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

Percentage Accurate: 99.9% → 99.9%

Time: 6.4s

Alternatives: 10

Speedup: 1.2×

• 26.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(t + 2 \cdot \left(y + z\right)\right) + y \cdot 5 \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (* x (+ t (* 2.0 (+ y z)))) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	return (x * (t + (2.0 * (y + z)))) + (y * 5.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (t + (2.0d0 * (y + z)))) + (y * 5.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (t + (2.0 * (y + z)))) + (y * 5.0);
}

Python

def code(x, y, z, t):
	return (x * (t + (2.0 * (y + z)))) + (y * 5.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(t + Float64(2.0 * Float64(y + z)))) + Float64(y * 5.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (t + (2.0 * (y + z)))) + (y * 5.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(t + N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-+l+ 100.0%

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

   2. *-un-lft-identity 100.0%

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

   3. +-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

   5. distribute-rgt-out 100.0%

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

   6. metadata-eval 100.0%

      \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

4. Applied egg-rr 100.0%

   \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

5. Final simplification 100.0%

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

Alternative 2: 92.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+76} \lor \neg \left(z \leq 9.2 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e+76) (not (<= z 9.2e-39)))
   (+ (* y 5.0) (* x (+ t (* z 2.0))))
   (+ (* y 5.0) (* x (+ t (* y 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e+76) || !(z <= 9.2e-39)) {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.85d+76)) .or. (.not. (z <= 9.2d-39))) then
        tmp = (y * 5.0d0) + (x * (t + (z * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (x * (t + (y * 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e+76) || !(z <= 9.2e-39)) {
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e+76) or not (z <= 9.2e-39):
		tmp = (y * 5.0) + (x * (t + (z * 2.0)))
	else:
		tmp = (y * 5.0) + (x * (t + (y * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.85e+76) || !(z <= 9.2e-39))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(z * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.85e+76) || ~((z <= 9.2e-39)))
		tmp = (y * 5.0) + (x * (t + (z * 2.0)));
	else
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.85e+76], N[Not[LessEqual[z, 9.2e-39]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e76 or 9.20000000000000033e-39 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.4%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot z} + t\right) + y \cdot 5 \]

   if -1.85e76 < z < 9.20000000000000033e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 96.3%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+76} \lor \neg \left(z \leq 9.2 \cdot 10^{-39}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+60} \lor \neg \left(t \leq 5.5 \cdot 10^{-100}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.7e+60) (not (<= t 5.5e-100)))
   (+ (* y 5.0) (* x (+ t (* y 2.0))))
   (+ (* y 5.0) (* x (* 2.0 (+ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.7e+60) || !(t <= 5.5e-100)) {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.7d+60)) .or. (.not. (t <= 5.5d-100))) then
        tmp = (y * 5.0d0) + (x * (t + (y * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (x * (2.0d0 * (y + z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.7e+60) || !(t <= 5.5e-100)) {
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.7e+60) or not (t <= 5.5e-100):
		tmp = (y * 5.0) + (x * (t + (y * 2.0)))
	else:
		tmp = (y * 5.0) + (x * (2.0 * (y + z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.7e+60) || !(t <= 5.5e-100))
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(2.0 * Float64(y + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.7e+60) || ~((t <= 5.5e-100)))
		tmp = (y * 5.0) + (x * (t + (y * 2.0)));
	else
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.7e+60], N[Not[LessEqual[t, 5.5e-100]], $MachinePrecision]], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6999999999999999e60 or 5.50000000000000011e-100 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.4%

      \[\leadsto x \cdot \left(\color{blue}{2 \cdot y} + t\right) + y \cdot 5 \]

   if -2.6999999999999999e60 < t < 5.50000000000000011e-100

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. +-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. distribute-rgt-out 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around 0 95.5%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right)} + y \cdot 5 \]
   6. Step-by-step derivation

      1. *-commutative 95.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + y \cdot 5 \]

      2. associate-*r* 95.5%

         \[\leadsto \color{blue}{x \cdot \left(\left(y + z\right) \cdot 2\right)} + y \cdot 5 \]

      3. *-commutative 95.5%

         \[\leadsto x \cdot \color{blue}{\left(2 \cdot \left(y + z\right)\right)} + y \cdot 5 \]

      4. +-commutative 95.5%

         \[\leadsto x \cdot \left(2 \cdot \color{blue}{\left(z + y\right)}\right) + y \cdot 5 \]

