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

Percentage Accurate: 99.9% → 100.0%

Time: 7.1s

Alternatives: 8

Speedup: 1.0×

• 20.6% 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. 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-define 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: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-43}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+33} \lor \neg \left(x \leq 1.65 \cdot 10^{+220}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45e-91)
   (* x y)
   (if (<= x 6e-179)
     (* z 5.0)
     (if (<= x 7e-124)
       (* x y)
       (if (<= x 1.05e-43)
         (* z 5.0)
         (if (or (<= x 1.05e+33) (not (<= x 1.65e+220))) (* x y) (* z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45e-91) {
		tmp = x * y;
	} else if (x <= 6e-179) {
		tmp = z * 5.0;
	} else if (x <= 7e-124) {
		tmp = x * y;
	} else if (x <= 1.05e-43) {
		tmp = z * 5.0;
	} else if ((x <= 1.05e+33) || !(x <= 1.65e+220)) {
		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 <= (-1.45d-91)) then
        tmp = x * y
    else if (x <= 6d-179) then
        tmp = z * 5.0d0
    else if (x <= 7d-124) then
        tmp = x * y
    else if (x <= 1.05d-43) then
        tmp = z * 5.0d0
    else if ((x <= 1.05d+33) .or. (.not. (x <= 1.65d+220))) 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 <= -1.45e-91) {
		tmp = x * y;
	} else if (x <= 6e-179) {
		tmp = z * 5.0;
	} else if (x <= 7e-124) {
		tmp = x * y;
	} else if (x <= 1.05e-43) {
		tmp = z * 5.0;
	} else if ((x <= 1.05e+33) || !(x <= 1.65e+220)) {
		tmp = x * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45e-91:
		tmp = x * y
	elif x <= 6e-179:
		tmp = z * 5.0
	elif x <= 7e-124:
		tmp = x * y
	elif x <= 1.05e-43:
		tmp = z * 5.0
	elif (x <= 1.05e+33) or not (x <= 1.65e+220):
		tmp = x * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45e-91)
		tmp = Float64(x * y);
	elseif (x <= 6e-179)
		tmp = Float64(z * 5.0);
	elseif (x <= 7e-124)
		tmp = Float64(x * y);
	elseif (x <= 1.05e-43)
		tmp = Float64(z * 5.0);
	elseif ((x <= 1.05e+33) || !(x <= 1.65e+220))
		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 <= -1.45e-91)
		tmp = x * y;
	elseif (x <= 6e-179)
		tmp = z * 5.0;
	elseif (x <= 7e-124)
		tmp = x * y;
	elseif (x <= 1.05e-43)
		tmp = z * 5.0;
	elseif ((x <= 1.05e+33) || ~((x <= 1.65e+220)))
		tmp = x * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45e-91], N[(x * y), $MachinePrecision], If[LessEqual[x, 6e-179], N[(z * 5.0), $MachinePrecision], If[LessEqual[x, 7e-124], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.05e-43], N[(z * 5.0), $MachinePrecision], If[Or[LessEqual[x, 1.05e+33], N[Not[LessEqual[x, 1.65e+220]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e-91 or 6.00000000000000012e-179 < x < 6.9999999999999997e-124 or 1.05e-43 < x < 1.05e33 or 1.65000000000000011e220 < 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 61.9%

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

   if -1.45e-91 < x < 6.00000000000000012e-179 or 6.9999999999999997e-124 < x < 1.05e-43

