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

Percentage Accurate: 99.9% → 100.0%

Time: 5.7s

Alternatives: 9

Speedup: 1.0×

• 20.2% 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 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 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: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+159}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-59}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+102} \lor \neg \left(x \leq 4.8 \cdot 10^{+137}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e+159)
   (* z x)
   (if (<= x -1.5e-9)
     (* x y)
     (if (<= x -1.05e-79)
       (* z 5.0)
       (if (<= x -1.05e-140)
         (* x y)
         (if (<= x 5.6e-59)
           (* z 5.0)
           (if (or (<= x 9e+102) (not (<= x 4.8e+137))) (* x y) (* z x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e+159) {
		tmp = z * x;
	} else if (x <= -1.5e-9) {
		tmp = x * y;
	} else if (x <= -1.05e-79) {
		tmp = z * 5.0;
	} else if (x <= -1.05e-140) {
		tmp = x * y;
	} else if (x <= 5.6e-59) {
		tmp = z * 5.0;
	} else if ((x <= 9e+102) || !(x <= 4.8e+137)) {
		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 <= (-1.3d+159)) then
        tmp = z * x
    else if (x <= (-1.5d-9)) then
        tmp = x * y
    else if (x <= (-1.05d-79)) then
        tmp = z * 5.0d0
    else if (x <= (-1.05d-140)) then
        tmp = x * y
    else if (x <= 5.6d-59) then
        tmp = z * 5.0d0
    else if ((x <= 9d+102) .or. (.not. (x <= 4.8d+137))) 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 <= -1.3e+159) {
		tmp = z * x;
	} else if (x <= -1.5e-9) {
		tmp = x * y;
	} else if (x <= -1.05e-79) {
		tmp = z * 5.0;
	} else if (x <= -1.05e-140) {
		tmp = x * y;
	} else if (x <= 5.6e-59) {
		tmp = z * 5.0;
	} else if ((x <= 9e+102) || !(x <= 4.8e+137)) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e+159:
		tmp = z * x
	elif x <= -1.5e-9:
		tmp = x * y
	elif x <= -1.05e-79:
		tmp = z * 5.0
	elif x <= -1.05e-140:
		tmp = x * y
	elif x <= 5.6e-59:
		tmp = z * 5.0
	elif (x <= 9e+102) or not (x <= 4.8e+137):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e+159)
		tmp = Float64(z * x);
	elseif (x <= -1.5e-9)
		tmp = Float64(x * y);
	elseif (x <= -1.05e-79)
		tmp = Float64(z * 5.0);
	elseif (x <= -1.05e-140)
		tmp = Float64(x * y);
	elseif (x <= 5.6e-59)
		tmp = Float64(z * 5.0);
	elseif ((x <= 9e+102) || !(x <= 4.8e+137))
		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 <= -1.3e+159)
		tmp = z * x;
	elseif (x <= -1.5e-9)
		tmp = x * y;
	elseif (x <= -1.05e-79)
		tmp = z * 5.0;
	elseif (x <= -1.05e-140)
		tmp = x * y;
	elseif (x <= 5.6e-59)
		tmp = z * 5.0;
	elseif ((x <= 9e+102) || ~((x <= 4.8e+137)))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e+159], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.5e-9], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.05e-79], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, -1.05e-140], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.6e-59], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 9e+102], N[Not[LessEqual[x, 4.8e+137]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e159 or 9.00000000000000042e102 < x < 4.79999999999999966e137

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in y around 0 73.7%

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

   if -1.3e159 < x < -1.49999999999999999e-9 or -1.05e-79 < x < -1.05000000000000009e-140 or 5.59999999999999961e-59 < x < 9.00000000000000042e102 or 4.79999999999999966e137 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 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 z around 0 69.2%

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

   if -1.49999999999999999e-9 < x < -1.05e-79 or -1.05000000000000009e-140 < x < 5.59999999999999961e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.4%

