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

Percentage Accurate: 99.9% → 98.9%

Time: 5.8s

Alternatives: 9

Speedup: 1.0×

• 21.6% 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: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. distribute-lft-in 99.2%

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

   2. associate-+r+ 99.2%

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

   3. *-commutative 99.2%

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

   4. distribute-rgt-in 99.2%

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

   5. +-commutative 99.2%

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

   6. *-commutative 99.2%

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

   7. fma-define 99.6%

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

4. Applied egg-rr 99.6%

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

5. Final simplification 99.6%

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

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. distribute-rgt-in 99.2%

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

   2. associate-+l+ 99.2%

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

   3. *-commutative 99.2%

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

   4. fma-define 99.2%

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

   5. distribute-lft-out 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 3: 60.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-37}:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+42} \lor \neg \left(x \leq 3.6 \cdot 10^{+100}\right) \land \left(x \leq 5.7 \cdot 10^{+140} \lor \neg \left(x \leq 2.6 \cdot 10^{+216}\right) \land x \leq 2.5 \cdot 10^{+278}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e+39)
   (* x z)
   (if (<= x -1.42e-109)
     (* x y)
     (if (<= x 2e-37)
       (* 5.0 z)
       (if (or (<= x 1.7e+42)
               (and (not (<= x 3.6e+100))
                    (or (<= x 5.7e+140)
                        (and (not (<= x 2.6e+216)) (<= x 2.5e+278)))))
         (* x y)
         (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e+39) {
		tmp = x * z;
	} else if (x <= -1.42e-109) {
		tmp = x * y;
	} else if (x <= 2e-37) {
		tmp = 5.0 * z;
	} else if ((x <= 1.7e+42) || (!(x <= 3.6e+100) && ((x <= 5.7e+140) || (!(x <= 2.6e+216) && (x <= 2.5e+278))))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	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 <= (-3.5d+39)) then
        tmp = x * z
    else if (x <= (-1.42d-109)) then
        tmp = x * y
    else if (x <= 2d-37) then
        tmp = 5.0d0 * z
    else if ((x <= 1.7d+42) .or. (.not. (x <= 3.6d+100)) .and. (x <= 5.7d+140) .or. (.not. (x <= 2.6d+216)) .and. (x <= 2.5d+278)) then
        tmp = x * y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e+39) {
		tmp = x * z;
	} else if (x <= -1.42e-109) {
		tmp = x * y;
	} else if (x <= 2e-37) {
		tmp = 5.0 * z;
	} else if ((x <= 1.7e+42) || (!(x <= 3.6e+100) && ((x <= 5.7e+140) || (!(x <= 2.6e+216) && (x <= 2.5e+278))))) {
		tmp = x * y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e+39:
		tmp = x * z
	elif x <= -1.42e-109:
		tmp = x * y
	elif x <= 2e-37:
		tmp = 5.0 * z
	elif (x <= 1.7e+42) or (not (x <= 3.6e+100) and ((x <= 5.7e+140) or (not (x <= 2.6e+216) and (x <= 2.5e+278)))):
		tmp = x * y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e+39)
		tmp = Float64(x * z);
	elseif (x <= -1.42e-109)
		tmp = Float64(x * y);
	elseif (x <= 2e-37)
		tmp = Float64(5.0 * z);
	elseif ((x <= 1.7e+42) || (!(x <= 3.6e+100) && ((x <= 5.7e+140) || (!(x <= 2.6e+216) && (x <= 2.5e+278)))))
		tmp = Float64(x * y);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.5e+39)
		tmp = x * z;
	elseif (x <= -1.42e-109)
		tmp = x * y;
	elseif (x <= 2e-37)
		tmp = 5.0 * z;
	elseif ((x <= 1.7e+42) || (~((x <= 3.6e+100)) && ((x <= 5.7e+140) || (~((x <= 2.6e+216)) && (x <= 2.5e+278)))))
		tmp = x * y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e+39], N[(x * z), $MachinePrecision], If[LessEqual[x, -1.42e-109], N[(x * y), $MachinePrecision], If[LessEqual[x, 2e-37], N[(5.0 * z), $MachinePrecision], If[Or[LessEqual[x, 1.7e+42], And[N[Not[LessEqual[x, 3.6e+100]], $MachinePrecision], Or[LessEqual[x, 5.7e+140], And[N[Not[LessEqual[x, 2.6e+216]], $MachinePrecision], LessEqual[x, 2.5e+278]]]]], N[(x * y), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5000000000000002e39 or 1.69999999999999988e42 < x < 3.6e100 or 5.70000000000000015e140 < x < 2.5999999999999999e216 or 2.50000000000000014e278 < x

