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

Percentage Accurate: 99.9% → 100.0%

Time: 6.3s

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: 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: 61.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+57}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-68}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+32} \lor \neg \left(x \leq 9.8 \cdot 10^{+92} \lor \neg \left(x \leq 6.5 \cdot 10^{+183}\right) \land x \leq 1.9 \cdot 10^{+267}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.8e+57)
   (* z x)
   (if (<= x -2.25e-17)
     (* x y)
     (if (<= x 1.08e-68)
       (* z 5.0)
       (if (or (<= x 2e+32)
               (not
                (or (<= x 9.8e+92)
                    (and (not (<= x 6.5e+183)) (<= x 1.9e+267)))))
         (* x y)
         (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.8e+57) {
		tmp = z * x;
	} else if (x <= -2.25e-17) {
		tmp = x * y;
	} else if (x <= 1.08e-68) {
		tmp = z * 5.0;
	} else if ((x <= 2e+32) || !((x <= 9.8e+92) || (!(x <= 6.5e+183) && (x <= 1.9e+267)))) {
		tmp = x * y;
	} 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 <= (-8.8d+57)) then
        tmp = z * x
    else if (x <= (-2.25d-17)) then
        tmp = x * y
    else if (x <= 1.08d-68) then
        tmp = z * 5.0d0
    else if ((x <= 2d+32) .or. (.not. (x <= 9.8d+92) .or. (.not. (x <= 6.5d+183)) .and. (x <= 1.9d+267))) then
        tmp = x * y
    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 <= -8.8e+57) {
		tmp = z * x;
	} else if (x <= -2.25e-17) {
		tmp = x * y;
	} else if (x <= 1.08e-68) {
		tmp = z * 5.0;
	} else if ((x <= 2e+32) || !((x <= 9.8e+92) || (!(x <= 6.5e+183) && (x <= 1.9e+267)))) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.8e+57:
		tmp = z * x
	elif x <= -2.25e-17:
		tmp = x * y
	elif x <= 1.08e-68:
		tmp = z * 5.0
	elif (x <= 2e+32) or not ((x <= 9.8e+92) or (not (x <= 6.5e+183) and (x <= 1.9e+267))):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.8e+57)
		tmp = Float64(z * x);
	elseif (x <= -2.25e-17)
		tmp = Float64(x * y);
	elseif (x <= 1.08e-68)
		tmp = Float64(z * 5.0);
	elseif ((x <= 2e+32) || !((x <= 9.8e+92) || (!(x <= 6.5e+183) && (x <= 1.9e+267))))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.8e+57)
		tmp = z * x;
	elseif (x <= -2.25e-17)
		tmp = x * y;
	elseif (x <= 1.08e-68)
		tmp = z * 5.0;
	elseif ((x <= 2e+32) || ~(((x <= 9.8e+92) || (~((x <= 6.5e+183)) && (x <= 1.9e+267)))))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.8e+57], N[(z * x), $MachinePrecision], If[LessEqual[x, -2.25e-17], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.08e-68], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2e+32], N[Not[Or[LessEqual[x, 9.8e+92], And[N[Not[LessEqual[x, 6.5e+183]], $MachinePrecision], LessEqual[x, 1.9e+267]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.8000000000000003e57 or 2.00000000000000011e32 < x < 9.8000000000000003e92 or 6.49999999999999983e183 < x < 1.90000000000000009e267

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. associate-/l* 74.4%

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

      2. distribute-rgt-out 87.6%

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

   5. Simplified 87.6%

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

      1. *-commutative 87.6%

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

      2. clear-num 87.6%

         \[\leadsto y \cdot \left(x + \left(5 + x\right) \cdot \color{blue}{\frac{1}{\frac{y}{z}}}\right) \]

      3. un-div-inv 87.6%

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

      4. +-commutative 87.6%

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

   7. Applied egg-rr 87.6%

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

   8. Taylor expanded in z around inf 49.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(5 \cdot \frac{1}{y} + \frac{x}{y}\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 49.1%

         \[\leadsto \color{blue}{\left(z \cdot \left(5 \cdot \frac{1}{y} + \frac{x}{y}\right)\right) \cdot y} \]

