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

Percentage Accurate: 99.9% → 99.9%

Time: 11.5s

Alternatives: 14

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-def 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: 57.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(x + 5\right)\\ t_3 := x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-186}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z)))
        (t_2 (* y (+ x 5.0)))
        (t_3 (* x (+ t (* 2.0 y)))))
   (if (<= z -5.6e+140)
     t_1
     (if (<= z -1.8e+125)
       t_3
       (if (<= z -1.1e+118)
         t_1
         (if (<= z -5.2e+80)
           t_2
           (if (<= z -3.1e-186)
             t_3
             (if (<= z -5.2e-300) t_2 (if (<= z 6.7e+50) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double t_2 = y * (x + 5.0);
	double t_3 = x * (t + (2.0 * y));
	double tmp;
	if (z <= -5.6e+140) {
		tmp = t_1;
	} else if (z <= -1.8e+125) {
		tmp = t_3;
	} else if (z <= -1.1e+118) {
		tmp = t_1;
	} else if (z <= -5.2e+80) {
		tmp = t_2;
	} else if (z <= -3.1e-186) {
		tmp = t_3;
	} else if (z <= -5.2e-300) {
		tmp = t_2;
	} else if (z <= 6.7e+50) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    t_2 = y * (x + 5.0d0)
    t_3 = x * (t + (2.0d0 * y))
    if (z <= (-5.6d+140)) then
        tmp = t_1
    else if (z <= (-1.8d+125)) then
        tmp = t_3
    else if (z <= (-1.1d+118)) then
        tmp = t_1
    else if (z <= (-5.2d+80)) then
        tmp = t_2
    else if (z <= (-3.1d-186)) then
        tmp = t_3
    else if (z <= (-5.2d-300)) then
        tmp = t_2
    else if (z <= 6.7d+50) then
        tmp = t_3
    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 t_2 = y * (x + 5.0);
	double t_3 = x * (t + (2.0 * y));
	double tmp;
	if (z <= -5.6e+140) {
		tmp = t_1;
	} else if (z <= -1.8e+125) {
		tmp = t_3;
	} else if (z <= -1.1e+118) {
		tmp = t_1;
	} else if (z <= -5.2e+80) {
		tmp = t_2;
	} else if (z <= -3.1e-186) {
		tmp = t_3;
	} else if (z <= -5.2e-300) {
		tmp = t_2;
	} else if (z <= 6.7e+50) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	t_2 = y * (x + 5.0)
	t_3 = x * (t + (2.0 * y))
	tmp = 0
	if z <= -5.6e+140:
		tmp = t_1
	elif z <= -1.8e+125:
		tmp = t_3
	elif z <= -1.1e+118:
		tmp = t_1
	elif z <= -5.2e+80:
		tmp = t_2
	elif z <= -3.1e-186:
		tmp = t_3
	elif z <= -5.2e-300:
		tmp = t_2
	elif z <= 6.7e+50:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	t_2 = Float64(y * Float64(x + 5.0))
	t_3 = Float64(x * Float64(t + Float64(2.0 * y)))
	tmp = 0.0
	if (z <= -5.6e+140)
		tmp = t_1;
	elseif (z <= -1.8e+125)
		tmp = t_3;
	elseif (z <= -1.1e+118)
		tmp = t_1;
	elseif (z <= -5.2e+80)
		tmp = t_2;
	elseif (z <= -3.1e-186)
		tmp = t_3;
	elseif (z <= -5.2e-300)
		tmp = t_2;
	elseif (z <= 6.7e+50)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	t_2 = y * (x + 5.0);
	t_3 = x * (t + (2.0 * y));
	tmp = 0.0;
	if (z <= -5.6e+140)
		tmp = t_1;
	elseif (z <= -1.8e+125)
		tmp = t_3;
	elseif (z <= -1.1e+118)
		tmp = t_1;
	elseif (z <= -5.2e+80)
		tmp = t_2;
	elseif (z <= -3.1e-186)
		tmp = t_3;
	elseif (z <= -5.2e-300)
		tmp = t_2;
	elseif (z <= 6.7e+50)
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(t + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+140], t$95$1, If[LessEqual[z, -1.8e+125], t$95$3, If[LessEqual[z, -1.1e+118], t$95$1, If[LessEqual[z, -5.2e+80], t$95$2, If[LessEqual[z, -3.1e-186], t$95$3, If[LessEqual[z, -5.2e-300], t$95$2, If[LessEqual[z, 6.7e+50], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999966e140 or -1.8000000000000002e125 < z < -1.09999999999999993e118 or 6.6999999999999999e50 < 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 71.9%

