elif x <= -1.4e-11:
		tmp = x * y
	elif x <= 5.0:
		tmp = z * 5.0
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3e+256)
		tmp = Float64(x * y);
	elseif (x <= -3.8e+194)
		tmp = Float64(z * x);
	elseif (x <= -1.4e-11)
		tmp = Float64(x * y);
	elseif (x <= 5.0)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3e+256)
		tmp = x * y;
	elseif (x <= -3.8e+194)
		tmp = z * x;
	elseif (x <= -1.4e-11)
		tmp = x * y;
	elseif (x <= 5.0)
		tmp = z * 5.0;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3e+256], N[(x * y), $MachinePrecision], If[LessEqual[x, -3.8e+194], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.4e-11], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.0], N[(z * 5.0), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000001e256 or -3.7999999999999999e194 < x < -1.4e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.3%

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

   if -3.0000000000000001e256 < x < -3.7999999999999999e194 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 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. Taylor expanded in z around inf 60.9%

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

   if -1.4e-11 < x < 5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 68.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+256}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+194}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -185000 \lor \neg \left(x \leq 1.55\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z \cdot \frac{5}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -185000.0) (not (<= x 1.55)))
   (* x (+ z y))
   (* y (+ x (* z (/ 5.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -185000.0) || !(x <= 1.55)) {
		tmp = x * (z + y);
	} else {
		tmp = y * (x + (z * (5.0 / 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 <= (-185000.0d0)) .or. (.not. (x <= 1.55d0))) then
        tmp = x * (z + y)
    else
        tmp = y * (x + (z * (5.0d0 / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -185000.0) || !(x <= 1.55)) {
		tmp = x * (z + y);
	} else {
		tmp = y * (x + (z * (5.0 / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -185000.0) or not (x <= 1.55):
		tmp = x * (z + y)
	else:
		tmp = y * (x + (z * (5.0 / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -185000.0) || !(x <= 1.55))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(y * Float64(x + Float64(z * Float64(5.0 / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -185000.0) || ~((x <= 1.55)))
		tmp = x * (z + y);
	else
		tmp = y * (x + (z * (5.0 / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -185000.0], N[Not[LessEqual[x, 1.55]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(z * N[(5.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -185000 or 1.55000000000000004 < 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 98.6%

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

      1. +-commutative 98.6%

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

   5. Simplified 98.6%

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

   if -185000 < x < 1.55000000000000004

   1. Initial program 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. associate-+l+ 99.9%

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

      3. *-commutative 99.9%

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

      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. Step-by-step derivation

      1. fma-undefine 99.9%

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

      2. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 93.1%

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

      1. associate-/l* 93.0%

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

      2. +-commutative 93.0%

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

   9. Simplified 93.0%

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

   10. Taylor expanded in x around 0 92.1%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -185000 \lor \neg \left(x \leq 1.55\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z \cdot \frac{5}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000285 \lor \neg \left(x \leq 7200\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x + z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.000285) (not (<= x 7200.0)))
   (* x (+ z y))
   (+ (* z x) (* z 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.000285) || !(x <= 7200.0)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * x) + (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 <= (-0.000285d0)) .or. (.not. (x <= 7200.0d0))) then
        tmp = x * (z + y)
    else
        tmp = (z * x) + (z * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.000285) || !(x <= 7200.0)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * x) + (z * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.000285) or not (x <= 7200.0):
		tmp = x * (z + y)
	else:
		tmp = (z * x) + (z * 5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.000285) || !(x <= 7200.0))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(z * x) + Float64(z * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.000285) || ~((x <= 7200.0)))
		tmp = x * (z + y);
	else
		tmp = (z * x) + (z * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.000285], N[Not[LessEqual[x, 7200.0]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8499999999999999e-4 or 7200 < 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 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -2.8499999999999999e-4 < x < 7200

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.4%

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

      1. *-commutative 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000285 \lor \neg \left(x \leq 7200\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x + z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-10} \lor \neg \left(x \leq 9.2 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e-10) (not (<= x 9.2e-53))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e-10) || !(x <= 9.2e-53)) {
		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 <= (-8.2d-10)) .or. (.not. (x <= 9.2d-53))) 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 <= -8.2e-10) || !(x <= 9.2e-53)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e-10) or not (x <= 9.2e-53):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e-10) || !(x <= 9.2e-53))
		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 <= -8.2e-10) || ~((x <= 9.2e-53)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e-10], N[Not[LessEqual[x, 9.2e-53]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999996e-10 or 9.2000000000000005e-53 < 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 95.4%

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

      1. +-commutative 95.4%

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

   5. Simplified 95.4%

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

   if -8.1999999999999996e-10 < x < 9.2000000000000005e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 70.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-10} \lor \neg \left(x \leq 9.2 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-5} \lor \neg \left(x \leq 3000\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-5) (not (<= x 3000.0))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-5) || !(x <= 3000.0)) {
		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 <= (-2.1d-5)) .or. (.not. (x <= 3000.0d0))) 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 <= -2.1e-5) || !(x <= 3000.0)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-5) or not (x <= 3000.0):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-5) || !(x <= 3000.0))
		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 <= -2.1e-5) || ~((x <= 3000.0)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-5], N[Not[LessEqual[x, 3000.0]], $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 < -2.09999999999999988e-5 or 3e3 < 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 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   if -2.09999999999999988e-5 < x < 3e3

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.4%

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

      1. distribute-rgt-in 69.4%

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

   5. Simplified 69.4%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-5} \lor \neg \left(x \leq 3000\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-11} \lor \neg \left(x \leq 3000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-11) (not (<= x 3000.0))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-11) || !(x <= 3000.0)) {
		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 <= (-2.1d-11)) .or. (.not. (x <= 3000.0d0))) 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 <= -2.1e-11) || !(x <= 3000.0)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-11) or not (x <= 3000.0):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-11) || !(x <= 3000.0))
		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 <= -2.1e-11) || ~((x <= 3000.0)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-11], N[Not[LessEqual[x, 3000.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e-11 or 3e3 < 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 53.2%

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

   if -2.0999999999999999e-11 < x < 3e3

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 67.9%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-11} \lor \neg \left(x \leq 3000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

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

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 9: 37.6% 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 34.6%

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

4. Final simplification 34.6%

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

Developer target: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x + 5.0d0) * z) + (x * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024082 
(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)))