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

Percentage Accurate: 99.9% → 100.0%

Time: 5.2s

Alternatives: 8

Speedup: 1.0×

• 21.0% 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 99.5%

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

   1. +-commutative 99.5%

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

   2. fma-def 99.9%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. distribute-lft-in 98.7%

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

   2. associate-+l+ 98.7%

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

   3. *-commutative 98.7%

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

   4. fma-def 99.1%

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

   5. distribute-lft-out 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 3: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+148}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-67}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1600000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+169}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.1e+148)
   (* x y)
   (if (<= x -8.2e+99)
     (* z x)
     (if (<= x -4.6e-8)
       (* x y)
       (if (<= x 3e-67)
         (* z 5.0)
         (if (<= x 1600000000000.0)
           (* x y)
           (if (<= x 6.6e+169) (* z x) (* x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.1e+148) {
		tmp = x * y;
	} else if (x <= -8.2e+99) {
		tmp = z * x;
	} else if (x <= -4.6e-8) {
		tmp = x * y;
	} else if (x <= 3e-67) {
		tmp = z * 5.0;
	} else if (x <= 1600000000000.0) {
		tmp = x * y;
	} else if (x <= 6.6e+169) {
		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 <= (-3.1d+148)) then
        tmp = x * y
    else if (x <= (-8.2d+99)) then
        tmp = z * x
    else if (x <= (-4.6d-8)) then
        tmp = x * y
    else if (x <= 3d-67) then
        tmp = z * 5.0d0
    else if (x <= 1600000000000.0d0) then
        tmp = x * y
    else if (x <= 6.6d+169) 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 <= -3.1e+148) {
		tmp = x * y;
	} else if (x <= -8.2e+99) {
		tmp = z * x;
	} else if (x <= -4.6e-8) {
		tmp = x * y;
	} else if (x <= 3e-67) {
		tmp = z * 5.0;
	} else if (x <= 1600000000000.0) {
		tmp = x * y;
	} else if (x <= 6.6e+169) {
		tmp = z * x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.1e+148:
		tmp = x * y
	elif x <= -8.2e+99:
		tmp = z * x
	elif x <= -4.6e-8:
		tmp = x * y
	elif x <= 3e-67:
		tmp = z * 5.0
	elif x <= 1600000000000.0:
		tmp = x * y
	elif x <= 6.6e+169:
		tmp = z * x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.1e+148)
		tmp = Float64(x * y);
	elseif (x <= -8.2e+99)
		tmp = Float64(z * x);
	elseif (x <= -4.6e-8)
		tmp = Float64(x * y);
	elseif (x <= 3e-67)
		tmp = Float64(z * 5.0);
	elseif (x <= 1600000000000.0)
		tmp = Float64(x * y);
	elseif (x <= 6.6e+169)
		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 <= -3.1e+148)
		tmp = x * y;
	elseif (x <= -8.2e+99)
		tmp = z * x;
	elseif (x <= -4.6e-8)
		tmp = x * y;
	elseif (x <= 3e-67)
		tmp = z * 5.0;
	elseif (x <= 1600000000000.0)
		tmp = x * y;
	elseif (x <= 6.6e+169)
		tmp = z * x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.1e+148], N[(x * y), $MachinePrecision], If[LessEqual[x, -8.2e+99], N[(z * x), $MachinePrecision], If[LessEqual[x, -4.6e-8], N[(x * y), $MachinePrecision], If[LessEqual[x, 3e-67], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 1600000000000.0], N[(x * y), $MachinePrecision], If[LessEqual[x, 6.6e+169], N[(z * x), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.09999999999999975e148 or -8.19999999999999959e99 < x < -4.6000000000000002e-8 or 3.00000000000000032e-67 < x < 1.6e12 or 6.5999999999999994e169 < x

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 64.5%

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

   if -3.09999999999999975e148 < x < -8.19999999999999959e99 or 1.6e12 < x < 6.5999999999999994e169

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. *-commutative 68.5%

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

      3. distribute-rgt-in 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in x around inf 67.7%

