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

Percentage Accurate: 99.9% → 99.9%

Time: 9.5s

Alternatives: 12

Speedup: 1.2×

• 26.5% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. fma-define 100.0%

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

   2. associate-+l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. count-2 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-88} \lor \neg \left(x \leq -3.8 \cdot 10^{-192}\right) \land \left(x \leq -6 \cdot 10^{-238} \lor \neg \left(x \leq 5.2 \cdot 10^{-142}\right)\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))))
   (if (<= x -3.4e+83)
     t_1
     (if (<= x -3e+36)
       (* 2.0 (* x y))
       (if (or (<= x -2.5e-88)
               (and (not (<= x -3.8e-192))
                    (or (<= x -6e-238) (not (<= x 5.2e-142)))))
         t_1
         (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double tmp;
	if (x <= -3.4e+83) {
		tmp = t_1;
	} else if (x <= -3e+36) {
		tmp = 2.0 * (x * y);
	} else if ((x <= -2.5e-88) || (!(x <= -3.8e-192) && ((x <= -6e-238) || !(x <= 5.2e-142)))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * z))
    if (x <= (-3.4d+83)) then
        tmp = t_1
    else if (x <= (-3d+36)) then
        tmp = 2.0d0 * (x * y)
    else if ((x <= (-2.5d-88)) .or. (.not. (x <= (-3.8d-192))) .and. (x <= (-6d-238)) .or. (.not. (x <= 5.2d-142))) then
        tmp = t_1
    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 t_1 = x * (t + (2.0 * z));
	double tmp;
	if (x <= -3.4e+83) {
		tmp = t_1;
	} else if (x <= -3e+36) {
		tmp = 2.0 * (x * y);
	} else if ((x <= -2.5e-88) || (!(x <= -3.8e-192) && ((x <= -6e-238) || !(x <= 5.2e-142)))) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	tmp = 0
	if x <= -3.4e+83:
		tmp = t_1
	elif x <= -3e+36:
		tmp = 2.0 * (x * y)
	elif (x <= -2.5e-88) or (not (x <= -3.8e-192) and ((x <= -6e-238) or not (x <= 5.2e-142))):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	tmp = 0.0
	if (x <= -3.4e+83)
		tmp = t_1;
	elseif (x <= -3e+36)
		tmp = Float64(2.0 * Float64(x * y));
	elseif ((x <= -2.5e-88) || (!(x <= -3.8e-192) && ((x <= -6e-238) || !(x <= 5.2e-142))))
		tmp = t_1;
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * z));
	tmp = 0.0;
	if (x <= -3.4e+83)
		tmp = t_1;
	elseif (x <= -3e+36)
		tmp = 2.0 * (x * y);
	elseif ((x <= -2.5e-88) || (~((x <= -3.8e-192)) && ((x <= -6e-238) || ~((x <= 5.2e-142)))))
		tmp = t_1;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+83], t$95$1, If[LessEqual[x, -3e+36], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.5e-88], And[N[Not[LessEqual[x, -3.8e-192]], $MachinePrecision], Or[LessEqual[x, -6e-238], N[Not[LessEqual[x, 5.2e-142]], $MachinePrecision]]]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3999999999999998e83 or -3e36 < x < -2.50000000000000004e-88 or -3.8000000000000001e-192 < x < -5.9999999999999999e-238 or 5.1999999999999999e-142 < x

   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 73.7%

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

   if -3.3999999999999998e83 < x < -3e36

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

   6. Taylor expanded in z around 0 89.2%

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

      1. *-commutative 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in t around 0 79.1%

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

   if -2.50000000000000004e-88 < x < -3.8000000000000001e-192 or -5.9999999999999999e-238 < x < 5.1999999999999999e-142

