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

Percentage Accurate: 99.9% → 100.0%

Time: 5.5s

Alternatives: 10

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 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-def 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 3: 62.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+267}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+120} \lor \neg \left(x \leq 10^{+155}\right) \land x \leq 5.5 \cdot 10^{+282}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.05e+267)
   (* z x)
   (if (<= x -9.5e-30)
     (* x y)
     (if (<= x 3.75e-6)
       (* z 5.0)
       (if (or (<= x 2.8e+120) (and (not (<= x 1e+155)) (<= x 5.5e+282)))
         (* x y)
         (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.05e+267) {
		tmp = z * x;
	} else if (x <= -9.5e-30) {
		tmp = x * y;
	} else if (x <= 3.75e-6) {
		tmp = z * 5.0;
	} else if ((x <= 2.8e+120) || (!(x <= 1e+155) && (x <= 5.5e+282))) {
		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 <= (-2.05d+267)) then
        tmp = z * x
    else if (x <= (-9.5d-30)) then
        tmp = x * y
    else if (x <= 3.75d-6) then
        tmp = z * 5.0d0
    else if ((x <= 2.8d+120) .or. (.not. (x <= 1d+155)) .and. (x <= 5.5d+282)) 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 <= -2.05e+267) {
		tmp = z * x;
	} else if (x <= -9.5e-30) {
		tmp = x * y;
	} else if (x <= 3.75e-6) {
		tmp = z * 5.0;
	} else if ((x <= 2.8e+120) || (!(x <= 1e+155) && (x <= 5.5e+282))) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.05e+267:
		tmp = z * x
	elif x <= -9.5e-30:
		tmp = x * y
	elif x <= 3.75e-6:
		tmp = z * 5.0
	elif (x <= 2.8e+120) or (not (x <= 1e+155) and (x <= 5.5e+282)):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.05e+267)
		tmp = Float64(z * x);
	elseif (x <= -9.5e-30)
		tmp = Float64(x * y);
	elseif (x <= 3.75e-6)
		tmp = Float64(z * 5.0);
	elseif ((x <= 2.8e+120) || (!(x <= 1e+155) && (x <= 5.5e+282)))
		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 <= -2.05e+267)
		tmp = z * x;
	elseif (x <= -9.5e-30)
		tmp = x * y;
	elseif (x <= 3.75e-6)
		tmp = z * 5.0;
	elseif ((x <= 2.8e+120) || (~((x <= 1e+155)) && (x <= 5.5e+282)))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.05e+267], N[(z * x), $MachinePrecision], If[LessEqual[x, -9.5e-30], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.75e-6], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 2.8e+120], And[N[Not[LessEqual[x, 1e+155]], $MachinePrecision], LessEqual[x, 5.5e+282]]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.04999999999999999e267 or 2.8000000000000001e120 < x < 1.00000000000000001e155 or 5.4999999999999999e282 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 83.8%

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

   if -2.04999999999999999e267 < x < -9.49999999999999939e-30 or 3.7500000000000001e-6 < x < 2.8000000000000001e120 or 1.00000000000000001e155 < x < 5.4999999999999999e282

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.9%

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

   if -9.49999999999999939e-30 < x < 3.7500000000000001e-6

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.0%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+267}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+120} \lor \neg \left(x \leq 10^{+155}\right) \land x \leq 5.5 \cdot 10^{+282}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -25000:\\ \;\;\;\;x \cdot y + z \cdot x\\ \mathbf{elif}\;x \leq 3.45:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -25000.0)
   (+ (* x y) (* z x))
   (if (<= x 3.45) (- (* x y) (* z -5.0)) (* x (+ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -25000.0) {
		tmp = (x * y) + (z * x);
	} else if (x <= 3.45) {
		tmp = (x * y) - (z * -5.0);
	} 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 (x <= (-25000.0d0)) then
        tmp = (x * y) + (z * x)
    else if (x <= 3.45d0) then
        tmp = (x * y) - (z * (-5.0d0))
    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 (x <= -25000.0) {
		tmp = (x * y) + (z * x);
	} else if (x <= 3.45) {
		tmp = (x * y) - (z * -5.0);
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -25000.0:
		tmp = (x * y) + (z * x)
	elif x <= 3.45:
		tmp = (x * y) - (z * -5.0)
	else:
		tmp = x * (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -25000.0)
		tmp = Float64(Float64(x * y) + Float64(z * x));
	elseif (x <= 3.45)
		tmp = Float64(Float64(x * y) - Float64(z * -5.0));
	else
		tmp = Float64(x * Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -25000.0)
		tmp = (x * y) + (z * x);
	elseif (x <= 3.45)
		tmp = (x * y) - (z * -5.0);
	else
		tmp = x * (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -25000.0], N[(N[(x * y), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.45], N[(N[(x * y), $MachinePrecision] - N[(z * -5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -25000

