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

Percentage Accurate: 99.9% → 100.0%

Time: 4.5s

Alternatives: 8

Speedup: 1.0×

• 20.4% 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: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16200000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+61} \lor \neg \left(x \leq 5 \cdot 10^{+195}\right) \land x \leq 1.08 \cdot 10^{+248}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -16200000.0)
   (* z x)
   (if (<= x 3.5e-50)
     (* z 5.0)
     (if (or (<= x 2.2e+61) (and (not (<= x 5e+195)) (<= x 1.08e+248)))
       (* x y)
       (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -16200000.0) {
		tmp = z * x;
	} else if (x <= 3.5e-50) {
		tmp = z * 5.0;
	} else if ((x <= 2.2e+61) || (!(x <= 5e+195) && (x <= 1.08e+248))) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-16200000.0d0)) then
        tmp = z * x
    else if (x <= 3.5d-50) then
        tmp = z * 5.0d0
    else if ((x <= 2.2d+61) .or. (.not. (x <= 5d+195)) .and. (x <= 1.08d+248)) then
        tmp = x * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -16200000.0) {
		tmp = z * x;
	} else if (x <= 3.5e-50) {
		tmp = z * 5.0;
	} else if ((x <= 2.2e+61) || (!(x <= 5e+195) && (x <= 1.08e+248))) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -16200000.0:
		tmp = z * x
	elif x <= 3.5e-50:
		tmp = z * 5.0
	elif (x <= 2.2e+61) or (not (x <= 5e+195) and (x <= 1.08e+248)):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -16200000.0)
		tmp = Float64(z * x);
	elseif (x <= 3.5e-50)
		tmp = Float64(z * 5.0);
	elseif ((x <= 2.2e+61) || (!(x <= 5e+195) && (x <= 1.08e+248)))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -16200000.0)
		tmp = z * x;
	elseif (x <= 3.5e-50)
		tmp = z * 5.0;
	elseif ((x <= 2.2e+61) || (~((x <= 5e+195)) && (x <= 1.08e+248)))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -16200000.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 3.5e-50], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.2e+61], And[N[Not[LessEqual[x, 5e+195]], $MachinePrecision], LessEqual[x, 1.08e+248]]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.62e7 or 2.2e61 < x < 4.9999999999999998e195 or 1.08e248 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. *-commutative 67.5%

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

      3. distribute-rgt-in 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in x around inf 66.6%

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

   if -1.62e7 < x < 3.49999999999999997e-50

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 73.2%

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

   if 3.49999999999999997e-50 < x < 2.2e61 or 4.9999999999999998e195 < x < 1.08e248

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 64.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16200000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+61} \lor \neg \left(x \leq 5 \cdot 10^{+195}\right) \land x \leq 1.08 \cdot 10^{+248}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 71.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-101} \lor \neg \left(z \leq 1.2 \cdot 10^{-273}\right) \land \left(z \leq 6.6 \cdot 10^{-218} \lor \neg \left(z \leq 1.85 \cdot 10^{-121}\right)\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.45e-101)
         (and (not (<= z 1.2e-273))
              (or (<= z 6.6e-218) (not (<= z 1.85e-121)))))
   (* z (+ 5.0 x))
   (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.45e-101) || (!(z <= 1.2e-273) && ((z <= 6.6e-218) || !(z <= 1.85e-121)))) {
		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 <= (-1.45d-101)) .or. (.not. (z <= 1.2d-273)) .and. (z <= 6.6d-218) .or. (.not. (z <= 1.85d-121))) 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 <= -1.45e-101) || (!(z <= 1.2e-273) && ((z <= 6.6e-218) || !(z <= 1.85e-121)))) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.45e-101) or (not (z <= 1.2e-273) and ((z <= 6.6e-218) or not (z <= 1.85e-121))):
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.45e-101) || (!(z <= 1.2e-273) && ((z <= 6.6e-218) || !(z <= 1.85e-121))))
		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 <= -1.45e-101) || (~((z <= 1.2e-273)) && ((z <= 6.6e-218) || ~((z <= 1.85e-121)))))
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.45e-101], And[N[Not[LessEqual[z, 1.2e-273]], $MachinePrecision], Or[LessEqual[z, 6.6e-218], N[Not[LessEqual[z, 1.85e-121]], $MachinePrecision]]]], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e-101 or 1.19999999999999991e-273 < z < 6.60000000000000046e-218 or 1.8500000000000001e-121 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. *-commutative 79.1%