   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 x around 0 73.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-88} \lor \neg \left(x \leq -3.8 \cdot 10^{-192}\right) \land \left(x \leq -6 \cdot 10^{-238} \lor \neg \left(x \leq 5.2 \cdot 10^{-142}\right)\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* x (+ t (* 2.0 y)))))
   (if (<= y -1.05e+54)
     t_2
     (if (<= y 9800000000000.0)
       t_1
       (if (<= y 5.5e+57) (* y 5.0) (if (<= y 1.9e+93) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (y <= -1.05e+54) {
		tmp = t_2;
	} else if (y <= 9800000000000.0) {
		tmp = t_1;
	} else if (y <= 5.5e+57) {
		tmp = y * 5.0;
	} else if (y <= 1.9e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (2.0d0 * z))
    t_2 = x * (t + (2.0d0 * y))
    if (y <= (-1.05d+54)) then
        tmp = t_2
    else if (y <= 9800000000000.0d0) then
        tmp = t_1
    else if (y <= 5.5d+57) then
        tmp = y * 5.0d0
    else if (y <= 1.9d+93) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * z));
	double t_2 = x * (t + (2.0 * y));
	double tmp;
	if (y <= -1.05e+54) {
		tmp = t_2;
	} else if (y <= 9800000000000.0) {
		tmp = t_1;
	} else if (y <= 5.5e+57) {
		tmp = y * 5.0;
	} else if (y <= 1.9e+93) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * z))
	t_2 = x * (t + (2.0 * y))
	tmp = 0
	if y <= -1.05e+54:
		tmp = t_2
	elif y <= 9800000000000.0:
		tmp = t_1
	elif y <= 5.5e+57:
		tmp = y * 5.0
	elif y <= 1.9e+93:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * z)))
	t_2 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (y <= -1.05e+54)
		tmp = t_2;
	elseif (y <= 9800000000000.0)
		tmp = t_1;
	elseif (y <= 5.5e+57)
		tmp = Float64(y * 5.0);
	elseif (y <= 1.9e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * z));
	t_2 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (y <= -1.05e+54)
		tmp = t_2;
	elseif (y <= 9800000000000.0)
		tmp = t_1;
	elseif (y <= 5.5e+57)
		tmp = y * 5.0;
	elseif (y <= 1.9e+93)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+54], t$95$2, If[LessEqual[y, 9800000000000.0], t$95$1, If[LessEqual[y, 5.5e+57], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, 1.9e+93], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999993e54 or 1.8999999999999999e93 < 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. Step-by-step derivation

      1. fma-define 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 64.8%

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

   6. Taylor expanded in z around 0 60.8%

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

      1. *-commutative 60.8%

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

   8. Simplified 60.8%

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

   if -1.04999999999999993e54 < y < 9.8e12 or 5.5000000000000002e57 < y < 1.8999999999999999e93

   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 82.3%

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

   if 9.8e12 < y < 5.5000000000000002e57

   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 x around 0 67.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;y \leq 9800000000000:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+57}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-263}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 19:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= z -6e+89)
     t_1
     (if (<= z 7.5e-263)
       (* x t)
       (if (<= z 1.7e-202) (* 2.0 (* x y)) (if (<= z 19.0) (* x t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (z <= -6e+89) {
		tmp = t_1;
	} else if (z <= 7.5e-263) {
		tmp = x * t;
	} else if (z <= 1.7e-202) {
		tmp = 2.0 * (x * y);
	} else if (z <= 19.0) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (z <= (-6d+89)) then
        tmp = t_1
    else if (z <= 7.5d-263) then
        tmp = x * t
    else if (z <= 1.7d-202) then
        tmp = 2.0d0 * (x * y)
    else if (z <= 19.0d0) then
        tmp = x * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (z <= -6e+89) {
		tmp = t_1;
	} else if (z <= 7.5e-263) {
		tmp = x * t;
	} else if (z <= 1.7e-202) {
		tmp = 2.0 * (x * y);
	} else if (z <= 19.0) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if z <= -6e+89:
		tmp = t_1
	elif z <= 7.5e-263:
		tmp = x * t
	elif z <= 1.7e-202:
		tmp = 2.0 * (x * y)
	elif z <= 19.0:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -6e+89)
		tmp = t_1;
	elseif (z <= 7.5e-263)
		tmp = Float64(x * t);
	elseif (z <= 1.7e-202)
		tmp = Float64(2.0 * Float64(x * y));
	elseif (z <= 19.0)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (z <= -6e+89)
		tmp = t_1;
	elseif (z <= 7.5e-263)
		tmp = x * t;
	elseif (z <= 1.7e-202)
		tmp = 2.0 * (x * y);
	elseif (z <= 19.0)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+89], t$95$1, If[LessEqual[z, 7.5e-263], N[(x * t), $MachinePrecision], If[LessEqual[z, 1.7e-202], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 19.0], N[(x * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.00000000000000025e89 or 19 < z