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 79.5%

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

   if 1.05e33 < x < 1.65000000000000011e220

   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. Taylor expanded in z around inf 62.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-179}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-124}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-43}:\\ \;\;\;\;z \cdot 5\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+33} \lor \neg \left(x \leq 1.65 \cdot 10^{+220}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-85} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 8.5 \cdot 10^{-124}\right) \land x \leq 1.35 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.16e-85)
         (not (or (<= x 6e-179) (and (not (<= x 8.5e-124)) (<= x 1.35e-47)))))
   (* x (+ z y))
   (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.16e-85) || !((x <= 6e-179) || (!(x <= 8.5e-124) && (x <= 1.35e-47)))) {
		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 <= (-1.16d-85)) .or. (.not. (x <= 6d-179) .or. (.not. (x <= 8.5d-124)) .and. (x <= 1.35d-47))) 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 <= -1.16e-85) || !((x <= 6e-179) || (!(x <= 8.5e-124) && (x <= 1.35e-47)))) {
		tmp = x * (z + y);
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.16e-85) or not ((x <= 6e-179) or (not (x <= 8.5e-124) and (x <= 1.35e-47))):
		tmp = x * (z + y)
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.16e-85) || !((x <= 6e-179) || (!(x <= 8.5e-124) && (x <= 1.35e-47))))
		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 <= -1.16e-85) || ~(((x <= 6e-179) || (~((x <= 8.5e-124)) && (x <= 1.35e-47)))))
		tmp = x * (z + y);
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.16e-85], N[Not[Or[LessEqual[x, 6e-179], And[N[Not[LessEqual[x, 8.5e-124]], $MachinePrecision], LessEqual[x, 1.35e-47]]]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.16e-85 or 6.00000000000000012e-179 < x < 8.5000000000000002e-124 or 1.3499999999999999e-47 < 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 91.0%

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

      1. +-commutative 91.0%

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

   5. Simplified 91.0%

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

   if -1.16e-85 < x < 6.00000000000000012e-179 or 8.5000000000000002e-124 < x < 1.3499999999999999e-47

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 78.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-85} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 8.5 \cdot 10^{-124}\right) \land x \leq 1.35 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-86} \lor \neg \left(x \leq 6 \cdot 10^{-179}\right) \land \left(x \leq 8 \cdot 10^{-124} \lor \neg \left(x \leq 2.65 \cdot 10^{-52}\right)\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e-86)
         (and (not (<= x 6e-179)) (or (<= x 8e-124) (not (<= x 2.65e-52)))))
   (* x (+ z y))
   (* z (+ 5.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e-86) || (!(x <= 6e-179) && ((x <= 8e-124) || !(x <= 2.65e-52)))) {
		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 <= (-2.5d-86)) .or. (.not. (x <= 6d-179)) .and. (x <= 8d-124) .or. (.not. (x <= 2.65d-52))) 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 <= -2.5e-86) || (!(x <= 6e-179) && ((x <= 8e-124) || !(x <= 2.65e-52)))) {
		tmp = x * (z + y);
	} else {
		tmp = z * (5.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e-86) or (not (x <= 6e-179) and ((x <= 8e-124) or not (x <= 2.65e-52))):
		tmp = x * (z + y)
	else:
		tmp = z * (5.0 + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e-86) || (!(x <= 6e-179) && ((x <= 8e-124) || !(x <= 2.65e-52))))
		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 <= -2.5e-86) || (~((x <= 6e-179)) && ((x <= 8e-124) || ~((x <= 2.65e-52)))))
		tmp = x * (z + y);
	else
		tmp = z * (5.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.5e-86], And[N[Not[LessEqual[x, 6e-179]], $MachinePrecision], Or[LessEqual[x, 8e-124], N[Not[LessEqual[x, 2.65e-52]], $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 < -2.4999999999999999e-86 or 6.00000000000000012e-179 < x < 7.99999999999999947e-124 or 2.6500000000000002e-52 < 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 91.0%

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

      1. +-commutative 91.0%

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

   5. Simplified 91.0%

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

   if -2.4999999999999999e-86 < x < 6.00000000000000012e-179 or 7.99999999999999947e-124 < x < 2.6500000000000002e-52