   7. Simplified 95.5%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+60} \lor \neg \left(t \leq 5.5 \cdot 10^{-100}\right):\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+95}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.8e+61)
   (* t (+ x (* 5.0 (/ y t))))
   (if (<= t 1.28e+95)
     (+ (* y 5.0) (* x (* 2.0 (+ y z))))
     (+ (* y 5.0) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.8e+61) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (t <= 1.28e+95) {
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8.8d+61)) then
        tmp = t * (x + (5.0d0 * (y / t)))
    else if (t <= 1.28d+95) then
        tmp = (y * 5.0d0) + (x * (2.0d0 * (y + z)))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.8e+61) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (t <= 1.28e+95) {
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.8e+61:
		tmp = t * (x + (5.0 * (y / t)))
	elif t <= 1.28e+95:
		tmp = (y * 5.0) + (x * (2.0 * (y + z)))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.8e+61)
		tmp = Float64(t * Float64(x + Float64(5.0 * Float64(y / t))));
	elseif (t <= 1.28e+95)
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(2.0 * Float64(y + z))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.8e+61)
		tmp = t * (x + (5.0 * (y / t)));
	elseif (t <= 1.28e+95)
		tmp = (y * 5.0) + (x * (2.0 * (y + z)));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.8e+61], N[(t * N[(x + N[(5.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.28e+95], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.8000000000000001e61

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. *-un-lft-identity 99.9%

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

      3. +-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. distribute-rgt-out 99.9%

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

      6. metadata-eval 99.9%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 99.9%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around inf 81.7%

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

      1. *-commutative 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in t around inf 81.8%

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

   if -8.8000000000000001e61 < t < 1.28000000000000006e95

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. +-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. distribute-rgt-out 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around 0 90.4%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(y + z\right)\right)} + y \cdot 5 \]
   6. Step-by-step derivation

      1. *-commutative 90.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y + z\right)\right) \cdot 2} + y \cdot 5 \]

      2. associate-*r* 90.4%

         \[\leadsto \color{blue}{x \cdot \left(\left(y + z\right) \cdot 2\right)} + y \cdot 5 \]

      3. *-commutative 90.4%

         \[\leadsto x \cdot \color{blue}{\left(2 \cdot \left(y + z\right)\right)} + y \cdot 5 \]

      4. +-commutative 90.4%

         \[\leadsto x \cdot \left(2 \cdot \color{blue}{\left(z + y\right)}\right) + y \cdot 5 \]

   7. Simplified 90.4%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \left(z + y\right)\right)} + y \cdot 5 \]

   if 1.28000000000000006e95 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.0%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+95}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(2 \cdot \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-100}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.2e+59)
   (* t (+ x (* 5.0 (/ y t))))
   (if (<= t 6.6e-100) (+ (* y 5.0) (* 2.0 (* x z))) (+ (* y 5.0) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.2e+59) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (t <= 6.6e-100) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-6.2d+59)) then
        tmp = t * (x + (5.0d0 * (y / t)))
    else if (t <= 6.6d-100) then
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.2e+59) {
		tmp = t * (x + (5.0 * (y / t)));
	} else if (t <= 6.6e-100) {
		tmp = (y * 5.0) + (2.0 * (x * z));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.2e+59:
		tmp = t * (x + (5.0 * (y / t)))
	elif t <= 6.6e-100:
		tmp = (y * 5.0) + (2.0 * (x * z))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.2e+59)
		tmp = Float64(t * Float64(x + Float64(5.0 * Float64(y / t))));
	elseif (t <= 6.6e-100)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.2e+59)
		tmp = t * (x + (5.0 * (y / t)));
	elseif (t <= 6.6e-100)
		tmp = (y * 5.0) + (2.0 * (x * z));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.2e+59], N[(t * N[(x + N[(5.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e-100], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000029e59

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. *-un-lft-identity 99.9%

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

      3. +-commutative 99.9%

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

      4. *-un-lft-identity 99.9%

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

      5. distribute-rgt-out 99.9%

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

      6. metadata-eval 99.9%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 99.9%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around inf 81.7%

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

      1. *-commutative 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in t around inf 81.8%

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

   if -6.20000000000000029e59 < t < 6.59999999999999993e-100

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 77.2%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot z\right)} + y \cdot 5 \]

   if 6.59999999999999993e-100 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(x + 5 \cdot \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-100}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-11} \lor \neg \left(y \leq 5.1 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.8e-11) (not (<= y 5.1e+97)))
   (* y (+ 5.0 (* x 2.0)))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.8e-11) || !(y <= 5.1e+97)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.8d-11)) .or. (.not. (y <= 5.1d+97))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.8e-11) || !(y <= 5.1e+97)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.8e-11) or not (y <= 5.1e+97):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.8e-11) || !(y <= 5.1e+97))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.8e-11) || ~((y <= 5.1e+97)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.8e-11], N[Not[LessEqual[y, 5.1e+97]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.7999999999999998e-11 or 5.10000000000000034e97 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 87.6%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   if -9.7999999999999998e-11 < y < 5.10000000000000034e97

