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

Percentage Accurate: 99.9% → 100.0%

Time: 4.4s

Alternatives: 8

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: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-43}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+238}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -17000000.0)
   (* z x)
   (if (<= x 3e-43)
     (* z 5.0)
     (if (<= x 2.1e+17) (* x y) (if (<= x 5e+238) (* z x) (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -17000000.0) {
		tmp = z * x;
	} else if (x <= 3e-43) {
		tmp = z * 5.0;
	} else if (x <= 2.1e+17) {
		tmp = x * y;
	} else if (x <= 5e+238) {
		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 <= (-17000000.0d0)) then
        tmp = z * x
    else if (x <= 3d-43) then
        tmp = z * 5.0d0
    else if (x <= 2.1d+17) then
        tmp = x * y
    else if (x <= 5d+238) 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 <= -17000000.0) {
		tmp = z * x;
	} else if (x <= 3e-43) {
		tmp = z * 5.0;
	} else if (x <= 2.1e+17) {
		tmp = x * y;
	} else if (x <= 5e+238) {
		tmp = z * x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -17000000.0:
		tmp = z * x
	elif x <= 3e-43:
		tmp = z * 5.0
	elif x <= 2.1e+17:
		tmp = x * y
	elif x <= 5e+238:
		tmp = z * x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -17000000.0)
		tmp = Float64(z * x);
	elseif (x <= 3e-43)
		tmp = Float64(z * 5.0);
	elseif (x <= 2.1e+17)
		tmp = Float64(x * y);
	elseif (x <= 5e+238)
		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 <= -17000000.0)
		tmp = z * x;
	elseif (x <= 3e-43)
		tmp = z * 5.0;
	elseif (x <= 2.1e+17)
		tmp = x * y;
	elseif (x <= 5e+238)
		tmp = z * x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -17000000.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 3e-43], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 2.1e+17], N[(x * y), $MachinePrecision], If[LessEqual[x, 5e+238], N[(z * x), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e7 or 2.1e17 < x < 4.99999999999999995e238

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. +-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. distribute-rgt-in 64.2%

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

   4. Simplified 64.2%

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

   5. Taylor expanded in x around inf 63.7%

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

   if -1.7e7 < x < 3.00000000000000003e-43

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 70.5%

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

   if 3.00000000000000003e-43 < x < 2.1e17 or 4.99999999999999995e238 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 69.8%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -17000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-43}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+238}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17000000:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 0.52:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -17000000.0)
   (* x (+ z y))
   (if (<= x 0.52) (- (* x y) (* z -5.0)) (+ (* x y) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -17000000.0) {
		tmp = x * (z + y);
	} else if (x <= 0.52) {
		tmp = (x * y) - (z * -5.0);
	} else {
		tmp = (x * y) + (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 <= (-17000000.0d0)) then
        tmp = x * (z + y)
    else if (x <= 0.52d0) then
        tmp = (x * y) - (z * (-5.0d0))
    else
        tmp = (x * y) + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -17000000.0) {
		tmp = x * (z + y);
	} else if (x <= 0.52) {
		tmp = (x * y) - (z * -5.0);
	} else {
		tmp = (x * y) + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -17000000.0:
		tmp = x * (z + y)
	elif x <= 0.52:
		tmp = (x * y) - (z * -5.0)
	else:
		tmp = (x * y) + (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -17000000.0)
		tmp = Float64(x * Float64(z + y));
	elseif (x <= 0.52)
		tmp = Float64(Float64(x * y) - Float64(z * -5.0));
	else
		tmp = Float64(Float64(x * y) + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -17000000.0)
		tmp = x * (z + y);
	elseif (x <= 0.52)
		tmp = (x * y) - (z * -5.0);
	else
		tmp = (x * y) + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -17000000.0], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.52], N[(N[(x * y), $MachinePrecision] - N[(z * -5.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7e7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.0%

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

      1. +-commutative 99.0%

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

   4. Simplified 99.0%

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

   if -1.7e7 < x < 0.52000000000000002

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      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. Taylor expanded in z around -inf 99.8%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(-1 \cdot x - 5\right)\right) + y \cdot x} \]
   5. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{y \cdot x + -1 \cdot \left(z \cdot \left(-1 \cdot x - 5\right)\right)} \]

