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

Percentage Accurate: 99.8% → 100.0%

Time: 4.5s

Alternatives: 7

Speedup: 1.0×

• 21.6% 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: 99.8% 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: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-65}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-9}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+182} \lor \neg \left(x \leq 2.3 \cdot 10^{+206}\right) \land x \leq 2.25 \cdot 10^{+291}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.9e+58)
   (* z x)
   (if (<= x -4.4e-25)
     (* x y)
     (if (<= x 1.1e-65)
       (* z 5.0)
       (if (<= x 2.3e-35)
         (* x y)
         (if (<= x 1.7e-9)
           (* z 5.0)
           (if (<= x 3e+71)
             (* x y)
             (if (or (<= x 3.5e+182)
                     (and (not (<= x 2.3e+206)) (<= x 2.25e+291)))
               (* z x)
               (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.9e+58) {
		tmp = z * x;
	} else if (x <= -4.4e-25) {
		tmp = x * y;
	} else if (x <= 1.1e-65) {
		tmp = z * 5.0;
	} else if (x <= 2.3e-35) {
		tmp = x * y;
	} else if (x <= 1.7e-9) {
		tmp = z * 5.0;
	} else if (x <= 3e+71) {
		tmp = x * y;
	} else if ((x <= 3.5e+182) || (!(x <= 2.3e+206) && (x <= 2.25e+291))) {
		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 (x <= (-3.9d+58)) then
        tmp = z * x
    else if (x <= (-4.4d-25)) then
        tmp = x * y
    else if (x <= 1.1d-65) then
        tmp = z * 5.0d0
    else if (x <= 2.3d-35) then
        tmp = x * y
    else if (x <= 1.7d-9) then
        tmp = z * 5.0d0
    else if (x <= 3d+71) then
        tmp = x * y
    else if ((x <= 3.5d+182) .or. (.not. (x <= 2.3d+206)) .and. (x <= 2.25d+291)) 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 (x <= -3.9e+58) {
		tmp = z * x;
	} else if (x <= -4.4e-25) {
		tmp = x * y;
	} else if (x <= 1.1e-65) {
		tmp = z * 5.0;
	} else if (x <= 2.3e-35) {
		tmp = x * y;
	} else if (x <= 1.7e-9) {
		tmp = z * 5.0;
	} else if (x <= 3e+71) {
		tmp = x * y;
	} else if ((x <= 3.5e+182) || (!(x <= 2.3e+206) && (x <= 2.25e+291))) {
		tmp = z * x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.9e+58:
		tmp = z * x
	elif x <= -4.4e-25:
		tmp = x * y
	elif x <= 1.1e-65:
		tmp = z * 5.0
	elif x <= 2.3e-35:
		tmp = x * y
	elif x <= 1.7e-9:
		tmp = z * 5.0
	elif x <= 3e+71:
		tmp = x * y
	elif (x <= 3.5e+182) or (not (x <= 2.3e+206) and (x <= 2.25e+291)):
		tmp = z * x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.9e+58)
		tmp = Float64(z * x);
	elseif (x <= -4.4e-25)
		tmp = Float64(x * y);
	elseif (x <= 1.1e-65)
		tmp = Float64(z * 5.0);
	elseif (x <= 2.3e-35)
		tmp = Float64(x * y);
	elseif (x <= 1.7e-9)
		tmp = Float64(z * 5.0);
	elseif (x <= 3e+71)
		tmp = Float64(x * y);
	elseif ((x <= 3.5e+182) || (!(x <= 2.3e+206) && (x <= 2.25e+291)))
		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 (x <= -3.9e+58)
		tmp = z * x;
	elseif (x <= -4.4e-25)
		tmp = x * y;
	elseif (x <= 1.1e-65)
		tmp = z * 5.0;
	elseif (x <= 2.3e-35)
		tmp = x * y;
	elseif (x <= 1.7e-9)
		tmp = z * 5.0;
	elseif (x <= 3e+71)
		tmp = x * y;
	elseif ((x <= 3.5e+182) || (~((x <= 2.3e+206)) && (x <= 2.25e+291)))
		tmp = z * x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.9e+58], N[(z * x), $MachinePrecision], If[LessEqual[x, -4.4e-25], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.1e-65], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 2.3e-35], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.7e-9], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 3e+71], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 3.5e+182], And[N[Not[LessEqual[x, 2.3e+206]], $MachinePrecision], LessEqual[x, 2.25e+291]]], N[(z * x), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9000000000000001e58 or 3.00000000000000013e71 < x < 3.50000000000000023e182 or 2.30000000000000016e206 < x < 2.24999999999999997e291

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.6%

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

      1. +-commutative 69.6%

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

      2. *-commutative 69.6%

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

      3. distribute-rgt-in 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in x around inf 69.6%

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

   if -3.9000000000000001e58 < x < -4.4000000000000004e-25 or 1.10000000000000011e-65 < x < 2.2999999999999999e-35 or 1.6999999999999999e-9 < x < 3.00000000000000013e71 or 3.50000000000000023e182 < x < 2.30000000000000016e206 or 2.24999999999999997e291 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 76.5%

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

   if -4.4000000000000004e-25 < x < 1.10000000000000011e-65 or 2.2999999999999999e-35 < x < 1.6999999999999999e-9