   1. Initial program 99.0%

      \[x \cdot \left(y + z\right) + z \cdot 5 \]
   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 65.3%

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

      1. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   if -3.5000000000000002e39 < x < -1.41999999999999994e-109 or 2.00000000000000013e-37 < x < 1.69999999999999988e42 or 3.6e100 < x < 5.70000000000000015e140 or 2.5999999999999999e216 < x < 2.50000000000000014e278

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 69.5%

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

   if -1.41999999999999994e-109 < x < 2.00000000000000013e-37

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;x \leq -1.42 \cdot 10^{-109}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-37}:\\ \;\;\;\;5 \cdot z\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+42} \lor \neg \left(x \leq 3.6 \cdot 10^{+100}\right) \land \left(x \leq 5.7 \cdot 10^{+140} \lor \neg \left(x \leq 2.6 \cdot 10^{+216}\right) \land x \leq 2.5 \cdot 10^{+278}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 360:\\ \;\;\;\;\left(x + 5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e-99)
   (* x (+ z y))
   (if (<= x 360.0) (* (+ x 5.0) z) (+ (* x y) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-99) {
		tmp = x * (z + y);
	} else if (x <= 360.0) {
		tmp = (x + 5.0) * z;
	} else {
		tmp = (x * y) + (x * z);
	}
	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 <= (-1.5d-99)) then
        tmp = x * (z + y)
    else if (x <= 360.0d0) then
        tmp = (x + 5.0d0) * z
    else
        tmp = (x * y) + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-99) {
		tmp = x * (z + y);
	} else if (x <= 360.0) {
		tmp = (x + 5.0) * z;
	} else {
		tmp = (x * y) + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e-99:
		tmp = x * (z + y)
	elif x <= 360.0:
		tmp = (x + 5.0) * z
	else:
		tmp = (x * y) + (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e-99)
		tmp = Float64(x * Float64(z + y));
	elseif (x <= 360.0)
		tmp = Float64(Float64(x + 5.0) * z);
	else
		tmp = Float64(Float64(x * y) + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e-99)
		tmp = x * (z + y);
	elseif (x <= 360.0)
		tmp = (x + 5.0) * z;
	else
		tmp = (x * y) + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e-99], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 360.0], N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.50000000000000003e-99

