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

Percentage Accurate: 99.9% → 99.9%

Time: 10.0s

Alternatives: 12

Speedup: 1.0×

• 26.6% 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 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. Final simplification 99.9%

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

Alternative 2: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-99}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 y)))))
   (if (<= y -3.9e+46)
     (* y 5.0)
     (if (<= y -4.8e-74)
       t_1
       (if (<= y -1.15e-99)
         (* y 5.0)
         (if (<= y 2.45e+28)
           (* x (+ t (* 2.0 z)))
           (if (<= y 1.02e+101) (* y 5.0) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (2.0 * y));
	double tmp;
	if (y <= -3.9e+46) {
		tmp = y * 5.0;
	} else if (y <= -4.8e-74) {
		tmp = t_1;
	} else if (y <= -1.15e-99) {
		tmp = y * 5.0;
	} else if (y <= 2.45e+28) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 1.02e+101) {
		tmp = y * 5.0;
	} 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 = x * (t + (2.0d0 * y))
    if (y <= (-3.9d+46)) then
        tmp = y * 5.0d0
    else if (y <= (-4.8d-74)) then
        tmp = t_1
    else if (y <= (-1.15d-99)) then
        tmp = y * 5.0d0
    else if (y <= 2.45d+28) then
        tmp = x * (t + (2.0d0 * z))
    else if (y <= 1.02d+101) then
        tmp = y * 5.0d0
    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 = x * (t + (2.0 * y));
	double tmp;
	if (y <= -3.9e+46) {
		tmp = y * 5.0;
	} else if (y <= -4.8e-74) {
		tmp = t_1;
	} else if (y <= -1.15e-99) {
		tmp = y * 5.0;
	} else if (y <= 2.45e+28) {
		tmp = x * (t + (2.0 * z));
	} else if (y <= 1.02e+101) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (2.0 * y))
	tmp = 0
	if y <= -3.9e+46:
		tmp = y * 5.0
	elif y <= -4.8e-74:
		tmp = t_1
	elif y <= -1.15e-99:
		tmp = y * 5.0
	elif y <= 2.45e+28:
		tmp = x * (t + (2.0 * z))
	elif y <= 1.02e+101:
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (y <= -3.9e+46)
		tmp = Float64(y * 5.0);
	elseif (y <= -4.8e-74)
		tmp = t_1;
	elseif (y <= -1.15e-99)
		tmp = Float64(y * 5.0);
	elseif (y <= 2.45e+28)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	elseif (y <= 1.02e+101)
		tmp = Float64(y * 5.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (y <= -3.9e+46)
		tmp = y * 5.0;
	elseif (y <= -4.8e-74)
		tmp = t_1;
	elseif (y <= -1.15e-99)
		tmp = y * 5.0;
	elseif (y <= 2.45e+28)
		tmp = x * (t + (2.0 * z));
	elseif (y <= 1.02e+101)
		tmp = y * 5.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+46], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, -4.8e-74], t$95$1, If[LessEqual[y, -1.15e-99], N[(y * 5.0), $MachinePrecision], If[LessEqual[y, 2.45e+28], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+101], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.89999999999999995e46 or -4.7999999999999998e-74 < y < -1.1499999999999999e-99 or 2.4499999999999998e28 < y < 1.02000000000000002e101

   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 67.3%

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

   if -3.89999999999999995e46 < y < -4.7999999999999998e-74 or 1.02000000000000002e101 < 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 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 65.3%