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

   if -4.6000000000000002e-8 < x < 3.00000000000000032e-67

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 75.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+148}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-67}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1600000000000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+169}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1100000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+115} \lor \neg \left(y \leq 5 \cdot 10^{+189}\right) \land y \leq 5.7 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1100000.0)
   (* x y)
   (if (or (<= y 3.9e+115) (and (not (<= y 5e+189)) (<= y 5.7e+226)))
     (* z (+ 5.0 x))
     (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1100000.0) {
		tmp = x * y;
	} else if ((y <= 3.9e+115) || (!(y <= 5e+189) && (y <= 5.7e+226))) {
		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 <= (-1100000.0d0)) then
        tmp = x * y
    else if ((y <= 3.9d+115) .or. (.not. (y <= 5d+189)) .and. (y <= 5.7d+226)) 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 <= -1100000.0) {
		tmp = x * y;
	} else if ((y <= 3.9e+115) || (!(y <= 5e+189) && (y <= 5.7e+226))) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1100000.0:
		tmp = x * y
	elif (y <= 3.9e+115) or (not (y <= 5e+189) and (y <= 5.7e+226)):
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1100000.0)
		tmp = Float64(x * y);
	elseif ((y <= 3.9e+115) || (!(y <= 5e+189) && (y <= 5.7e+226)))
		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 <= -1100000.0)
		tmp = x * y;
	elseif ((y <= 3.9e+115) || (~((y <= 5e+189)) && (y <= 5.7e+226)))
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1100000.0], N[(x * y), $MachinePrecision], If[Or[LessEqual[y, 3.9e+115], And[N[Not[LessEqual[y, 5e+189]], $MachinePrecision], LessEqual[y, 5.7e+226]]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e6 or 3.90000000000000006e115 < y < 5.0000000000000004e189 or 5.69999999999999948e226 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 73.3%

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

   if -1.1e6 < y < 3.90000000000000006e115 or 5.0000000000000004e189 < y < 5.69999999999999948e226

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. *-commutative 82.0%

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

      3. distribute-rgt-in 82.7%

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

   4. Simplified 82.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1100000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+115} \lor \neg \left(y \leq 5 \cdot 10^{+189}\right) \land y \leq 5.7 \cdot 10^{+226}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -28 \lor \neg \left(x \leq 1.75 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -28.0) (not (<= x 1.75e-65))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -28.0) || !(x <= 1.75e-65)) {
		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 ((x <= (-28.0d0)) .or. (.not. (x <= 1.75d-65))) 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 ((x <= -28.0) || !(x <= 1.75e-65)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -28.0) or not (x <= 1.75e-65):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -28.0) || !(x <= 1.75e-65))
		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 ((x <= -28.0) || ~((x <= 1.75e-65)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -28.0], N[Not[LessEqual[x, 1.75e-65]], $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 x < -28 or 1.75000000000000002e-65 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 96.1%

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

      1. +-commutative 96.1%

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

   4. Simplified 96.1%

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

   if -28 < x < 1.75000000000000002e-65

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. *-commutative 76.4%

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

      3. distribute-rgt-in 76.4%

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

   4. Simplified 76.4%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -28 \lor \neg \left(x \leq 1.75 \cdot 10^{-65}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 6: 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 99.5%

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

2. Final simplification 99.5%

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

Alternative 7: 60.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e-8) (* x y) (if (<= x 7.2e-66) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e-8) {
		tmp = x * y;
	} else if (x <= 7.2e-66) {
		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 <= (-4.6d-8)) then
        tmp = x * y
    else if (x <= 7.2d-66) 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 <= -4.6e-8) {
		tmp = x * y;
	} else if (x <= 7.2e-66) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e-8:
		tmp = x * y
	elif x <= 7.2e-66:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e-8)
		tmp = Float64(x * y);
	elseif (x <= 7.2e-66)
		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 <= -4.6e-8)
		tmp = x * y;
	elseif (x <= 7.2e-66)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e-8], N[(x * y), $MachinePrecision], If[LessEqual[x, 7.2e-66], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6000000000000002e-8 or 7.20000000000000025e-66 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 53.8%

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

   if -4.6000000000000002e-8 < x < 7.20000000000000025e-66

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 75.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 36.5% 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 99.5%

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

2. Taylor expanded in x around 0 39.0%

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

3. Final simplification 39.0%

   \[\leadsto z \cdot 5 \]

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 2023229 
(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)))