      2. distribute-rgt-in 36.0%

         \[\leadsto \color{blue}{\left(\left(5 \cdot \frac{1}{y}\right) \cdot z + \frac{x}{y} \cdot z\right)} \cdot y \]

      3. associate-*r/ 36.0%

         \[\leadsto \left(\color{blue}{\frac{5 \cdot 1}{y}} \cdot z + \frac{x}{y} \cdot z\right) \cdot y \]

      4. metadata-eval 36.0%

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

      5. associate-*l/ 36.0%

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

      6. associate-*r/ 36.0%

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

      7. associate-*l/ 40.1%

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

      8. associate-/l* 39.9%

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

      9. distribute-rgt-in 53.1%

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

      10. +-commutative 53.1%

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

      11. associate-*l* 68.6%

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

      12. +-commutative 68.6%

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

   10. Simplified 68.6%

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

   11. Taylor expanded in x around inf 65.6%

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

       1. *-commutative 65.6%

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

   13. Simplified 65.6%

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

   if -8.8000000000000003e57 < x < -2.24999999999999989e-17 or 1.0799999999999999e-68 < x < 2.00000000000000011e32 or 9.8000000000000003e92 < x < 6.49999999999999983e183 or 1.90000000000000009e267 < 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 68.3%

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

   if -2.24999999999999989e-17 < x < 1.0799999999999999e-68

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+57}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-68}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+32} \lor \neg \left(x \leq 9.8 \cdot 10^{+92} \lor \neg \left(x \leq 6.5 \cdot 10^{+183}\right) \land x \leq 1.9 \cdot 10^{+267}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5200000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5200000.0) (not (<= x 5.0)))
   (* x (+ z y))
   (+ (* x y) (* z 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5200000.0) || !(x <= 5.0)) {
		tmp = x * (z + y);
	} 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 <= (-5200000.0d0)) .or. (.not. (x <= 5.0d0))) then
        tmp = x * (z + y)
    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 <= -5200000.0) || !(x <= 5.0)) {
		tmp = x * (z + y);
	} else {
		tmp = (x * y) + (z * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5200000.0) or not (x <= 5.0):
		tmp = x * (z + y)
	else:
		tmp = (x * y) + (z * 5.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5200000.0) || !(x <= 5.0))
		tmp = Float64(x * Float64(z + y));
	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 <= -5200000.0) || ~((x <= 5.0)))
		tmp = x * (z + y);
	else
		tmp = (x * y) + (z * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5200000.0], N[Not[LessEqual[x, 5.0]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2e6 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 99.2%

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

      1. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   if -5.2e6 < 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 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5200000 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-15} \lor \neg \left(x \leq 7.6 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.4e-15) (not (<= x 7.6e-76))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.4e-15) || !(x <= 7.6e-76)) {
		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 <= (-4.4d-15)) .or. (.not. (x <= 7.6d-76))) 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 <= -4.4e-15) || !(x <= 7.6e-76)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.4e-15) or not (x <= 7.6e-76):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.4e-15) || !(x <= 7.6e-76))
		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 <= -4.4e-15) || ~((x <= 7.6e-76)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.4e-15], N[Not[LessEqual[x, 7.6e-76]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.39999999999999971e-15 or 7.6000000000000004e-76 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

   if -4.39999999999999971e-15 < x < 7.6000000000000004e-76

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-15} \lor \neg \left(x \leq 7.6 \cdot 10^{-76}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-17} \lor \neg \left(x \leq 3.8 \cdot 10^{-69}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e-17) (not (<= x 3.8e-69))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-17) || !(x <= 3.8e-69)) {
		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 <= (-1.7d-17)) .or. (.not. (x <= 3.8d-69))) 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 <= -1.7e-17) || !(x <= 3.8e-69)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e-17) or not (x <= 3.8e-69):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e-17) || !(x <= 3.8e-69))
		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 <= -1.7e-17) || ~((x <= 3.8e-69)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-17], N[Not[LessEqual[x, 3.8e-69]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e-17 or 3.7999999999999998e-69 < 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 53.4%

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

   if -1.6999999999999999e-17 < x < 3.7999999999999998e-69

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.7%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-17} \lor \neg \left(x \leq 3.8 \cdot 10^{-69}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 7: 36.4% 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 33.9%

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

4. Final simplification 33.9%

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

Developer target: 97.9% 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 2024111 
(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)))