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

Percentage Accurate: 99.9% → 100.0%

Time: 6.1s

Alternatives: 9

Speedup: 1.0×

• 21.2% 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: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

Alternative 3: 61.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+284}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+226}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+129}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-18} \lor \neg \left(x \leq 2.95 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.1e+284)
   (* x y)
   (if (<= x -6.6e+226)
     (* z x)
     (if (<= x -6.8e+190)
       (* x y)
       (if (<= x -2.3e+129)
         (* z x)
         (if (or (<= x -1.32e-18) (not (<= x 2.95e-13)))
           (* x y)
           (* z 5.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.1e+284) {
		tmp = x * y;
	} else if (x <= -6.6e+226) {
		tmp = z * x;
	} else if (x <= -6.8e+190) {
		tmp = x * y;
	} else if (x <= -2.3e+129) {
		tmp = z * x;
	} else if ((x <= -1.32e-18) || !(x <= 2.95e-13)) {
		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 <= (-1.1d+284)) then
        tmp = x * y
    else if (x <= (-6.6d+226)) then
        tmp = z * x
    else if (x <= (-6.8d+190)) then
        tmp = x * y
    else if (x <= (-2.3d+129)) then
        tmp = z * x
    else if ((x <= (-1.32d-18)) .or. (.not. (x <= 2.95d-13))) 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 <= -1.1e+284) {
		tmp = x * y;
	} else if (x <= -6.6e+226) {
		tmp = z * x;
	} else if (x <= -6.8e+190) {
		tmp = x * y;
	} else if (x <= -2.3e+129) {
		tmp = z * x;
	} else if ((x <= -1.32e-18) || !(x <= 2.95e-13)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.1e+284:
		tmp = x * y
	elif x <= -6.6e+226:
		tmp = z * x
	elif x <= -6.8e+190:
		tmp = x * y
	elif x <= -2.3e+129:
		tmp = z * x
	elif (x <= -1.32e-18) or not (x <= 2.95e-13):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.1e+284)
		tmp = Float64(x * y);
	elseif (x <= -6.6e+226)
		tmp = Float64(z * x);
	elseif (x <= -6.8e+190)
		tmp = Float64(x * y);
	elseif (x <= -2.3e+129)
		tmp = Float64(z * x);
	elseif ((x <= -1.32e-18) || !(x <= 2.95e-13))
		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 <= -1.1e+284)
		tmp = x * y;
	elseif (x <= -6.6e+226)
		tmp = z * x;
	elseif (x <= -6.8e+190)
		tmp = x * y;
	elseif (x <= -2.3e+129)
		tmp = z * x;
	elseif ((x <= -1.32e-18) || ~((x <= 2.95e-13)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.1e+284], N[(x * y), $MachinePrecision], If[LessEqual[x, -6.6e+226], N[(z * x), $MachinePrecision], If[LessEqual[x, -6.8e+190], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.3e+129], N[(z * x), $MachinePrecision], If[Or[LessEqual[x, -1.32e-18], N[Not[LessEqual[x, 2.95e-13]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.09999999999999997e284 or -6.59999999999999956e226 < x < -6.7999999999999999e190 or -2.2999999999999999e129 < x < -1.3199999999999999e-18 or 2.95000000000000005e-13 < 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 67.7%

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

   if -1.09999999999999997e284 < x < -6.59999999999999956e226 or -6.7999999999999999e190 < x < -2.2999999999999999e129

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.2%

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

      1. distribute-rgt-in 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in x around inf 79.2%

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

   if -1.3199999999999999e-18 < x < 2.95000000000000005e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+284}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+226}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+190}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+129}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.32 \cdot 10^{-18} \lor \neg \left(x \leq 2.95 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9} \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55e-9) (not (<= x 5.0)))
   (* x (+ z y))
   (+ (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e-9) || !(x <= 5.0)) {
		tmp = x * (z + y);
	} 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 <= (-1.55d-9)) .or. (.not. (x <= 5.0d0))) then
        tmp = x * (z + y)
    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 <= -1.55e-9) || !(x <= 5.0)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55e-9) or not (x <= 5.0):
		tmp = x * (z + y)
	else:
		tmp = (z * 5.0) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55e-9) || !(x <= 5.0))
		tmp = Float64(x * Float64(z + y));
	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 <= -1.55e-9) || ~((x <= 5.0)))
		tmp = x * (z + y);
	else
		tmp = (z * 5.0) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55e-9], N[Not[LessEqual[x, 5.0]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(z * 5.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000002e-9 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%

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

   if -1.55000000000000002e-9 < x < 5

   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. Taylor expanded in y around inf 84.1%

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

      1. associate-/l* 83.9%

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

      2. distribute-rgt-out 84.6%

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

      3. +-commutative 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in x around 0 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 84.7%

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

      3. associate-*r/ 84.6%

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

   10. Simplified 84.6%

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

   11. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9} \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-20} \lor \neg \left(x \leq 6.8 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e-20) (not (<= x 6.8e-13))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e-20) || !(x <= 6.8e-13)) {
		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 <= (-7.2d-20)) .or. (.not. (x <= 6.8d-13))) 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 <= -7.2e-20) || !(x <= 6.8e-13)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e-20) or not (x <= 6.8e-13):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e-20) || !(x <= 6.8e-13))
		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 <= -7.2e-20) || ~((x <= 6.8e-13)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e-20], N[Not[LessEqual[x, 6.8e-13]], $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 < -7.19999999999999948e-20 or 6.80000000000000031e-13 < 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 -7.19999999999999948e-20 < x < 6.80000000000000031e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.3%

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

      1. distribute-rgt-in 80.3%

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

   5. Simplified 80.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-20} \lor \neg \left(x \leq 6.8 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-19} \lor \neg \left(x \leq 2.05 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-19) (not (<= x 2.05e-14))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-19) || !(x <= 2.05e-14)) {
		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 <= (-8.5d-19)) .or. (.not. (x <= 2.05d-14))) 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 <= -8.5e-19) || !(x <= 2.05e-14)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-19) or not (x <= 2.05e-14):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-19) || !(x <= 2.05e-14))
		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 <= -8.5e-19) || ~((x <= 2.05e-14)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-19], N[Not[LessEqual[x, 2.05e-14]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000003e-19 or 2.0500000000000001e-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 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 -8.50000000000000003e-19 < x < 2.0500000000000001e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-19} \lor \neg \left(x \leq 2.05 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-19} \lor \neg \left(x \leq 1.6 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e-19) (not (<= x 1.6e-13))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-19) || !(x <= 1.6e-13)) {
		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 <= (-3d-19)) .or. (.not. (x <= 1.6d-13))) 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 <= -3e-19) || !(x <= 1.6e-13)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e-19) or not (x <= 1.6e-13):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e-19) || !(x <= 1.6e-13))
		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 <= -3e-19) || ~((x <= 1.6e-13)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e-19], N[Not[LessEqual[x, 1.6e-13]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.99999999999999993e-19 or 1.6e-13 < 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 59.1%

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

   if -2.99999999999999993e-19 < x < 1.6e-13

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-19} \lor \neg \left(x \leq 1.6 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
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: 37.0% 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 41.2%

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

4. Final simplification 41.2%

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

Developer target: 97.8% 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 2024103 
(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)))