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

Percentage Accurate: 99.9% → 100.0%

Time: 4.5s

Alternatives: 9

Speedup: 1.0×

• 20.7% 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. 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%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-58}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-133}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-42}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+94)
   (* x y)
   (if (<= y -1.08e-58)
     (* z 5.0)
     (if (<= y -1.3e-133)
       (* z x)
       (if (<= y 6.8e-140)
         (* z 5.0)
         (if (<= y 2e-55) (* z x) (if (<= y 8.5e-42) (* z 5.0) (* x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= -1.08e-58) {
		tmp = z * 5.0;
	} else if (y <= -1.3e-133) {
		tmp = z * x;
	} else if (y <= 6.8e-140) {
		tmp = z * 5.0;
	} else if (y <= 2e-55) {
		tmp = z * x;
	} else if (y <= 8.5e-42) {
		tmp = z * 5.0;
	} 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 (y <= (-2.3d+94)) then
        tmp = x * y
    else if (y <= (-1.08d-58)) then
        tmp = z * 5.0d0
    else if (y <= (-1.3d-133)) then
        tmp = z * x
    else if (y <= 6.8d-140) then
        tmp = z * 5.0d0
    else if (y <= 2d-55) then
        tmp = z * x
    else if (y <= 8.5d-42) then
        tmp = z * 5.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= -1.08e-58) {
		tmp = z * 5.0;
	} else if (y <= -1.3e-133) {
		tmp = z * x;
	} else if (y <= 6.8e-140) {
		tmp = z * 5.0;
	} else if (y <= 2e-55) {
		tmp = z * x;
	} else if (y <= 8.5e-42) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+94:
		tmp = x * y
	elif y <= -1.08e-58:
		tmp = z * 5.0
	elif y <= -1.3e-133:
		tmp = z * x
	elif y <= 6.8e-140:
		tmp = z * 5.0
	elif y <= 2e-55:
		tmp = z * x
	elif y <= 8.5e-42:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+94)
		tmp = Float64(x * y);
	elseif (y <= -1.08e-58)
		tmp = Float64(z * 5.0);
	elseif (y <= -1.3e-133)
		tmp = Float64(z * x);
	elseif (y <= 6.8e-140)
		tmp = Float64(z * 5.0);
	elseif (y <= 2e-55)
		tmp = Float64(z * x);
	elseif (y <= 8.5e-42)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+94)
		tmp = x * y;
	elseif (y <= -1.08e-58)
		tmp = z * 5.0;
	elseif (y <= -1.3e-133)
		tmp = z * x;
	elseif (y <= 6.8e-140)
		tmp = z * 5.0;
	elseif (y <= 2e-55)
		tmp = z * x;
	elseif (y <= 8.5e-42)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+94], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.08e-58], N[(z * 5.0), $MachinePrecision], If[LessEqual[y, -1.3e-133], N[(z * x), $MachinePrecision], If[LessEqual[y, 6.8e-140], N[(z * 5.0), $MachinePrecision], If[LessEqual[y, 2e-55], N[(z * x), $MachinePrecision], If[LessEqual[y, 8.5e-42], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e94 or 8.4999999999999996e-42 < y

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 85.3%

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

   if -2.3e94 < y < -1.08e-58 or -1.3e-133 < y < 6.80000000000000017e-140 or 1.99999999999999999e-55 < y < 8.4999999999999996e-42

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 53.2%

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

   if -1.08e-58 < y < -1.3e-133 or 6.80000000000000017e-140 < y < 1.99999999999999999e-55

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. distribute-rgt-in 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in x around inf 50.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-58}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-133}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-42}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-58}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-138}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{0.2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+94)
   (* x y)
   (if (<= y -1.08e-58)
     (* z 5.0)
     (if (<= y -8.4e-138)
       (* z x)
       (if (<= y 6.8e-140)
         (* z 5.0)
         (if (<= y 1.2e-55) (* z x) (if (<= y 7e-43) (/ z 0.2) (* x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= -1.08e-58) {
		tmp = z * 5.0;
	} else if (y <= -8.4e-138) {
		tmp = z * x;
	} else if (y <= 6.8e-140) {
		tmp = z * 5.0;
	} else if (y <= 1.2e-55) {
		tmp = z * x;
	} else if (y <= 7e-43) {
		tmp = z / 0.2;
	} 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 (y <= (-2.3d+94)) then
        tmp = x * y
    else if (y <= (-1.08d-58)) then
        tmp = z * 5.0d0
    else if (y <= (-8.4d-138)) then
        tmp = z * x
    else if (y <= 6.8d-140) then
        tmp = z * 5.0d0
    else if (y <= 1.2d-55) then
        tmp = z * x
    else if (y <= 7d-43) then
        tmp = z / 0.2d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= -1.08e-58) {
		tmp = z * 5.0;
	} else if (y <= -8.4e-138) {
		tmp = z * x;
	} else if (y <= 6.8e-140) {
		tmp = z * 5.0;
	} else if (y <= 1.2e-55) {
		tmp = z * x;
	} else if (y <= 7e-43) {
		tmp = z / 0.2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+94:
		tmp = x * y
	elif y <= -1.08e-58:
		tmp = z * 5.0
	elif y <= -8.4e-138:
		tmp = z * x
	elif y <= 6.8e-140:
		tmp = z * 5.0
	elif y <= 1.2e-55:
		tmp = z * x
	elif y <= 7e-43:
		tmp = z / 0.2
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+94)
		tmp = Float64(x * y);
	elseif (y <= -1.08e-58)
		tmp = Float64(z * 5.0);
	elseif (y <= -8.4e-138)
		tmp = Float64(z * x);
	elseif (y <= 6.8e-140)
		tmp = Float64(z * 5.0);
	elseif (y <= 1.2e-55)
		tmp = Float64(z * x);
	elseif (y <= 7e-43)
		tmp = Float64(z / 0.2);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+94)
		tmp = x * y;
	elseif (y <= -1.08e-58)
		tmp = z * 5.0;
	elseif (y <= -8.4e-138)
		tmp = z * x;
	elseif (y <= 6.8e-140)
		tmp = z * 5.0;
	elseif (y <= 1.2e-55)
		tmp = z * x;
	elseif (y <= 7e-43)
		tmp = z / 0.2;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+94], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.08e-58], N[(z * 5.0), $MachinePrecision], If[LessEqual[y, -8.4e-138], N[(z * x), $MachinePrecision], If[LessEqual[y, 6.8e-140], N[(z * 5.0), $MachinePrecision], If[LessEqual[y, 1.2e-55], N[(z * x), $MachinePrecision], If[LessEqual[y, 7e-43], N[(z / 0.2), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.3e94 or 6.99999999999999994e-43 < y

