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

Percentage Accurate: 99.9% → 100.0%

Time: 5.8s

Alternatives: 8

Speedup: 1.0×

• 20.8% 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: 60.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+218}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+179}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+136}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-42}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+53} \lor \neg \left(x \leq 2.5 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e+218)
   (* z x)
   (if (<= x -1.05e+179)
     (* x y)
     (if (<= x -1.2e+136)
       (* z x)
       (if (<= x -6.6e+44)
         (* x y)
         (if (<= x -5.0)
           (* z x)
           (if (<= x -1.55e-42)
             (* z 5.0)
             (if (<= x -2e-64)
               (* x y)
               (if (<= x 1.6e-97)
                 (* z 5.0)
                 (if (or (<= x 6.8e+53) (not (<= x 2.5e+135)))
                   (* x y)
                   (* z x)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e+218) {
		tmp = z * x;
	} else if (x <= -1.05e+179) {
		tmp = x * y;
	} else if (x <= -1.2e+136) {
		tmp = z * x;
	} else if (x <= -6.6e+44) {
		tmp = x * y;
	} else if (x <= -5.0) {
		tmp = z * x;
	} else if (x <= -1.55e-42) {
		tmp = z * 5.0;
	} else if (x <= -2e-64) {
		tmp = x * y;
	} else if (x <= 1.6e-97) {
		tmp = z * 5.0;
	} else if ((x <= 6.8e+53) || !(x <= 2.5e+135)) {
		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 <= (-2.8d+218)) then
        tmp = z * x
    else if (x <= (-1.05d+179)) then
        tmp = x * y
    else if (x <= (-1.2d+136)) then
        tmp = z * x
    else if (x <= (-6.6d+44)) then
        tmp = x * y
    else if (x <= (-5.0d0)) then
        tmp = z * x
    else if (x <= (-1.55d-42)) then
        tmp = z * 5.0d0
    else if (x <= (-2d-64)) then
        tmp = x * y
    else if (x <= 1.6d-97) then
        tmp = z * 5.0d0
    else if ((x <= 6.8d+53) .or. (.not. (x <= 2.5d+135))) 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 <= -2.8e+218) {
		tmp = z * x;
	} else if (x <= -1.05e+179) {
		tmp = x * y;
	} else if (x <= -1.2e+136) {
		tmp = z * x;
	} else if (x <= -6.6e+44) {
		tmp = x * y;
	} else if (x <= -5.0) {
		tmp = z * x;
	} else if (x <= -1.55e-42) {
		tmp = z * 5.0;
	} else if (x <= -2e-64) {
		tmp = x * y;
	} else if (x <= 1.6e-97) {
		tmp = z * 5.0;
	} else if ((x <= 6.8e+53) || !(x <= 2.5e+135)) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e+218:
		tmp = z * x
	elif x <= -1.05e+179:
		tmp = x * y
	elif x <= -1.2e+136:
		tmp = z * x
	elif x <= -6.6e+44:
		tmp = x * y
	elif x <= -5.0:
		tmp = z * x
	elif x <= -1.55e-42:
		tmp = z * 5.0
	elif x <= -2e-64:
		tmp = x * y
	elif x <= 1.6e-97:
		tmp = z * 5.0
	elif (x <= 6.8e+53) or not (x <= 2.5e+135):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e+218)
		tmp = Float64(z * x);
	elseif (x <= -1.05e+179)
		tmp = Float64(x * y);
	elseif (x <= -1.2e+136)
		tmp = Float64(z * x);
	elseif (x <= -6.6e+44)
		tmp = Float64(x * y);
	elseif (x <= -5.0)
		tmp = Float64(z * x);
	elseif (x <= -1.55e-42)
		tmp = Float64(z * 5.0);
	elseif (x <= -2e-64)
		tmp = Float64(x * y);
	elseif (x <= 1.6e-97)
		tmp = Float64(z * 5.0);
	elseif ((x <= 6.8e+53) || !(x <= 2.5e+135))
		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 <= -2.8e+218)
		tmp = z * x;
	elseif (x <= -1.05e+179)
		tmp = x * y;
	elseif (x <= -1.2e+136)
		tmp = z * x;
	elseif (x <= -6.6e+44)
		tmp = x * y;
	elseif (x <= -5.0)
		tmp = z * x;
	elseif (x <= -1.55e-42)
		tmp = z * 5.0;
	elseif (x <= -2e-64)
		tmp = x * y;
	elseif (x <= 1.6e-97)
		tmp = z * 5.0;
	elseif ((x <= 6.8e+53) || ~((x <= 2.5e+135)))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e+218], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.05e+179], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.2e+136], N[(z * x), $MachinePrecision], If[LessEqual[x, -6.6e+44], N[(x * y), $MachinePrecision], If[LessEqual[x, -5.0], N[(z * x), $MachinePrecision], If[LessEqual[x, -1.55e-42], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, -2e-64], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.6e-97], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 6.8e+53], N[Not[LessEqual[x, 2.5e+135]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7999999999999998e218 or -1.0499999999999999e179 < x < -1.2e136 or -6.60000000000000027e44 < x < -5 or 6.79999999999999995e53 < x < 2.50000000000000015e135