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 78.8%

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

      1. distribute-rgt-in 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-86} \lor \neg \left(x \leq 6 \cdot 10^{-179}\right) \land \left(x \leq 8 \cdot 10^{-124} \lor \neg \left(x \leq 2.65 \cdot 10^{-52}\right)\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(5 + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-90} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 3.4 \cdot 10^{-123}\right) \land x \leq 3.9 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e-90)
         (not (or (<= x 6e-179) (and (not (<= x 3.4e-123)) (<= x 3.9e-49)))))
   (* x y)
   (* z 5.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-90) || !((x <= 6e-179) || (!(x <= 3.4e-123) && (x <= 3.9e-49)))) {
		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 <= (-1.4d-90)) .or. (.not. (x <= 6d-179) .or. (.not. (x <= 3.4d-123)) .and. (x <= 3.9d-49))) 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 <= -1.4e-90) || !((x <= 6e-179) || (!(x <= 3.4e-123) && (x <= 3.9e-49)))) {
		tmp = x * y;
	} else {
		tmp = z * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e-90) or not ((x <= 6e-179) or (not (x <= 3.4e-123) and (x <= 3.9e-49))):
		tmp = x * y
	else:
		tmp = z * 5.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e-90) || !((x <= 6e-179) || (!(x <= 3.4e-123) && (x <= 3.9e-49))))
		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 <= -1.4e-90) || ~(((x <= 6e-179) || (~((x <= 3.4e-123)) && (x <= 3.9e-49)))))
		tmp = x * y;
	else
		tmp = z * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e-90], N[Not[Or[LessEqual[x, 6e-179], And[N[Not[LessEqual[x, 3.4e-123]], $MachinePrecision], LessEqual[x, 3.9e-49]]]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999e-90 or 6.00000000000000012e-179 < x < 3.4000000000000001e-123 or 3.90000000000000011e-49 < 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 58.1%

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

   if -1.3999999999999999e-90 < x < 6.00000000000000012e-179 or 3.4000000000000001e-123 < x < 3.90000000000000011e-49

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 79.5%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-90} \lor \neg \left(x \leq 6 \cdot 10^{-179} \lor \neg \left(x \leq 3.4 \cdot 10^{-123}\right) \land x \leq 3.9 \cdot 10^{-49}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -5 or 5 < 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 98.4%

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

      1. +-commutative 98.4%

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

   5. Simplified 98.4%

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

   if -5 < x < 5

   1. Initial program 99.8%

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

      1. distribute-rgt-in 99.8%

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

      2. associate-+l+ 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-define 99.8%

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

      5. distribute-lft-out 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. flip-+ 99.8%

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

      3. associate-*l/ 99.7%

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

      4. fma-neg 99.7%

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

      5. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -\color{blue}{25}\right) \cdot z}{x - 5}\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, \color{blue}{-25}\right) \cdot z}{x - 5}\right) \]

      7. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{\color{blue}{x + \left(-5\right)}}\right) \]

      8. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{x + \color{blue}{-5}}\right) \]

   6. Applied egg-rr 99.7%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{x + -5}}\right) \]

   7. Taylor expanded in x around 0 98.5%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{-25 \cdot z}}{x + -5}\right) \]
   8. Step-by-step derivation

      1. *-commutative 98.5%

         \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot -25}}{x + -5}\right) \]

   9. Simplified 98.5%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot -25}}{x + -5}\right) \]
   10. Step-by-step derivation

       1. fma-undefine 98.5%

          \[\leadsto \color{blue}{x \cdot y + \frac{z \cdot -25}{x + -5}} \]

       2. *-commutative 98.5%

          \[\leadsto x \cdot y + \frac{\color{blue}{-25 \cdot z}}{x + -5} \]

       3. associate-/l* 98.5%

          \[\leadsto x \cdot y + \color{blue}{-25 \cdot \frac{z}{x + -5}} \]

   11. Applied egg-rr 98.5%

       \[\leadsto \color{blue}{x \cdot y + -25 \cdot \frac{z}{x + -5}} \]

   12. Taylor expanded in x around 0 98.0%

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

       1. *-commutative 98.0%

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

   14. Simplified 98.0%

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

4. Final simplification 98.2%

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

Alternative 7: 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 8: 37.1% 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. Add Preprocessing

3. Taylor expanded in x around 0 33.1%

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

4. Final simplification 33.1%

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

Developer target: 97.7% 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 2024039 
(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)))