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+58}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-65}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-9}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+71}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+182} \lor \neg \left(x \leq 2.3 \cdot 10^{+206}\right) \land x \leq 2.25 \cdot 10^{+291}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z + y\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-10}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ z y))))
   (if (<= x -1.25e-24)
     t_0
     (if (<= x 3.4e-61)
       (* z 5.0)
       (if (<= x 1.8e-36) (* x y) (if (<= x 1.45e-10) (* z 5.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z + y);
	double tmp;
	if (x <= -1.25e-24) {
		tmp = t_0;
	} else if (x <= 3.4e-61) {
		tmp = z * 5.0;
	} else if (x <= 1.8e-36) {
		tmp = x * y;
	} else if (x <= 1.45e-10) {
		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 <= (-1.25d-24)) then
        tmp = t_0
    else if (x <= 3.4d-61) then
        tmp = z * 5.0d0
    else if (x <= 1.8d-36) then
        tmp = x * y
    else if (x <= 1.45d-10) 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 <= -1.25e-24) {
		tmp = t_0;
	} else if (x <= 3.4e-61) {
		tmp = z * 5.0;
	} else if (x <= 1.8e-36) {
		tmp = x * y;
	} else if (x <= 1.45e-10) {
		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 <= -1.25e-24:
		tmp = t_0
	elif x <= 3.4e-61:
		tmp = z * 5.0
	elif x <= 1.8e-36:
		tmp = x * y
	elif x <= 1.45e-10:
		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 <= -1.25e-24)
		tmp = t_0;
	elseif (x <= 3.4e-61)
		tmp = Float64(z * 5.0);
	elseif (x <= 1.8e-36)
		tmp = Float64(x * y);
	elseif (x <= 1.45e-10)
		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 <= -1.25e-24)
		tmp = t_0;
	elseif (x <= 3.4e-61)
		tmp = z * 5.0;
	elseif (x <= 1.8e-36)
		tmp = x * y;
	elseif (x <= 1.45e-10)
		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, -1.25e-24], t$95$0, If[LessEqual[x, 3.4e-61], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 1.8e-36], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.45e-10], N[(z * 5.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.24999999999999995e-24 or 1.4499999999999999e-10 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.9%

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

      1. +-commutative 98.9%

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

   4. Simplified 98.9%

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

   if -1.24999999999999995e-24 < x < 3.3999999999999998e-61 or 1.80000000000000016e-36 < x < 1.4499999999999999e-10

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.2%

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

   if 3.3999999999999998e-61 < x < 1.80000000000000016e-36

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 85.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-61}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-10}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]

Alternative 4: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-61} \lor \neg \left(x \leq 1.8 \cdot 10^{-36}\right) \land x \leq 8 \cdot 10^{-7}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.1e-25)
   (* x y)
   (if (or (<= x 6e-61) (and (not (<= x 1.8e-36)) (<= x 8e-7)))
     (* z 5.0)
     (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.1e-25) {
		tmp = x * y;
	} else if ((x <= 6e-61) || (!(x <= 1.8e-36) && (x <= 8e-7))) {
		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 (x <= (-3.1d-25)) then
        tmp = x * y
    else if ((x <= 6d-61) .or. (.not. (x <= 1.8d-36)) .and. (x <= 8d-7)) 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 (x <= -3.1e-25) {
		tmp = x * y;
	} else if ((x <= 6e-61) || (!(x <= 1.8e-36) && (x <= 8e-7))) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.1e-25:
		tmp = x * y
	elif (x <= 6e-61) or (not (x <= 1.8e-36) and (x <= 8e-7)):
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.1e-25)
		tmp = Float64(x * y);
	elseif ((x <= 6e-61) || (!(x <= 1.8e-36) && (x <= 8e-7)))
		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 (x <= -3.1e-25)
		tmp = x * y;
	elseif ((x <= 6e-61) || (~((x <= 1.8e-36)) && (x <= 8e-7)))
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.1e-25], N[(x * y), $MachinePrecision], If[Or[LessEqual[x, 6e-61], And[N[Not[LessEqual[x, 1.8e-36]], $MachinePrecision], LessEqual[x, 8e-7]]], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.09999999999999995e-25 or 6.00000000000000024e-61 < x < 1.80000000000000016e-36 or 7.9999999999999996e-7 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 51.3%

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

   if -3.09999999999999995e-25 < x < 6.00000000000000024e-61 or 1.80000000000000016e-36 < x < 7.9999999999999996e-7

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-61} \lor \neg \left(x \leq 1.8 \cdot 10^{-36}\right) \land x \leq 8 \cdot 10^{-7}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-183} \lor \neg \left(z \leq 4.7 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.1e-183) (not (<= z 4.7e+54))) (* z (+ 5.0 x)) (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e-183) || !(z <= 4.7e+54)) {
		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 ((z <= (-3.1d-183)) .or. (.not. (z <= 4.7d+54))) 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 ((z <= -3.1e-183) || !(z <= 4.7e+54)) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.1e-183) or not (z <= 4.7e+54):
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.1e-183) || !(z <= 4.7e+54))
		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 ((z <= -3.1e-183) || ~((z <= 4.7e+54)))
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.1e-183], N[Not[LessEqual[z, 4.7e+54]], $MachinePrecision]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e-183 or 4.69999999999999993e54 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 85.8%

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

      1. +-commutative 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-in 85.8%

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

   4. Simplified 85.8%

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

   if -3.1e-183 < z < 4.69999999999999993e54

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 71.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-183} \lor \neg \left(z \leq 4.7 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 99.8% 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 7: 36.3% 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 38.9%

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

3. Final simplification 38.9%

   \[\leadsto z \cdot 5 \]

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 2023199 
(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)))