      2. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -1 \cdot \left(z \cdot \left(-1 \cdot x - 5\right)\right)\right)} \]

      3. mul-1-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{-z \cdot \left(-1 \cdot x - 5\right)}\right) \]

      4. fma-neg 99.8%

         \[\leadsto \color{blue}{y \cdot x - z \cdot \left(-1 \cdot x - 5\right)} \]

      5. sub-neg 99.8%

         \[\leadsto y \cdot x - z \cdot \color{blue}{\left(-1 \cdot x + \left(-5\right)\right)} \]

      6. +-commutative 99.8%

         \[\leadsto y \cdot x - z \cdot \color{blue}{\left(\left(-5\right) + -1 \cdot x\right)} \]

      7. mul-1-neg 99.8%

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

      8. unsub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 99.4%

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

      1. *-commutative 99.4%

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

   9. Simplified 99.4%

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

   if 0.52000000000000002 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.0%

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

      1. +-commutative 99.0%

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

   4. Simplified 99.0%

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

   5. Taylor expanded in z around 0 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -17000000:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 0.52:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot x\\ \end{array} \]

Alternative 4: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+72} \lor \neg \left(y \leq 4.4 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.3e+72) (not (<= y 4.4e-17))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.3e+72) || !(y <= 4.4e-17)) {
		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 <= (-1.3d+72)) .or. (.not. (y <= 4.4d-17))) 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 <= -1.3e+72) || !(y <= 4.4e-17)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.3e+72) or not (y <= 4.4e-17):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.3e+72) || !(y <= 4.4e-17))
		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 <= -1.3e+72) || ~((y <= 4.4e-17)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.3e+72], N[Not[LessEqual[y, 4.4e-17]], $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 < -1.29999999999999991e72 or 4.4e-17 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 76.8%

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

      1. +-commutative 76.8%

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

   4. Simplified 76.8%

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

   if -1.29999999999999991e72 < y < 4.4e-17

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. *-commutative 89.5%

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

      3. distribute-rgt-in 89.5%

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

   4. Simplified 89.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+72} \lor \neg \left(y \leq 4.4 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]

Alternative 5: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+161}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 0.37:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+161) (* x y) (if (<= y 0.37) (* z (+ 5.0 x)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+161) {
		tmp = x * y;
	} else if (y <= 0.37) {
		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 <= (-3.4d+161)) then
        tmp = x * y
    else if (y <= 0.37d0) 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 <= -3.4e+161) {
		tmp = x * y;
	} else if (y <= 0.37) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+161:
		tmp = x * y
	elif y <= 0.37:
		tmp = z * (5.0 + x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+161)
		tmp = Float64(x * y);
	elseif (y <= 0.37)
		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 <= -3.4e+161)
		tmp = x * y;
	elseif (y <= 0.37)
		tmp = z * (5.0 + x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+161], N[(x * y), $MachinePrecision], If[LessEqual[y, 0.37], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999993e161 or 0.37 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 73.9%

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

   if -3.39999999999999993e161 < y < 0.37

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. *-commutative 85.4%

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

      3. distribute-rgt-in 85.4%

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

   4. Simplified 85.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+161}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 0.37:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 7: 61.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-46}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e-11) (* x y) (if (<= x 3.5e-46) (* z 5.0) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e-11) {
		tmp = x * y;
	} else if (x <= 3.5e-46) {
		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 <= (-1.9d-11)) then
        tmp = x * y
    else if (x <= 3.5d-46) 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 <= -1.9e-11) {
		tmp = x * y;
	} else if (x <= 3.5e-46) {
		tmp = z * 5.0;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e-11:
		tmp = x * y
	elif x <= 3.5e-46:
		tmp = z * 5.0
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e-11)
		tmp = Float64(x * y);
	elseif (x <= 3.5e-46)
		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 <= -1.9e-11)
		tmp = x * y;
	elseif (x <= 3.5e-46)
		tmp = z * 5.0;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e-11], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.5e-46], N[(z * 5.0), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e-11 or 3.5000000000000002e-46 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 47.9%

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

   if -1.8999999999999999e-11 < x < 3.5000000000000002e-46

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 71.5%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-11}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-46}:\\ \;\;\;\;z \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 36.4% 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 39.9%

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

3. Final simplification 39.9%

   \[\leadsto z \cdot 5 \]

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 2023196 
(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)))