   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 54.6%

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

   if -6.00000000000000025e89 < z < 7.50000000000000044e-263 or 1.70000000000000006e-202 < z < 19

   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 t around inf 51.4%

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

   5. Simplified 51.4%

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

   if 7.50000000000000044e-263 < z < 1.70000000000000006e-202

   1. Initial program 100.0%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 72.6%

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

   6. Taylor expanded in z around 0 72.6%

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

      1. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in t around 0 72.6%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+89}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-263}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-202}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 19:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-6} \lor \neg \left(x \leq 0.00355\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.05e-6) (not (<= x 0.00355)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ t (+ y y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e-6) || !(x <= 0.00355)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	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 <= (-1.05d-6)) .or. (.not. (x <= 0.00355d0))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e-6) || !(x <= 0.00355)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.05e-6) or not (x <= 0.00355):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.05e-6) || !(x <= 0.00355))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.05e-6) || ~((x <= 0.00355)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (t + (y + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.05e-6], N[Not[LessEqual[x, 0.00355]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0499999999999999e-6 or 0.0035500000000000002 < 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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 99.7%

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

   if -1.0499999999999999e-6 < x < 0.0035500000000000002

   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 83.8%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-6} \lor \neg \left(x \leq 0.00355\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+117}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-213}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.05e+117)
   (* x t)
   (if (<= t 1.1e-213) (* y 5.0) (if (<= t 1.2e+72) (* 2.0 (* x y)) (* x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e+117) {
		tmp = x * t;
	} else if (t <= 1.1e-213) {
		tmp = y * 5.0;
	} else if (t <= 1.2e+72) {
		tmp = 2.0 * (x * y);
	} 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 (t <= (-2.05d+117)) then
        tmp = x * t
    else if (t <= 1.1d-213) then
        tmp = y * 5.0d0
    else if (t <= 1.2d+72) then
        tmp = 2.0d0 * (x * y)
    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 (t <= -2.05e+117) {
		tmp = x * t;
	} else if (t <= 1.1e-213) {
		tmp = y * 5.0;
	} else if (t <= 1.2e+72) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.05e+117:
		tmp = x * t
	elif t <= 1.1e-213:
		tmp = y * 5.0
	elif t <= 1.2e+72:
		tmp = 2.0 * (x * y)
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.05e+117)
		tmp = Float64(x * t);
	elseif (t <= 1.1e-213)
		tmp = Float64(y * 5.0);
	elseif (t <= 1.2e+72)
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.05e+117)
		tmp = x * t;
	elseif (t <= 1.1e-213)
		tmp = y * 5.0;
	elseif (t <= 1.2e+72)
		tmp = 2.0 * (x * y);
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.05e+117], N[(x * t), $MachinePrecision], If[LessEqual[t, 1.1e-213], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 1.2e+72], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e117 or 1.20000000000000005e72 < 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 71.6%

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

   5. Simplified 71.6%

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

   if -2.05e117 < t < 1.10000000000000005e-213

   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 x around 0 40.1%

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

   if 1.10000000000000005e-213 < t < 1.20000000000000005e72

   1. Initial program 99.9%

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

      1. fma-define 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.7%

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

   6. Taylor expanded in z around 0 51.7%

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

      1. *-commutative 51.7%

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

   8. Simplified 51.7%

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

   9. Taylor expanded in t around 0 37.4%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+117}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-213}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+85} \lor \neg \left(y \leq 9800000000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e+85) (not (<= y 9800000000000.0)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ (* 2.0 (+ y z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e+85) || !(y <= 9800000000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * ((2.0 * (y + z)) + 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 <= (-1.05d+85)) .or. (.not. (y <= 9800000000000.0d0))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * ((2.0d0 * (y + z)) + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e+85) || !(y <= 9800000000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * ((2.0 * (y + z)) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e+85) or not (y <= 9800000000000.0):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * ((2.0 * (y + z)) + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e+85) || !(y <= 9800000000000.0))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e+85) || ~((y <= 9800000000000.0)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * ((2.0 * (y + z)) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e+85], N[Not[LessEqual[y, 9800000000000.0]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000005e85 or 9.8e12 < 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 83.8%