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

      1. *-commutative 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+159}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-59}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+102} \lor \neg \left(x \leq 4.8 \cdot 10^{+137}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -0.0016:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-58}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -0.0016)
     t_0
     (if (<= x -1.05e-79)
       (* z 5.0)
       (if (<= x -1.2e-140) (* x y) (if (<= x 4.9e-58) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.0016) {
		tmp = t_0;
	} else if (x <= -1.05e-79) {
		tmp = z * 5.0;
	} else if (x <= -1.2e-140) {
		tmp = x * y;
	} else if (x <= 4.9e-58) {
		tmp = z * 5.0;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x * (z + y)
    if (x <= (-0.0016d0)) then
        tmp = t_0
    else if (x <= (-1.05d-79)) then
        tmp = z * 5.0d0
    else if (x <= (-1.2d-140)) then
        tmp = x * y
    else if (x <= 4.9d-58) then
        tmp = z * 5.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.0016) {
		tmp = t_0;
	} else if (x <= -1.05e-79) {
		tmp = z * 5.0;
	} else if (x <= -1.2e-140) {
		tmp = x * y;
	} else if (x <= 4.9e-58) {
		tmp = z * 5.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	tmp = 0
	if x <= -0.0016:
		tmp = t_0
	elif x <= -1.05e-79:
		tmp = z * 5.0
	elif x <= -1.2e-140:
		tmp = x * y
	elif x <= 4.9e-58:
		tmp = z * 5.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	tmp = 0.0
	if (x <= -0.0016)
		tmp = t_0;
	elseif (x <= -1.05e-79)
		tmp = Float64(z * 5.0);
	elseif (x <= -1.2e-140)
		tmp = Float64(x * y);
	elseif (x <= 4.9e-58)
		tmp = Float64(z * 5.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	tmp = 0.0;
	if (x <= -0.0016)
		tmp = t_0;
	elseif (x <= -1.05e-79)
		tmp = z * 5.0;
	elseif (x <= -1.2e-140)
		tmp = x * y;
	elseif (x <= 4.9e-58)
		tmp = z * 5.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0016], t$95$0, If[LessEqual[x, -1.05e-79], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, -1.2e-140], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.9e-58], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.00160000000000000008 or 4.9000000000000003e-58 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.0%

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

   if -0.00160000000000000008 < x < -1.05e-79 or -1.19999999999999993e-140 < x < 4.9000000000000003e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 83.4%

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

      1. *-commutative 83.4%

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

   5. Simplified 83.4%

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

   if -1.05e-79 < x < -1.19999999999999993e-140

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 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 z around 0 76.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0016:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-58}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ t_1 := z \cdot \left(5 + x\right)\\ \mathbf{if}\;x \leq -18500:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))) (t_1 (* z (+ 5.0 x))))
   (if (<= x -18500.0)
     t_0
     (if (<= x -1.7e-79)
       t_1
       (if (<= x -1.2e-140) (* x y) (if (<= x 6.5e-58) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double t_1 = z * (5.0 + x);
	double tmp;
	if (x <= -18500.0) {
		tmp = t_0;
	} else if (x <= -1.7e-79) {
		tmp = t_1;
	} else if (x <= -1.2e-140) {
		tmp = x * y;
	} else if (x <= 6.5e-58) {
		tmp = t_1;
	} else {
		tmp = t_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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z + y)
    t_1 = z * (5.0d0 + x)
    if (x <= (-18500.0d0)) then
        tmp = t_0
    else if (x <= (-1.7d-79)) then
        tmp = t_1
    else if (x <= (-1.2d-140)) then
        tmp = x * y
    else if (x <= 6.5d-58) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double t_1 = z * (5.0 + x);
	double tmp;
	if (x <= -18500.0) {
		tmp = t_0;
	} else if (x <= -1.7e-79) {
		tmp = t_1;
	} else if (x <= -1.2e-140) {
		tmp = x * y;
	} else if (x <= 6.5e-58) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z + y)
	t_1 = z * (5.0 + x)
	tmp = 0
	if x <= -18500.0:
		tmp = t_0
	elif x <= -1.7e-79:
		tmp = t_1
	elif x <= -1.2e-140:
		tmp = x * y
	elif x <= 6.5e-58:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z + y))
	t_1 = Float64(z * Float64(5.0 + x))
	tmp = 0.0
	if (x <= -18500.0)
		tmp = t_0;
	elseif (x <= -1.7e-79)
		tmp = t_1;
	elseif (x <= -1.2e-140)
		tmp = Float64(x * y);
	elseif (x <= 6.5e-58)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z + y);
	t_1 = z * (5.0 + x);
	tmp = 0.0;
	if (x <= -18500.0)
		tmp = t_0;
	elseif (x <= -1.7e-79)
		tmp = t_1;
	elseif (x <= -1.2e-140)
		tmp = x * y;
	elseif (x <= 6.5e-58)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -18500.0], t$95$0, If[LessEqual[x, -1.7e-79], t$95$1, If[LessEqual[x, -1.2e-140], N[(x * y), $MachinePrecision], If[LessEqual[x, 6.5e-58], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -18500 or 6.49999999999999964e-58 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.5%

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

   if -18500 < x < -1.69999999999999988e-79 or -1.19999999999999993e-140 < x < 6.49999999999999964e-58