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 92.5%

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

      1. +-commutative 92.5%

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

   5. Simplified 92.5%

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

   if -1.50000000000000003e-99 < x < 360

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 73.6%

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

      1. distribute-rgt-in 73.6%

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

   5. Simplified 73.6%

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

   if 360 < 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 99.8%

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

      1. +-commutative 99.8%

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

   5. Simplified 99.8%

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

      1. distribute-lft-in 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-99}:\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{elif}\;x \leq 360:\\ \;\;\;\;\left(x + 5\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-100} \lor \neg \left(x \leq 4.2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e-100) (not (<= x 4.2e-36))) (* x (+ z y)) (* 5.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e-100) || !(x <= 4.2e-36)) {
		tmp = x * (z + y);
	} else {
		tmp = 5.0 * z;
	}
	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 <= (-8.2d-100)) .or. (.not. (x <= 4.2d-36))) then
        tmp = x * (z + y)
    else
        tmp = 5.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e-100) || !(x <= 4.2e-36)) {
		tmp = x * (z + y);
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e-100) or not (x <= 4.2e-36):
		tmp = x * (z + y)
	else:
		tmp = 5.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e-100) || !(x <= 4.2e-36))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(5.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.2e-100) || ~((x <= 4.2e-36)))
		tmp = x * (z + y);
	else
		tmp = 5.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e-100], N[Not[LessEqual[x, 4.2e-36]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(5.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999998e-100 or 4.19999999999999982e-36 < x

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 92.0%

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

      1. +-commutative 92.0%

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

   5. Simplified 92.0%

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

   if -8.1999999999999998e-100 < x < 4.19999999999999982e-36

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 76.8%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-100} \lor \neg \left(x \leq 4.2 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-99} \lor \neg \left(x \leq 16000\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 5\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.5e-99) (not (<= x 16000.0))) (* x (+ z y)) (* (+ x 5.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-99) || !(x <= 16000.0)) {
		tmp = x * (z + y);
	} else {
		tmp = (x + 5.0) * z;
	}
	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 <= (-1.5d-99)) .or. (.not. (x <= 16000.0d0))) then
        tmp = x * (z + y)
    else
        tmp = (x + 5.0d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.5e-99) || !(x <= 16000.0)) {
		tmp = x * (z + y);
	} else {
		tmp = (x + 5.0) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.5e-99) or not (x <= 16000.0):
		tmp = x * (z + y)
	else:
		tmp = (x + 5.0) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.5e-99) || !(x <= 16000.0))
		tmp = Float64(x * Float64(z + y));
	else
		tmp = Float64(Float64(x + 5.0) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.5e-99) || ~((x <= 16000.0)))
		tmp = x * (z + y);
	else
		tmp = (x + 5.0) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.5e-99], N[Not[LessEqual[x, 16000.0]], $MachinePrecision]], N[(x * N[(z + y), $MachinePrecision]), $MachinePrecision], N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000003e-99 or 16000 < x

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 95.7%

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

      1. +-commutative 95.7%

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

   5. Simplified 95.7%

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

   if -1.50000000000000003e-99 < x < 16000

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 73.6%

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

      1. distribute-rgt-in 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-99} \lor \neg \left(x \leq 16000\right):\\ \;\;\;\;x \cdot \left(z + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 5\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-109} \lor \neg \left(x \leq 3.2 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e-109) (not (<= x 3.2e-39))) (* x y) (* 5.0 z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-109) || !(x <= 3.2e-39)) {
		tmp = x * y;
	} else {
		tmp = 5.0 * z;
	}
	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 <= (-2.7d-109)) .or. (.not. (x <= 3.2d-39))) then
        tmp = x * y
    else
        tmp = 5.0d0 * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-109) || !(x <= 3.2e-39)) {
		tmp = x * y;
	} else {
		tmp = 5.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e-109) or not (x <= 3.2e-39):
		tmp = x * y
	else:
		tmp = 5.0 * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e-109) || !(x <= 3.2e-39))
		tmp = Float64(x * y);
	else
		tmp = Float64(5.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.7e-109) || ~((x <= 3.2e-39)))
		tmp = x * y;
	else
		tmp = 5.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e-109], N[Not[LessEqual[x, 3.2e-39]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(5.0 * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e-109 or 3.1999999999999998e-39 < x

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 50.9%

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

   if -2.7e-109 < x < 3.1999999999999998e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-109} \lor \neg \left(x \leq 3.2 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;5 \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) + (5.0d0 * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Final simplification 99.5%

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

Alternative 9: 35.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ 5 \cdot z \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 5.0d0 * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in x around 0 31.1%

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

4. Final simplification 31.1%

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

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 2024059 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :alt
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))