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

   6. Taylor expanded in z around 0 57.7%

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

      1. *-commutative 57.7%

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

   8. Simplified 57.7%

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

   if -1.1499999999999999e-99 < y < 2.4499999999999998e28

   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 0 88.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+46}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-99}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+101}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-126}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right) + y \cdot 5\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (* 2.0 (+ y z)) t))))
   (if (<= x -1.12e-69)
     t_1
     (if (<= x -2.7e-126)
       (+ (* 2.0 (* x z)) (* y 5.0))
       (if (<= x -2.1e-153)
         (* x (+ t (* 2.0 z)))
         (if (<= x 1.75e-15) (+ (* y 5.0) (* x t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -1.12e-69) {
		tmp = t_1;
	} else if (x <= -2.7e-126) {
		tmp = (2.0 * (x * z)) + (y * 5.0);
	} else if (x <= -2.1e-153) {
		tmp = x * (t + (2.0 * z));
	} else if (x <= 1.75e-15) {
		tmp = (y * 5.0) + (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 = x * ((2.0d0 * (y + z)) + t)
    if (x <= (-1.12d-69)) then
        tmp = t_1
    else if (x <= (-2.7d-126)) then
        tmp = (2.0d0 * (x * z)) + (y * 5.0d0)
    else if (x <= (-2.1d-153)) then
        tmp = x * (t + (2.0d0 * z))
    else if (x <= 1.75d-15) then
        tmp = (y * 5.0d0) + (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 = x * ((2.0 * (y + z)) + t);
	double tmp;
	if (x <= -1.12e-69) {
		tmp = t_1;
	} else if (x <= -2.7e-126) {
		tmp = (2.0 * (x * z)) + (y * 5.0);
	} else if (x <= -2.1e-153) {
		tmp = x * (t + (2.0 * z));
	} else if (x <= 1.75e-15) {
		tmp = (y * 5.0) + (x * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((2.0 * (y + z)) + t)
	tmp = 0
	if x <= -1.12e-69:
		tmp = t_1
	elif x <= -2.7e-126:
		tmp = (2.0 * (x * z)) + (y * 5.0)
	elif x <= -2.1e-153:
		tmp = x * (t + (2.0 * z))
	elif x <= 1.75e-15:
		tmp = (y * 5.0) + (x * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t))
	tmp = 0.0
	if (x <= -1.12e-69)
		tmp = t_1;
	elseif (x <= -2.7e-126)
		tmp = Float64(Float64(2.0 * Float64(x * z)) + Float64(y * 5.0));
	elseif (x <= -2.1e-153)
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	elseif (x <= 1.75e-15)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((2.0 * (y + z)) + t);
	tmp = 0.0;
	if (x <= -1.12e-69)
		tmp = t_1;
	elseif (x <= -2.7e-126)
		tmp = (2.0 * (x * z)) + (y * 5.0);
	elseif (x <= -2.1e-153)
		tmp = x * (t + (2.0 * z));
	elseif (x <= 1.75e-15)
		tmp = (y * 5.0) + (x * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.12e-69], t$95$1, If[LessEqual[x, -2.7e-126], N[(N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-153], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-15], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.12e-69 or 1.75e-15 < 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 96.1%

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

   if -1.12e-69 < x < -2.69999999999999995e-126

   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 0 100.0%

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

   4. Taylor expanded in t around 0 93.6%

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

   if -2.69999999999999995e-126 < x < -2.10000000000000004e-153

   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 0 100.0%

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

   if -2.10000000000000004e-153 < x < 1.75e-15

   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 99.8%

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

   4. Taylor expanded in z around 0 89.9%

      \[\leadsto \color{blue}{5 \cdot y + t \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-126}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right) + y \cdot 5\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-83} \lor \neg \left(x \leq -1.2 \cdot 10^{-126}\right) \land \left(x \leq -4.4 \cdot 10^{-154} \lor \neg \left(x \leq 2.9 \cdot 10^{-91}\right)\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.5e-83)
         (and (not (<= x -1.2e-126))
              (or (<= x -4.4e-154) (not (<= x 2.9e-91)))))
   (* x (+ t (* 2.0 z)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e-83) || (!(x <= -1.2e-126) && ((x <= -4.4e-154) || !(x <= 2.9e-91)))) {
		tmp = x * (t + (2.0 * z));
	} 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 <= (-1.5d-83)) .or. (.not. (x <= (-1.2d-126))) .and. (x <= (-4.4d-154)) .or. (.not. (x <= 2.9d-91))) then
        tmp = x * (t + (2.0d0 * z))
    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 <= -1.5e-83) || (!(x <= -1.2e-126) && ((x <= -4.4e-154) || !(x <= 2.9e-91)))) {
		tmp = x * (t + (2.0 * z));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.5e-83) or (not (x <= -1.2e-126) and ((x <= -4.4e-154) or not (x <= 2.9e-91))):
		tmp = x * (t + (2.0 * z))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.5e-83) || (!(x <= -1.2e-126) && ((x <= -4.4e-154) || !(x <= 2.9e-91))))
		tmp = Float64(x * Float64(t + Float64(2.0 * z)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.5e-83) || (~((x <= -1.2e-126)) && ((x <= -4.4e-154) || ~((x <= 2.9e-91)))))
		tmp = x * (t + (2.0 * z));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.5e-83], And[N[Not[LessEqual[x, -1.2e-126]], $MachinePrecision], Or[LessEqual[x, -4.4e-154], N[Not[LessEqual[x, 2.9e-91]], $MachinePrecision]]]], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000005e-83 or -1.20000000000000003e-126 < x < -4.40000000000000015e-154 or 2.9000000000000001e-91 < 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 0 73.3%

