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

Percentage Accurate: 99.9% → 100.0%

Time: 5.2s

Alternatives: 7

Speedup: 1.1×

• 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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 100.0

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

   5. lift-*.f64 N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 100.0

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-57}:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+139}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0)
   (* x z)
   (if (<= x 7.5e-57) (* 5.0 z) (if (<= x 1.45e+139) (* y x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = x * z;
	} else if (x <= 7.5e-57) {
		tmp = 5.0 * z;
	} else if (x <= 1.45e+139) {
		tmp = y * x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.0d0)) then
        tmp = x * z
    else if (x <= 7.5d-57) then
        tmp = 5.0d0 * z
    else if (x <= 1.45d+139) then
        tmp = y * x
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = x * z;
	} else if (x <= 7.5e-57) {
		tmp = 5.0 * z;
	} else if (x <= 1.45e+139) {
		tmp = y * x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.0:
		tmp = x * z
	elif x <= 7.5e-57:
		tmp = 5.0 * z
	elif x <= 1.45e+139:
		tmp = y * x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(x * z);
	elseif (x <= 7.5e-57)
		tmp = Float64(5.0 * z);
	elseif (x <= 1.45e+139)
		tmp = Float64(y * x);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.0)
		tmp = x * z;
	elseif (x <= 7.5e-57)
		tmp = 5.0 * z;
	elseif (x <= 1.45e+139)
		tmp = y * x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(x * z), $MachinePrecision], If[LessEqual[x, 7.5e-57], N[(5.0 * z), $MachinePrecision], If[LessEqual[x, 1.45e+139], N[(y * x), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5 or 1.4499999999999999e139 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 64.4

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

   5. Applied rewrites 64.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 63.8%

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

   if -5 < x < 7.49999999999999973e-57

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 69.4

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

   5. Applied rewrites 69.4%

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

   if 7.49999999999999973e-57 < x < 1.4499999999999999e139

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 54.8

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

   5. Applied rewrites 54.8%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45}:\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-68}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, 5, x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e-45)
   (* (+ 5.0 x) z)
   (if (<= z 2.25e-68) (* (+ z y) x) (fma z 5.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e-45) {
		tmp = (5.0 + x) * z;
	} else if (z <= 2.25e-68) {
		tmp = (z + y) * x;
	} else {
		tmp = fma(z, 5.0, (x * z));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e-45)
		tmp = Float64(Float64(5.0 + x) * z);
	elseif (z <= 2.25e-68)
		tmp = Float64(Float64(z + y) * x);
	else
		tmp = fma(z, 5.0, Float64(x * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e-45], N[(N[(5.0 + x), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 2.25e-68], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision], N[(z * 5.0 + N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000011e-45

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 86.4

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

   5. Applied rewrites 86.4%

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

   if -3.00000000000000011e-45 < z < 2.25e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 24.2

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

   5. Applied rewrites 24.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 11.0%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. +-commutative N/A

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

       4. lower-+.f64 86.9

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

   11. Applied rewrites 86.9%

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

   if 2.25e-68 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 86.7

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

   5. Applied rewrites 86.7%

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

   7. Applied rewrites 86.8%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{5}, x \cdot z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-45) (not (<= z 2.25e-68))) (* (+ 5.0 x) z) (* (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-45) || !(z <= 2.25e-68)) {
		tmp = (5.0 + x) * z;
	} else {
		tmp = (z + y) * 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 ((z <= (-3d-45)) .or. (.not. (z <= 2.25d-68))) then
        tmp = (5.0d0 + x) * z
    else
        tmp = (z + y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-45) || !(z <= 2.25e-68)) {
		tmp = (5.0 + x) * z;
	} else {
		tmp = (z + y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-45) or not (z <= 2.25e-68):
		tmp = (5.0 + x) * z
	else:
		tmp = (z + y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3e-45) || !(z <= 2.25e-68))
		tmp = Float64(Float64(5.0 + x) * z);
	else
		tmp = Float64(Float64(z + y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3e-45) || ~((z <= 2.25e-68)))
		tmp = (5.0 + x) * z;
	else
		tmp = (z + y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-45], N[Not[LessEqual[z, 2.25e-68]], $MachinePrecision]], N[(N[(5.0 + x), $MachinePrecision] * z), $MachinePrecision], N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000011e-45 or 2.25e-68 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 86.6

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

   5. Applied rewrites 86.6%

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

   if -3.00000000000000011e-45 < z < 2.25e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 24.2

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

   5. Applied rewrites 24.2%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 11.0%

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

   9. Taylor expanded in x around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. +-commutative N/A

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

       4. lower-+.f64 86.9

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

   11. Applied rewrites 86.9%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-45} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e-55) (not (<= z 2.25e-68))) (* (+ 5.0 x) z) (* y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-55) || !(z <= 2.25e-68)) {
		tmp = (5.0 + x) * z;
	} else {
		tmp = y * 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 ((z <= (-3.5d-55)) .or. (.not. (z <= 2.25d-68))) then
        tmp = (5.0d0 + x) * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-55) || !(z <= 2.25e-68)) {
		tmp = (5.0 + x) * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e-55) or not (z <= 2.25e-68):
		tmp = (5.0 + x) * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e-55) || !(z <= 2.25e-68))
		tmp = Float64(Float64(5.0 + x) * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.5e-55) || ~((z <= 2.25e-68)))
		tmp = (5.0 + x) * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e-55], N[Not[LessEqual[z, 2.25e-68]], $MachinePrecision]], N[(N[(5.0 + x), $MachinePrecision] * z), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000025e-55 or 2.25e-68 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 86.2

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

   5. Applied rewrites 86.2%

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

   if -3.50000000000000025e-55 < z < 2.25e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 2.25 \cdot 10^{-68}\right):\\ \;\;\;\;\left(5 + x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 0.00034\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.0) (not (<= x 0.00034))) (* x z) (* 5.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 0.00034)) {
		tmp = x * z;
	} else {
		tmp = 5.0 * 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 <= (-5.0d0)) .or. (.not. (x <= 0.00034d0))) then
        tmp = x * z
    else
        tmp = 5.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 0.00034)) {
		tmp = x * z;
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.0) or not (x <= 0.00034):
		tmp = x * z
	else:
		tmp = 5.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.0) || !(x <= 0.00034))
		tmp = Float64(x * z);
	else
		tmp = Float64(5.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.0) || ~((x <= 0.00034)))
		tmp = x * z;
	else
		tmp = 5.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.0], N[Not[LessEqual[x, 0.00034]], $MachinePrecision]], N[(x * z), $MachinePrecision], N[(5.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5 or 3.4e-4 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-in N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 60.4

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

   5. Applied rewrites 60.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 59.3%

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

   if -5 < x < 3.4e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 67.6

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

   5. Applied rewrites 67.6%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 0.00034\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 27.0% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

   1. distribute-rgt-in N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-+.f64 63.9

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

5. Applied rewrites 63.9%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 33.3%

   \[\leadsto x \cdot \color{blue}{z} \]
9. Add Preprocessing

Developer Target 1: 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 2024320 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

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

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