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

Percentage Accurate: 99.9% → 100.0%

Time: 3.8s

Alternatives: 7

Speedup: 1.0×

• 21.1% 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 99.6%

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

   1. +-commutative 99.6%

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

   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: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+159}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-76} \lor \neg \left(z \leq 1.26 \cdot 10^{+17}\right) \land z \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.6e+159)
   (* z x)
   (if (<= z -1.15e+135)
     (* z 5.0)
     (if (<= z -5.2e+118)
       (* z x)
       (if (or (<= z 1.7e-76) (and (not (<= z 1.26e+17)) (<= z 8.2e+82)))
         (* x y)
         (* z 5.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e+159) {
		tmp = z * x;
	} else if (z <= -1.15e+135) {
		tmp = z * 5.0;
	} else if (z <= -5.2e+118) {
		tmp = z * x;
	} else if ((z <= 1.7e-76) || (!(z <= 1.26e+17) && (z <= 8.2e+82))) {
		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 (z <= (-7.6d+159)) then
        tmp = z * x
    else if (z <= (-1.15d+135)) then
        tmp = z * 5.0d0
    else if (z <= (-5.2d+118)) then
        tmp = z * x
    else if ((z <= 1.7d-76) .or. (.not. (z <= 1.26d+17)) .and. (z <= 8.2d+82)) 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 (z <= -7.6e+159) {
		tmp = z * x;
	} else if (z <= -1.15e+135) {
		tmp = z * 5.0;
	} else if (z <= -5.2e+118) {
		tmp = z * x;
	} else if ((z <= 1.7e-76) || (!(z <= 1.26e+17) && (z <= 8.2e+82))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.6e+159:
		tmp = z * x
	elif z <= -1.15e+135:
		tmp = z * 5.0
	elif z <= -5.2e+118:
		tmp = z * x
	elif (z <= 1.7e-76) or (not (z <= 1.26e+17) and (z <= 8.2e+82)):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.6e+159)
		tmp = Float64(z * x);
	elseif (z <= -1.15e+135)
		tmp = Float64(z * 5.0);
	elseif (z <= -5.2e+118)
		tmp = Float64(z * x);
	elseif ((z <= 1.7e-76) || (!(z <= 1.26e+17) && (z <= 8.2e+82)))
		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 (z <= -7.6e+159)
		tmp = z * x;
	elseif (z <= -1.15e+135)
		tmp = z * 5.0;
	elseif (z <= -5.2e+118)
		tmp = z * x;
	elseif ((z <= 1.7e-76) || (~((z <= 1.26e+17)) && (z <= 8.2e+82)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.6e+159], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.15e+135], N[(z * 5.0), $MachinePrecision], If[LessEqual[z, -5.2e+118], N[(z * x), $MachinePrecision], If[Or[LessEqual[z, 1.7e-76], And[N[Not[LessEqual[z, 1.26e+17]], $MachinePrecision], LessEqual[z, 8.2e+82]]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999993e159 or -1.1500000000000001e135 < z < -5.20000000000000032e118

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 93.2%

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

      1. +-commutative 93.2%

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

      2. *-commutative 93.2%

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

      3. distribute-rgt-in 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in x around inf 69.9%

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

   if -7.5999999999999993e159 < z < -1.1500000000000001e135 or 1.7e-76 < z < 1.26e17 or 8.1999999999999999e82 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 62.0%

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

   if -5.20000000000000032e118 < z < 1.7e-76 or 1.26e17 < z < 8.1999999999999999e82

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 71.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+159}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+135}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-76} \lor \neg \left(z \leq 1.26 \cdot 10^{+17}\right) \land z \leq 8.2 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]