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

   if -1.50000000000000005e-83 < x < -1.20000000000000003e-126 or -4.40000000000000015e-154 < x < 2.9000000000000001e-91

   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 74.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-83} \lor \neg \left(x \leq -1.2 \cdot 10^{-126}\right) \land \left(x \leq -4.4 \cdot 10^{-154} \lor \neg \left(x \leq 2.9 \cdot 10^{-91}\right)\right):\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+43} \lor \neg \left(x \leq 5.2 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-69)
   (* x t)
   (if (<= x 5.8e-19)
     (* y 5.0)
     (if (or (<= x 5.6e+43) (not (<= x 5.2e+149))) (* x t) (* z (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-69) {
		tmp = x * t;
	} else if (x <= 5.8e-19) {
		tmp = y * 5.0;
	} else if ((x <= 5.6e+43) || !(x <= 5.2e+149)) {
		tmp = x * t;
	} else {
		tmp = z * (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 <= (-2.2d-69)) then
        tmp = x * t
    else if (x <= 5.8d-19) then
        tmp = y * 5.0d0
    else if ((x <= 5.6d+43) .or. (.not. (x <= 5.2d+149))) then
        tmp = x * t
    else
        tmp = z * (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 <= -2.2e-69) {
		tmp = x * t;
	} else if (x <= 5.8e-19) {
		tmp = y * 5.0;
	} else if ((x <= 5.6e+43) || !(x <= 5.2e+149)) {
		tmp = x * t;
	} else {
		tmp = z * (x * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-69:
		tmp = x * t
	elif x <= 5.8e-19:
		tmp = y * 5.0
	elif (x <= 5.6e+43) or not (x <= 5.2e+149):
		tmp = x * t
	else:
		tmp = z * (x * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-69)
		tmp = Float64(x * t);
	elseif (x <= 5.8e-19)
		tmp = Float64(y * 5.0);
	elseif ((x <= 5.6e+43) || !(x <= 5.2e+149))
		tmp = Float64(x * t);
	else
		tmp = Float64(z * Float64(x * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.2e-69)
		tmp = x * t;
	elseif (x <= 5.8e-19)
		tmp = y * 5.0;
	elseif ((x <= 5.6e+43) || ~((x <= 5.2e+149)))
		tmp = x * t;
	else
		tmp = z * (x * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-69], N[(x * t), $MachinePrecision], If[LessEqual[x, 5.8e-19], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 5.6e+43], N[Not[LessEqual[x, 5.2e+149]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e-69 or 5.8e-19 < x < 5.60000000000000038e43 or 5.19999999999999957e149 < 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 t around inf 52.6%

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

   5. Simplified 52.6%

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

   if -2.2e-69 < x < 5.8e-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 x around 0 64.9%

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

   if 5.60000000000000038e43 < x < 5.19999999999999957e149

   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 53.7%

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

   5. Simplified 53.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+43} \lor \neg \left(x \leq 5.2 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-14} \lor \neg \left(x \leq 5 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.8e-14) (not (<= x 5e-58)))
   (* x (+ t (+ (* 2.0 (+ y z)) (* 5.0 (/ y x)))))
   (+ (* y 5.0) (* x (+ t (* 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.8e-14) || !(x <= 5e-58)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-6.8d-14)) .or. (.not. (x <= 5d-58))) then
        tmp = x * (t + ((2.0d0 * (y + z)) + (5.0d0 * (y / x))))
    else
        tmp = (y * 5.0d0) + (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 ((x <= -6.8e-14) || !(x <= 5e-58)) {
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	} else {
		tmp = (y * 5.0) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.8e-14) or not (x <= 5e-58):
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))))
	else:
		tmp = (y * 5.0) + (x * (t + (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.8e-14) || !(x <= 5e-58))
		tmp = Float64(x * Float64(t + Float64(Float64(2.0 * Float64(y + z)) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(y * 5.0) + 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 ((x <= -6.8e-14) || ~((x <= 5e-58)))
		tmp = x * (t + ((2.0 * (y + z)) + (5.0 * (y / x))));
	else
		tmp = (y * 5.0) + (x * (t + (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.8e-14], N[Not[LessEqual[x, 5e-58]], $MachinePrecision]], N[(x * N[(t + N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.80000000000000006e-14 or 4.99999999999999977e-58 < 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 100.0%