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in z around inf 71.7%

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

   if -2.7999999999999998e218 < x < -1.0499999999999999e179 or -1.2e136 < x < -6.60000000000000027e44 or -1.5500000000000001e-42 < x < -1.99999999999999993e-64 or 1.5999999999999999e-97 < x < 6.79999999999999995e53 or 2.50000000000000015e135 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.4%

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

   if -5 < x < -1.5500000000000001e-42 or -1.99999999999999993e-64 < x < 1.5999999999999999e-97

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.0%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+218}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+179}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+136}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-42}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+53} \lor \neg \left(x \leq 2.5 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -0.112:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-40}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -0.112)
     t_0
     (if (<= x -1.5e-40)
       (* z 5.0)
       (if (<= x -1.4e-64) (* x y) (if (<= x 1.6e-97) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -0.112) {
		tmp = t_0;
	} else if (x <= -1.5e-40) {
		tmp = z * 5.0;
	} else if (x <= -1.4e-64) {
		tmp = x * y;
	} else if (x <= 1.6e-97) {
		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 <= (-0.112d0)) then
        tmp = t_0
    else if (x <= (-1.5d-40)) then
        tmp = z * 5.0d0
    else if (x <= (-1.4d-64)) then
        tmp = x * y
    else if (x <= 1.6d-97) 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 <= -0.112) {
		tmp = t_0;
	} else if (x <= -1.5e-40) {
		tmp = z * 5.0;
	} else if (x <= -1.4e-64) {
		tmp = x * y;
	} else if (x <= 1.6e-97) {
		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 <= -0.112:
		tmp = t_0
	elif x <= -1.5e-40:
		tmp = z * 5.0
	elif x <= -1.4e-64:
		tmp = x * y
	elif x <= 1.6e-97:
		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 <= -0.112)
		tmp = t_0;
	elseif (x <= -1.5e-40)
		tmp = Float64(z * 5.0);
	elseif (x <= -1.4e-64)
		tmp = Float64(x * y);
	elseif (x <= 1.6e-97)
		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 <= -0.112)
		tmp = t_0;
	elseif (x <= -1.5e-40)
		tmp = z * 5.0;
	elseif (x <= -1.4e-64)
		tmp = x * y;
	elseif (x <= 1.6e-97)
		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, -0.112], t$95$0, If[LessEqual[x, -1.5e-40], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, -1.4e-64], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.6e-97], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.112000000000000002 or 1.5999999999999999e-97 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 94.1%

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

      1. +-commutative 94.1%

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

   5. Simplified 94.1%

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

   if -0.112000000000000002 < x < -1.5000000000000001e-40 or -1.40000000000000002e-64 < x < 1.5999999999999999e-97