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-rgt-in 100.0%

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

      2. *-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -25000 < x < 3.4500000000000002

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing
   3. 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%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around -inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. mul-1-neg 99.9%

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

      7. unsub-neg 99.9%

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

      8. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 98.6%

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

      1. *-commutative 98.6%

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

   10. Simplified 98.6%

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

   if 3.4500000000000002 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -25000:\\ \;\;\;\;x \cdot y + z \cdot x\\ \mathbf{elif}\;x \leq 3.45:\\ \;\;\;\;x \cdot y - z \cdot -5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-27} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.35e-27) (not (<= x 3.75e-6))) (* x (+ z y)) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.35e-27) || !(x <= 3.75e-6)) {
		tmp = x * (z + 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 ((x <= (-2.35d-27)) .or. (.not. (x <= 3.75d-6))) then
        tmp = x * (z + 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 ((x <= -2.35e-27) || !(x <= 3.75e-6)) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.35e-27) or not (x <= 3.75e-6):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.35e-27) || !(x <= 3.75e-6))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(z * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.35e-27) || ~((x <= 3.75e-6)))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.35e-27], N[Not[LessEqual[x, 3.75e-6]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.35000000000000016e-27 or 3.7500000000000001e-6 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 98.6%

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

      1. +-commutative 98.6%

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

   5. Simplified 98.6%

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

   if -2.35000000000000016e-27 < x < 3.7500000000000001e-6

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-27} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -31 \lor \neg \left(x \leq 0.0061\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -31.0) (not (<= x 0.0061))) (* x (+ z y)) (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -31.0) || !(x <= 0.0061)) {
		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 <= (-31.0d0)) .or. (.not. (x <= 0.0061d0))) 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 <= -31.0) || !(x <= 0.0061)) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -31.0) or not (x <= 0.0061):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -31.0) || !(x <= 0.0061))
		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 <= -31.0) || ~((x <= 0.0061)))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -31.0], N[Not[LessEqual[x, 0.0061]], $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 < -31 or 0.00610000000000000039 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -31 < x < 0.00610000000000000039

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.2%

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

      1. distribute-rgt-in 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -31 \lor \neg \left(x \leq 0.0061\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000105:\\ \;\;\;\;x \cdot y + z \cdot x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.000105)
   (+ (* x y) (* z x))
   (if (<= x 4e-6) (* z (+ 5.0 x)) (* x (+ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.000105) {
		tmp = (x * y) + (z * x);
	} else if (x <= 4e-6) {
		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 (x <= (-0.000105d0)) then
        tmp = (x * y) + (z * x)
    else if (x <= 4d-6) 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 (x <= -0.000105) {
		tmp = (x * y) + (z * x);
	} else if (x <= 4e-6) {
		tmp = z * (5.0 + x);
	} else {
		tmp = x * (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.000105:
		tmp = (x * y) + (z * x)
	elif x <= 4e-6:
		tmp = z * (5.0 + x)
	else:
		tmp = x * (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.000105)
		tmp = Float64(Float64(x * y) + Float64(z * x));
	elseif (x <= 4e-6)
		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 (x <= -0.000105)
		tmp = (x * y) + (z * x);
	elseif (x <= 4e-6)
		tmp = z * (5.0 + x);
	else
		tmp = x * (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.000105], N[(N[(x * y), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-6], N[(z * N[(5.0 + x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e-4

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

      1. distribute-rgt-in 100.0%

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

      2. *-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -1.05e-4 < x < 3.99999999999999982e-6

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.2%

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

      1. distribute-rgt-in 71.3%

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

   5. Simplified 71.3%

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

   if 3.99999999999999982e-6 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000105:\\ \;\;\;\;x \cdot y + z \cdot x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-29} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e-29) (not (<= x 3.75e-6))) (* x y) (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e-29) || !(x <= 3.75e-6)) {
		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 ((x <= (-2.4d-29)) .or. (.not. (x <= 3.75d-6))) 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 ((x <= -2.4e-29) || !(x <= 3.75e-6)) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e-29) or not (x <= 3.75e-6):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e-29) || !(x <= 3.75e-6))
		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 ((x <= -2.4e-29) || ~((x <= 3.75e-6)))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e-29], N[Not[LessEqual[x, 3.75e-6]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999992e-29 or 3.7500000000000001e-6 < x

   1. Initial program 100.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 58.0%

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

   if -2.39999999999999992e-29 < x < 3.7500000000000001e-6

   1. Initial program 99.9%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.0%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-29} \lor \neg \left(x \leq 3.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 100.0%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x \cdot \left(z + y\right) + z \cdot 5 \]
4. Add Preprocessing

Alternative 10: 38.2% 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 100.0%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in x around 0 33.7%

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

4. Final simplification 33.7%

   \[\leadsto z \cdot 5 \]
5. Add Preprocessing

Developer target: 98.1% 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 2024021 
(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)))