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.2%

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

      1. +-commutative 84.2%

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

      2. distribute-rgt-in 84.2%

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

   5. Simplified 84.2%

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

   if -1.69999999999999988e-79 < x < -1.19999999999999993e-140

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 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 z around 0 76.1%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -18500:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-79}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-140}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+31} \lor \neg \left(z \leq 1.9 \cdot 10^{+24}\right) \land \left(z \leq 2.1 \cdot 10^{+88} \lor \neg \left(z \leq 1.16 \cdot 10^{+128}\right)\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+31)
         (and (not (<= z 1.9e+24)) (or (<= z 2.1e+88) (not (<= z 1.16e+128)))))
   (* z x)
   (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+31) || (!(z <= 1.9e+24) && ((z <= 2.1e+88) || !(z <= 1.16e+128)))) {
		tmp = z * x;
	} else {
		tmp = 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 ((z <= (-1.35d+31)) .or. (.not. (z <= 1.9d+24)) .and. (z <= 2.1d+88) .or. (.not. (z <= 1.16d+128))) then
        tmp = z * x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+31) || (!(z <= 1.9e+24) && ((z <= 2.1e+88) || !(z <= 1.16e+128)))) {
		tmp = z * x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e+31) or (not (z <= 1.9e+24) and ((z <= 2.1e+88) or not (z <= 1.16e+128))):
		tmp = z * x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e+31) || (!(z <= 1.9e+24) && ((z <= 2.1e+88) || !(z <= 1.16e+128))))
		tmp = Float64(z * x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e+31) || (~((z <= 1.9e+24)) && ((z <= 2.1e+88) || ~((z <= 1.16e+128)))))
		tmp = z * x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e+31], And[N[Not[LessEqual[z, 1.9e+24]], $MachinePrecision], Or[LessEqual[z, 2.1e+88], N[Not[LessEqual[z, 1.16e+128]], $MachinePrecision]]]], N[(z * x), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999993e31 or 1.90000000000000008e24 < z < 2.1e88 or 1.1600000000000001e128 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 52.9%

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

   4. Taylor expanded in y around 0 49.2%

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

   if -1.34999999999999993e31 < z < 1.90000000000000008e24 or 2.1e88 < z < 1.1600000000000001e128

   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-def 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 z around 0 67.6%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+31} \lor \neg \left(z \leq 1.9 \cdot 10^{+24}\right) \land \left(z \leq 2.1 \cdot 10^{+88} \lor \neg \left(z \leq 1.16 \cdot 10^{+128}\right)\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 0.66\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.0) (not (<= x 0.66))) (* x (+ z y)) (+ (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.0) || !(x <= 0.66)) {
		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 <= (-5.0d0)) .or. (.not. (x <= 0.66d0))) 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 <= -5.0) || !(x <= 0.66)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.0) or not (x <= 0.66):
		tmp = x * (z + y)
	else:
		tmp = (z * 5.0) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.0) || !(x <= 0.66))
		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 <= -5.0) || ~((x <= 0.66)))
		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, -5.0], N[Not[LessEqual[x, 0.66]], $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 < -5 or 0.660000000000000031 < 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%

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

   if -5 < x < 0.660000000000000031

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \lor \neg \left(x \leq 0.66\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 0.66:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.0)
   (* x (+ z y))
   (if (<= x 0.66) (+ (* z 5.0) (* x y)) (+ (* x y) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.0) {
		tmp = x * (z + y);
	} else if (x <= 0.66) {
		tmp = (z * 5.0) + (x * y);
	} else {
		tmp = (x * y) + (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 <= (-5.0d0)) then
        tmp = x * (z + y)
    else if (x <= 0.66d0) then
        tmp = (z * 5.0d0) + (x * y)
    else
        tmp = (x * y) + (z * x)
    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 + y);
	} else if (x <= 0.66) {
		tmp = (z * 5.0) + (x * y);
	} else {
		tmp = (x * y) + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.0:
		tmp = x * (z + y)
	elif x <= 0.66:
		tmp = (z * 5.0) + (x * y)
	else:
		tmp = (x * y) + (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.0)
		tmp = Float64(x * Float64(z + y));
	elseif (x <= 0.66)
		tmp = Float64(Float64(z * 5.0) + Float64(x * y));
	else
		tmp = Float64(Float64(x * y) + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.0)
		tmp = x * (z + y);
	elseif (x <= 0.66)
		tmp = (z * 5.0) + (x * y);
	else
		tmp = (x * y) + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.0], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.66], N[(N[(z * 5.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.0%

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

   if -5 < x < 0.660000000000000031

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.0%

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

   if 0.660000000000000031 < 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 99.5%

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

      1. +-commutative 99.5%

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

      2. distribute-lft-in 99.5%

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

   5. Applied egg-rr 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 0.66:\\ \;\;\;\;z \cdot 5 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot x\\ \end{array} \]
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 100.0%

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

3. Final simplification 100.0%

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

Alternative 9: 41.9% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x * y), $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. +-commutative 100.0%

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

   2. fma-def 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 z around 0 43.7%

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

6. Final simplification 43.7%

   \[\leadsto x \cdot y \]
7. 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 2024018 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

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