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.0%

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

   if -1.5000000000000001e-40 < x < -1.40000000000000002e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.112:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-40}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -33000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-97}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -33000000000.0)
     t_0
     (if (<= x -4.8e-44)
       (* z (+ 5.0 x))
       (if (<= x -1.55e-64) (* x y) (if (<= x 1.42e-97) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -33000000000.0) {
		tmp = t_0;
	} else if (x <= -4.8e-44) {
		tmp = z * (5.0 + x);
	} else if (x <= -1.55e-64) {
		tmp = x * y;
	} else if (x <= 1.42e-97) {
		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 <= (-33000000000.0d0)) then
        tmp = t_0
    else if (x <= (-4.8d-44)) then
        tmp = z * (5.0d0 + x)
    else if (x <= (-1.55d-64)) then
        tmp = x * y
    else if (x <= 1.42d-97) 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 <= -33000000000.0) {
		tmp = t_0;
	} else if (x <= -4.8e-44) {
		tmp = z * (5.0 + x);
	} else if (x <= -1.55e-64) {
		tmp = x * y;
	} else if (x <= 1.42e-97) {
		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 <= -33000000000.0:
		tmp = t_0
	elif x <= -4.8e-44:
		tmp = z * (5.0 + x)
	elif x <= -1.55e-64:
		tmp = x * y
	elif x <= 1.42e-97:
		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 <= -33000000000.0)
		tmp = t_0;
	elseif (x <= -4.8e-44)
		tmp = Float64(z * Float64(5.0 + x));
	elseif (x <= -1.55e-64)
		tmp = Float64(x * y);
	elseif (x <= 1.42e-97)
		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 <= -33000000000.0)
		tmp = t_0;
	elseif (x <= -4.8e-44)
		tmp = z * (5.0 + x);
	elseif (x <= -1.55e-64)
		tmp = x * y;
	elseif (x <= 1.42e-97)
		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, -33000000000.0], t$95$0, If[LessEqual[x, -4.8e-44], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.55e-64], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.42e-97], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.3e10 or 1.42000000000000009e-97 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 95.0%

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

      1. +-commutative 95.0%

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

   5. Simplified 95.0%

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

   if -3.3e10 < x < -4.80000000000000017e-44

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 86.9%

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

      1. distribute-rgt-in 87.1%

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

   5. Simplified 87.1%

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

   if -4.80000000000000017e-44 < x < -1.55000000000000012e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -1.55000000000000012e-64 < x < 1.42000000000000009e-97

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 83.3%

      \[\leadsto \color{blue}{5 \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -33000000000:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-44}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-97}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0075 \lor \neg \left(x \leq -1.7 \cdot 10^{-42} \lor \neg \left(x \leq -1.8 \cdot 10^{-64}\right) \land x \leq 1.5 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0075)
         (not (or (<= x -1.7e-42) (and (not (<= x -1.8e-64)) (<= x 1.5e-97)))))
   (* x y)
   (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0075) || !((x <= -1.7e-42) || (!(x <= -1.8e-64) && (x <= 1.5e-97)))) {
		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 <= (-0.0075d0)) .or. (.not. (x <= (-1.7d-42)) .or. (.not. (x <= (-1.8d-64))) .and. (x <= 1.5d-97))) 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 <= -0.0075) || !((x <= -1.7e-42) || (!(x <= -1.8e-64) && (x <= 1.5e-97)))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0075) or not ((x <= -1.7e-42) or (not (x <= -1.8e-64) and (x <= 1.5e-97))):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0075) || !((x <= -1.7e-42) || (!(x <= -1.8e-64) && (x <= 1.5e-97))))
		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 <= -0.0075) || ~(((x <= -1.7e-42) || (~((x <= -1.8e-64)) && (x <= 1.5e-97)))))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0075], N[Not[Or[LessEqual[x, -1.7e-42], And[N[Not[LessEqual[x, -1.8e-64]], $MachinePrecision], LessEqual[x, 1.5e-97]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0074999999999999997 or -1.70000000000000011e-42 < x < -1.7999999999999999e-64 or 1.50000000000000012e-97 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 55.0%

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

   if -0.0074999999999999997 < x < -1.70000000000000011e-42 or -1.7999999999999999e-64 < x < 1.50000000000000012e-97

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0075 \lor \neg \left(x \leq -1.7 \cdot 10^{-42} \lor \neg \left(x \leq -1.8 \cdot 10^{-64}\right) \land x \leq 1.5 \cdot 10^{-97}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -5 or 5 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 97.9%

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

      1. +-commutative 97.9%

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

   5. Simplified 97.9%

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

   if -5 < x < 5

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      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 91.9%

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

      1. associate-/l* 91.7%

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

      2. distribute-rgt-out 92.1%

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

      3. +-commutative 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in x around 0 89.3%

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

4. Final simplification 93.8%

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

Alternative 7: 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 8: 36.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ z \cdot 5 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 34.9%

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

4. Final simplification 34.9%

   \[\leadsto z \cdot 5 \]
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 2024115 
(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)))