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 85.3%

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

   if -2.3e94 < y < -1.08e-58 or -8.39999999999999943e-138 < y < 6.80000000000000017e-140

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 51.4%

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

   if -1.08e-58 < y < -8.39999999999999943e-138 or 6.80000000000000017e-140 < y < 1.19999999999999996e-55

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. *-commutative 72.4%

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

      3. distribute-rgt-in 72.4%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in x around inf 50.6%

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

   if 1.19999999999999996e-55 < y < 6.99999999999999994e-43

   1. Initial program 99.6%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around 0 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-in 99.6%

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

   4. Simplified 99.6%

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

      1. flip-+ 99.6%

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

      2. associate-*r/ 99.6%

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

      3. metadata-eval 99.6%

         \[\leadsto \frac{z \cdot \left(\color{blue}{25} - x \cdot x\right)}{5 - x} \]

   6. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{z \cdot \left(25 - x \cdot x\right)}{5 - x}} \]
   7. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{z}{\frac{5 - x}{25 - x \cdot x}}} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{z}{\frac{5 - x}{25 - x \cdot x}}} \]

   9. Taylor expanded in x around 0 100.0%

      \[\leadsto \frac{z}{\color{blue}{0.2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-58}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-138}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-55}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-43}:\\ \;\;\;\;\frac{z}{0.2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94} \lor \neg \left(y \leq 8 \cdot 10^{-139}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e+94) (not (<= y 8e-139))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e+94) || !(y <= 8e-139)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.3d+94)) .or. (.not. (y <= 8d-139))) then
        tmp = x * (z + y)
    else
        tmp = z * (5.0d0 + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e+94) || !(y <= 8e-139)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e+94) or not (y <= 8e-139):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e+94) || !(y <= 8e-139))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * Float64(5.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.3e+94) || ~((y <= 8e-139)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e+94], N[Not[LessEqual[y, 8e-139]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e94 or 8.00000000000000024e-139 < y

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around inf 88.3%

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

      1. +-commutative 88.3%

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

   4. Simplified 88.3%

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

   if -2.3e94 < y < 8.00000000000000024e-139

   1. Initial program 99.8%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. *-commutative 81.8%

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

      3. distribute-rgt-in 81.8%

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

   4. Simplified 81.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94} \lor \neg \left(y \leq 8 \cdot 10^{-139}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 6: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+94) (* x y) (if (<= y 2e-41) (* z (+ 5.0 x)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+94) {
		tmp = x * y;
	} else if (y <= 2e-41) {
		tmp = z * (5.0 + 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 (y <= (-7d+94)) then
        tmp = x * y
    else if (y <= 2d-41) then
        tmp = z * (5.0d0 + 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 (y <= -7e+94) {
		tmp = x * y;
	} else if (y <= 2e-41) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e+94:
		tmp = x * y
	elif y <= 2e-41:
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+94)
		tmp = Float64(x * y);
	elseif (y <= 2e-41)
		tmp = Float64(z * Float64(5.0 + x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+94)
		tmp = x * y;
	elseif (y <= 2e-41)
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+94], N[(x * y), $MachinePrecision], If[LessEqual[y, 2e-41], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999994e94 or 2.00000000000000001e-41 < y

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 85.3%

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

   if -6.9999999999999994e94 < y < 2.00000000000000001e-41

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. *-commutative 79.6%

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

      3. distribute-rgt-in 79.6%

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

   4. Simplified 79.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

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. Final simplification 99.9%

   \[\leadsto x \cdot \left(z + y\right) + z \cdot 5 \]

Alternative 8: 53.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-127}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.3e+94) (* x y) (if (<= y 1.62e-127) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= 1.62e-127) {
		tmp = z * 5.0;
	} 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 (y <= (-2.3d+94)) then
        tmp = x * y
    else if (y <= 1.62d-127) then
        tmp = z * 5.0d0
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.3e+94) {
		tmp = x * y;
	} else if (y <= 1.62e-127) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.3e+94:
		tmp = x * y
	elif y <= 1.62e-127:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.3e+94)
		tmp = Float64(x * y);
	elseif (y <= 1.62e-127)
		tmp = Float64(z * 5.0);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.3e+94)
		tmp = x * y;
	elseif (y <= 1.62e-127)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.3e+94], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.62e-127], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e94 or 1.61999999999999993e-127 < y

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in y around inf 78.6%

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

   if -2.3e94 < y < 1.61999999999999993e-127

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]

   2. Taylor expanded in x around 0 47.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-127}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 36.9% 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. Taylor expanded in x around 0 30.7%

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

3. Final simplification 30.7%

   \[\leadsto z \cdot 5 \]

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 2023240 
(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)))