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

      3. distribute-rgt-in 79.1%

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

   4. Simplified 79.1%

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

   if -1.45e-101 < z < 1.19999999999999991e-273 or 6.60000000000000046e-218 < z < 1.8500000000000001e-121

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 72.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-101} \lor \neg \left(z \leq 1.2 \cdot 10^{-273}\right) \land \left(z \leq 6.6 \cdot 10^{-218} \lor \neg \left(z \leq 1.85 \cdot 10^{-121}\right)\right):\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -430 \lor \neg \left(x \leq 5.1 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -430.0) (not (<= x 5.1e-48)))
   (* x (+ z y))
   (+ (* z 5.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -430.0) || !(x <= 5.1e-48)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-430.0d0)) .or. (.not. (x <= 5.1d-48))) then
        tmp = x * (z + y)
    else
        tmp = (z * 5.0d0) + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -430.0) || !(x <= 5.1e-48)) {
		tmp = x * (z + y);
	} else {
		tmp = (z * 5.0) + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -430.0) or not (x <= 5.1e-48):
		tmp = x * (z + y)
	else:
		tmp = (z * 5.0) + (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -430.0) || !(x <= 5.1e-48))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(z * 5.0) + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -430.0) || ~((x <= 5.1e-48)))
		tmp = x * (z + y);
	else
		tmp = (z * 5.0) + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -430.0], N[Not[LessEqual[x, 5.1e-48]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(z * 5.0), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -430 or 5.10000000000000011e-48 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 96.2%

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

      1. +-commutative 96.2%

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

   4. Simplified 96.2%

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

   if -430 < x < 5.10000000000000011e-48

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.7%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -430 \lor \neg \left(x \leq 5.1 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5 + z \cdot x\\ \end{array} \]

Alternative 5: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -500 \lor \neg \left(x \leq 2.4 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -500.0) (not (<= x 2.4e-48))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -500.0) || !(x <= 2.4e-48)) {
		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 <= (-500.0d0)) .or. (.not. (x <= 2.4d-48))) 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 <= -500.0) || !(x <= 2.4e-48)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -500.0) or not (x <= 2.4e-48):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -500.0) || !(x <= 2.4e-48))
		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 <= -500.0) || ~((x <= 2.4e-48)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -500.0], N[Not[LessEqual[x, 2.4e-48]], $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 < -500 or 2.4e-48 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 96.2%

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

      1. +-commutative 96.2%

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

   4. Simplified 96.2%

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

   if -500 < x < 2.4e-48

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.7%

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

      1. +-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. distribute-rgt-in 75.7%

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

   4. Simplified 75.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -500 \lor \neg \left(x \leq 2.4 \cdot 10^{-48}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (z * 5.0) + (x * (z + 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 = (z * 5.0d0) + (x * (z + y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 7: 62.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-48}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e-52) (* x y) (if (<= x 5.1e-48) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e-52) {
		tmp = x * y;
	} else if (x <= 5.1e-48) {
		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 <= (-7.5d-52)) then
        tmp = x * y
    else if (x <= 5.1d-48) 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 <= -7.5e-52) {
		tmp = x * y;
	} else if (x <= 5.1e-48) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e-52:
		tmp = x * y
	elif x <= 5.1e-48:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e-52)
		tmp = Float64(x * y);
	elseif (x <= 5.1e-48)
		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 <= -7.5e-52)
		tmp = x * y;
	elseif (x <= 5.1e-48)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e-52], N[(x * y), $MachinePrecision], If[LessEqual[x, 5.1e-48], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000006e-52 or 5.10000000000000011e-48 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 45.8%

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

   if -7.50000000000000006e-52 < x < 5.10000000000000011e-48

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 78.4%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-48}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 36.8% 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 37.5%

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

3. Final simplification 37.5%

   \[\leadsto z \cdot 5 \]

Developer target: 98.0% 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 2023200 
(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)))