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.4%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-11} \lor \neg \left(y \leq 5.1 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-38} \lor \neg \left(y \leq 10^{-25}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e-38) (not (<= y 1e-25))) (* y (+ 5.0 (* x 2.0))) (* x t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-38) || !(y <= 1e-25)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.8d-38)) .or. (.not. (y <= 1d-25))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-38) || !(y <= 1e-25)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e-38) or not (y <= 1e-25):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e-38) || !(y <= 1e-25))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e-38) || ~((y <= 1e-25)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e-38], N[Not[LessEqual[y, 1e-25]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e-38 or 1.00000000000000004e-25 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 77.2%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   if -3.8e-38 < y < 1.00000000000000004e-25

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. +-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. distribute-rgt-out 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around inf 57.4%

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

      1. *-commutative 57.4%

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

   7. Simplified 57.4%

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

   8. Taylor expanded in t around inf 57.4%

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

   9. Taylor expanded in t around inf 46.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-38} \lor \neg \left(y \leq 10^{-25}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-64}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.75e-64) (* x t) (if (<= x 5.2e-16) (* y 5.0) (* y (* x 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.75e-64) {
		tmp = x * t;
	} else if (x <= 5.2e-16) {
		tmp = y * 5.0;
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.75d-64)) then
        tmp = x * t
    else if (x <= 5.2d-16) then
        tmp = y * 5.0d0
    else
        tmp = y * (x * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.75e-64) {
		tmp = x * t;
	} else if (x <= 5.2e-16) {
		tmp = y * 5.0;
	} else {
		tmp = y * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.75e-64:
		tmp = x * t
	elif x <= 5.2e-16:
		tmp = y * 5.0
	else:
		tmp = y * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.75e-64)
		tmp = Float64(x * t);
	elseif (x <= 5.2e-16)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(y * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.75e-64)
		tmp = x * t;
	elseif (x <= 5.2e-16)
		tmp = y * 5.0;
	else
		tmp = y * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.75e-64], N[(x * t), $MachinePrecision], If[LessEqual[x, 5.2e-16], N[(y * 5.0), $MachinePrecision], N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7499999999999999e-64

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. +-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. distribute-rgt-out 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around inf 52.6%

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

      1. *-commutative 52.6%

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

   7. Simplified 52.6%

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

   8. Taylor expanded in t around inf 52.6%

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

   9. Taylor expanded in t around inf 49.1%

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

   if -2.7499999999999999e-64 < x < 5.1999999999999997e-16

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 58.9%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   4. Taylor expanded in x around 0 58.9%

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

      1. *-commutative 58.9%

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

   6. Simplified 58.9%

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

   if 5.1999999999999997e-16 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 38.4%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   4. Taylor expanded in x around inf 38.3%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{-64}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-69} \lor \neg \left(x \leq 4.4 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.1e-69) (not (<= x 4.4e-30))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.1e-69) || !(x <= 4.4e-30)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.1d-69)) .or. (.not. (x <= 4.4d-30))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.1e-69) || !(x <= 4.4e-30)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.1e-69) or not (x <= 4.4e-30):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.1e-69) || !(x <= 4.4e-30))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.1e-69) || ~((x <= 4.4e-30)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.1e-69], N[Not[LessEqual[x, 4.4e-30]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0999999999999999e-69 or 4.39999999999999967e-30 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. +-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. distribute-rgt-out 100.0%

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

      6. metadata-eval 100.0%

         \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

   4. Applied egg-rr 100.0%

      \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

   5. Taylor expanded in t around inf 45.8%

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

      1. *-commutative 45.8%

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

   7. Simplified 45.8%

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

   8. Taylor expanded in t around inf 50.5%

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

   9. Taylor expanded in t around inf 43.3%

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

   if -4.0999999999999999e-69 < x < 4.39999999999999967e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 59.3%

      \[\leadsto \color{blue}{y \cdot \left(5 + 2 \cdot x\right)} \]

   4. Taylor expanded in x around 0 59.3%

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

      1. *-commutative 59.3%

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

   6. Simplified 59.3%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-69} \lor \neg \left(x \leq 4.4 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * t), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-+l+ 100.0%

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

   2. *-un-lft-identity 100.0%

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

   3. +-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

   5. distribute-rgt-out 100.0%

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

   6. metadata-eval 100.0%

      \[\leadsto x \cdot \left(\left(y + z\right) \cdot \color{blue}{2} + t\right) + y \cdot 5 \]

4. Applied egg-rr 100.0%

   \[\leadsto x \cdot \left(\color{blue}{\left(y + z\right) \cdot 2} + t\right) + y \cdot 5 \]

5. Taylor expanded in t around inf 58.3%

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

   1. *-commutative 58.3%

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

7. Simplified 58.3%

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

8. Taylor expanded in t around inf 55.4%

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

9. Taylor expanded in t around inf 31.0%

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

10. Final simplification 31.0%

    \[\leadsto x \cdot t \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))