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

   5. Simplified 83.8%

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

   if -1.05000000000000005e85 < y < 9.8e12

   1. Initial program 99.9%

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

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 87.8%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+85} \lor \neg \left(y \leq 9800000000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{-16} \lor \neg \left(x \leq 4.2 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.05e-16) (not (<= x 4.2e-132)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.05e-16) || !(x <= 4.2e-132)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} 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 ((x <= (-3.05d-16)) .or. (.not. (x <= 4.2d-132))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    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 ((x <= -3.05e-16) || !(x <= 4.2e-132)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.05e-16) or not (x <= 4.2e-132):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.05e-16) || !(x <= 4.2e-132))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	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 ((x <= -3.05e-16) || ~((x <= 4.2e-132)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.05e-16], N[Not[LessEqual[x, 4.2e-132]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.04999999999999976e-16 or 4.2000000000000002e-132 < 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. Step-by-step derivation

      1. fma-define 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2 \cdot \left(y + z\right) + t, y \cdot 5\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 95.5%

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

   if -3.04999999999999976e-16 < x < 4.2000000000000002e-132

   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 z around 0 87.3%

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

   5. Simplified 87.4%

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

      1. fma-undefine 87.3%

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

      2. *-commutative 87.3%

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

      3. *-commutative 87.3%

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

      4. count-2 87.3%

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

      5. +-commutative 87.3%

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

      6. +-commutative 87.3%

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

      7. distribute-lft-in 87.3%

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

      8. count-2 87.3%

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

      9. *-commutative 87.3%

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

      10. +-commutative 87.3%

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

      11. associate-+l+ 87.3%

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

      12. *-commutative 87.3%

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

      13. count-2 87.3%

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

      14. flip-+ 0.0%

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

      15. +-inverses 0.0%

          \[\leadsto x \cdot t + \left(x \cdot \frac{\color{blue}{0}}{y - y} + y \cdot 5\right) \]

      16. +-inverses 0.0%

          \[\leadsto x \cdot t + \left(x \cdot \frac{0}{\color{blue}{0}} + y \cdot 5\right) \]

   7. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{x \cdot t + \left(x \cdot \frac{0}{0} + y \cdot 5\right)} \]

   9. Simplified 87.3%

      \[\leadsto \color{blue}{x \cdot \left(0 + t\right) + y \cdot 5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.05 \cdot 10^{-16} \lor \neg \left(x \leq 4.2 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+84} \lor \neg \left(y \leq 82000000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.45e+84) (not (<= y 82000000000.0)))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.45e+84) || !(y <= 82000000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * 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 ((y <= (-3.45d+84)) .or. (.not. (y <= 82000000000.0d0))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (2.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.45e+84) || !(y <= 82000000000.0)) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.45e+84) or not (y <= 82000000000.0):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.45e+84) || !(y <= 82000000000.0))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.45e+84) || ~((y <= 82000000000.0)))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.45e+84], N[Not[LessEqual[y, 82000000000.0]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4499999999999998e84 or 8.2e10 < 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 83.8%

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

   5. Simplified 83.8%

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

   if -3.4499999999999998e84 < y < 8.2e10

   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 81.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+84} \lor \neg \left(y \leq 82000000000\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+117} \lor \neg \left(t \leq 5.4 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.05e+117) (not (<= t 5.4e+60))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.05e+117) || !(t <= 5.4e+60)) {
		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 ((t <= (-2.05d+117)) .or. (.not. (t <= 5.4d+60))) 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 ((t <= -2.05e+117) || !(t <= 5.4e+60)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.05e+117) or not (t <= 5.4e+60):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.05e+117) || !(t <= 5.4e+60))
		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 ((t <= -2.05e+117) || ~((t <= 5.4e+60)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.05e+117], N[Not[LessEqual[t, 5.4e+60]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05e117 or 5.3999999999999999e60 < 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 70.5%

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

   5. Simplified 70.5%

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

   if -2.05e117 < t < 5.3999999999999999e60

   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 x around 0 35.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+117} \lor \neg \left(t \leq 5.4 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y * 5.0) + (x * ((2.0 * (y + z)) + 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 = (y * 5.0d0) + (x * ((2.0d0 * (y + z)) + t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. +-commutative 99.9%

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

   3. count-2 99.9%

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

   4. *-commutative 99.9%

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

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

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

Alternative 12: 29.6% accurate, 5.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = y * 5.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 x around 0 26.4%

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

4. Final simplification 26.4%

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

Reproduce

herbie shell --seed 2024039 
(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)))