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

   if -6.80000000000000006e-14 < x < 4.99999999999999977e-58

   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 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-14} \lor \neg \left(x \leq 5 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(t + \left(2 \cdot \left(y + z\right) + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 0.108\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.5) (not (<= x 0.108)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ t (* 2.0 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.5) || !(x <= 0.108)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (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 ((x <= (-2.5d0)) .or. (.not. (x <= 0.108d0))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (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 ((x <= -2.5) || !(x <= 0.108)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (2.0 * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.5) or not (x <= 0.108):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (t + (2.0 * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.5) || !(x <= 0.108))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + 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 ((x <= -2.5) || ~((x <= 0.108)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (t + (2.0 * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.5], N[Not[LessEqual[x, 0.108]], $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[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5 or 0.107999999999999999 < 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 98.6%

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

   if -2.5 < x < 0.107999999999999999

   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 98.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \lor \neg \left(x \leq 0.108\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-82} \lor \neg \left(x \leq 1.8 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e-82) (not (<= x 1.8e-15)))
   (* 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 <= -1.35e-82) || !(x <= 1.8e-15)) {
		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 <= (-1.35d-82)) .or. (.not. (x <= 1.8d-15))) 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 <= -1.35e-82) || !(x <= 1.8e-15)) {
		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 <= -1.35e-82) or not (x <= 1.8e-15):
		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 <= -1.35e-82) || !(x <= 1.8e-15))
		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 <= -1.35e-82) || ~((x <= 1.8e-15)))
		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, -1.35e-82], N[Not[LessEqual[x, 1.8e-15]], $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 < -1.3500000000000001e-82 or 1.8000000000000001e-15 < 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 95.0%

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

   if -1.3500000000000001e-82 < x < 1.8000000000000001e-15

   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 99.9%

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

   4. Taylor expanded in z around 0 88.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-82} \lor \neg \left(x \leq 1.8 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-99} \lor \neg \left(y \leq 9.2 \cdot 10^{+26}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-99) (not (<= y 9.2e+26)))
   (* 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 <= -1.15e-99) || !(y <= 9.2e+26)) {
		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 <= (-1.15d-99)) .or. (.not. (y <= 9.2d+26))) 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 <= -1.15e-99) || !(y <= 9.2e+26)) {
		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 <= -1.15e-99) or not (y <= 9.2e+26):
		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 <= -1.15e-99) || !(y <= 9.2e+26))
		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 <= -1.15e-99) || ~((y <= 9.2e+26)))
		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, -1.15e-99], N[Not[LessEqual[y, 9.2e+26]], $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 < -1.1499999999999999e-99 or 9.2000000000000002e26 < 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 82.5%

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

   5. Simplified 82.5%

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

   if -1.1499999999999999e-99 < y < 9.2000000000000002e26

   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 0 88.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-99} \lor \neg \left(y \leq 9.2 \cdot 10^{+26}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 99.9%

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

Alternative 11: 47.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-67} \lor \neg \left(x \leq 7.2 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.35e-67) (not (<= x 7.2e-19))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.35e-67) || !(x <= 7.2e-19)) {
		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 <= (-2.35d-67)) .or. (.not. (x <= 7.2d-19))) 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 <= -2.35e-67) || !(x <= 7.2e-19)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.35e-67) or not (x <= 7.2e-19):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.35e-67) || !(x <= 7.2e-19))
		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 <= -2.35e-67) || ~((x <= 7.2e-19)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.35e-67], N[Not[LessEqual[x, 7.2e-19]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.35000000000000002e-67 or 7.2000000000000002e-19 < 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 t around inf 47.4%

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

   5. Simplified 47.4%

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

   if -2.35000000000000002e-67 < x < 7.2000000000000002e-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 x around 0 64.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-67} \lor \neg \left(x \leq 7.2 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.9% 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 31.3%

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

4. Final simplification 31.3%

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

Reproduce

herbie shell --seed 2024055 
(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)))