Alternative 3: 52.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-76} \lor \neg \left(z \leq 80000000\right) \land z \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.2e+129)
   (* z 5.0)
   (if (or (<= z 2e-76) (and (not (<= z 80000000.0)) (<= z 9.5e+82)))
     (* x y)
     (* z 5.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e+129) {
		tmp = z * 5.0;
	} else if ((z <= 2e-76) || (!(z <= 80000000.0) && (z <= 9.5e+82))) {
		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 (z <= (-5.2d+129)) then
        tmp = z * 5.0d0
    else if ((z <= 2d-76) .or. (.not. (z <= 80000000.0d0)) .and. (z <= 9.5d+82)) 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 (z <= -5.2e+129) {
		tmp = z * 5.0;
	} else if ((z <= 2e-76) || (!(z <= 80000000.0) && (z <= 9.5e+82))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.2e+129:
		tmp = z * 5.0
	elif (z <= 2e-76) or (not (z <= 80000000.0) and (z <= 9.5e+82)):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.2e+129)
		tmp = Float64(z * 5.0);
	elseif ((z <= 2e-76) || (!(z <= 80000000.0) && (z <= 9.5e+82)))
		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 (z <= -5.2e+129)
		tmp = z * 5.0;
	elseif ((z <= 2e-76) || (~((z <= 80000000.0)) && (z <= 9.5e+82)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.2e+129], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[z, 2e-76], And[N[Not[LessEqual[z, 80000000.0]], $MachinePrecision], LessEqual[z, 9.5e+82]]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000024e129 or 1.99999999999999985e-76 < z < 8e7 or 9.50000000000000049e82 < z

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 54.2%

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

   if -5.20000000000000024e129 < z < 1.99999999999999985e-76 or 8e7 < z < 9.50000000000000049e82

   1. Initial program 100.0%

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

   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 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-76} \lor \neg \left(z \leq 80000000\right) \land z \leq 9.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]

Alternative 4: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-41} \lor \neg \left(z \leq 1.5 \cdot 10^{-76}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-41) (not (<= z 1.5e-76))) (* z (+ 5.0 x)) (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-41) || !(z <= 1.5e-76)) {
		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 <= (-1.7d-41)) .or. (.not. (z <= 1.5d-76))) 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 <= -1.7e-41) || !(z <= 1.5e-76)) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-41) or not (z <= 1.5e-76):
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.7e-41) || !(z <= 1.5e-76))
		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 <= -1.7e-41) || ~((z <= 1.5e-76)))
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.7e-41], N[Not[LessEqual[z, 1.5e-76]], $MachinePrecision]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e-41 or 1.50000000000000012e-76 < z

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. *-commutative 83.5%

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

      3. distribute-rgt-in 84.2%

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

   4. Simplified 84.2%

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

   if -1.6999999999999999e-41 < z < 1.50000000000000012e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-41} \lor \neg \left(z \leq 1.5 \cdot 10^{-76}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 78.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+129} \lor \neg \left(z \leq 1.8 \cdot 10^{-76}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e+129) (not (<= z 1.8e-76))) (* z (+ 5.0 x)) (* x (+ z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+129) || !(z <= 1.8e-76)) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * (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 ((z <= (-4.2d+129)) .or. (.not. (z <= 1.8d-76))) then
        tmp = z * (5.0d0 + x)
    else
        tmp = x * (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+129) || !(z <= 1.8e-76)) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e+129) or not (z <= 1.8e-76):
		tmp = z * (5.0 + x)
	else:
		tmp = x * (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e+129) || !(z <= 1.8e-76))
		tmp = Float64(z * Float64(5.0 + x));
	else
		tmp = Float64(x * Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.2e+129) || ~((z <= 1.8e-76)))
		tmp = z * (5.0 + x);
	else
		tmp = x * (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e+129], N[Not[LessEqual[z, 1.8e-76]], $MachinePrecision]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999993e129 or 1.8e-76 < z

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. *-commutative 89.6%

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

      3. distribute-rgt-in 90.5%

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

   4. Simplified 90.5%

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

   if -4.19999999999999993e129 < z < 1.8e-76

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.2%

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

      1. +-commutative 82.2%

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

   4. Simplified 82.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+129} \lor \neg \left(z \leq 1.8 \cdot 10^{-76}\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]

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 99.6%

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

2. Final simplification 99.6%

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

Alternative 7: 36.0% 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 99.6%

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

2. Taylor expanded in x around 0 33.3%

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

3. Final simplification 33.3%

   \[\leadsto z \cdot 5 \]

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 2023230 
(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)))