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

   if -5.59999999999999966e140 < z < -1.8000000000000002e125 or -5.19999999999999963e80 < z < -3.10000000000000009e-186 or -5.19999999999999993e-300 < z < 6.6999999999999999e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 87.1%

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

   4. Taylor expanded in x around inf 62.6%

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

   if -1.09999999999999993e118 < z < -5.19999999999999963e80 or -3.10000000000000009e-186 < z < -5.19999999999999993e-300

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 96.9%

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

   4. Taylor expanded in y around inf 76.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+140}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+118}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + 2 \cdot z\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* 2.0 z)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -1.08e+161)
     t_2
     (if (<= y -1.35e+62)
       t_1
       (if (<= y -9.5e-14)
         t_2
         (if (<= y 3.7e-53)
           t_1
           (if (<= y 8.5e-11)
             (+ (* y 5.0) (* x t))
             (if (<= y 1.4e+107) 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 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.08e+161) {
		tmp = t_2;
	} else if (y <= -1.35e+62) {
		tmp = t_1;
	} else if (y <= -9.5e-14) {
		tmp = t_2;
	} else if (y <= 3.7e-53) {
		tmp = t_1;
	} else if (y <= 8.5e-11) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.4e+107) {
		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 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-1.08d+161)) then
        tmp = t_2
    else if (y <= (-1.35d+62)) then
        tmp = t_1
    else if (y <= (-9.5d-14)) then
        tmp = t_2
    else if (y <= 3.7d-53) then
        tmp = t_1
    else if (y <= 8.5d-11) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 1.4d+107) 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 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -1.08e+161) {
		tmp = t_2;
	} else if (y <= -1.35e+62) {
		tmp = t_1;
	} else if (y <= -9.5e-14) {
		tmp = t_2;
	} else if (y <= 3.7e-53) {
		tmp = t_1;
	} else if (y <= 8.5e-11) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.4e+107) {
		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 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -1.08e+161:
		tmp = t_2
	elif y <= -1.35e+62:
		tmp = t_1
	elif y <= -9.5e-14:
		tmp = t_2
	elif y <= 3.7e-53:
		tmp = t_1
	elif y <= 8.5e-11:
		tmp = (y * 5.0) + (x * t)
	elif y <= 1.4e+107:
		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(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -1.08e+161)
		tmp = t_2;
	elseif (y <= -1.35e+62)
		tmp = t_1;
	elseif (y <= -9.5e-14)
		tmp = t_2;
	elseif (y <= 3.7e-53)
		tmp = t_1;
	elseif (y <= 8.5e-11)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 1.4e+107)
		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 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -1.08e+161)
		tmp = t_2;
	elseif (y <= -1.35e+62)
		tmp = t_1;
	elseif (y <= -9.5e-14)
		tmp = t_2;
	elseif (y <= 3.7e-53)
		tmp = t_1;
	elseif (y <= 8.5e-11)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 1.4e+107)
		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[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.08e+161], t$95$2, If[LessEqual[y, -1.35e+62], t$95$1, If[LessEqual[y, -9.5e-14], t$95$2, If[LessEqual[y, 3.7e-53], t$95$1, If[LessEqual[y, 8.5e-11], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+107], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e161 or -1.35e62 < y < -9.4999999999999999e-14 or 1.39999999999999992e107 < 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 86.3%

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

   5. Simplified 86.3%

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

   if -1.08e161 < y < -1.35e62 or -9.4999999999999999e-14 < y < 3.69999999999999982e-53 or 8.50000000000000037e-11 < y < 1.39999999999999992e107

   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 83.7%

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

   if 3.69999999999999982e-53 < y < 8.50000000000000037e-11

   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. distribute-rgt-in 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. *-commutative 99.9%

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

      7. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around inf 80.8%

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

   7. Simplified 80.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x + 5\right)\\ t_2 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-285}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-34}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ x 5.0))) (t_2 (* 2.0 (* x z))))
   (if (<= y -1.3e+130)
     t_1
     (if (<= y -2.9e+62)
       t_2
       (if (<= y -3.6e-20)
         t_1
         (if (<= y 3.6e-285)
           (* x t)
           (if (<= y 3.6e-213) t_2 (if (<= y 5e-34) (* x t) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x + 5.0);
	double t_2 = 2.0 * (x * z);
	double tmp;
	if (y <= -1.3e+130) {
		tmp = t_1;
	} else if (y <= -2.9e+62) {
		tmp = t_2;
	} else if (y <= -3.6e-20) {
		tmp = t_1;
	} else if (y <= 3.6e-285) {
		tmp = x * t;
	} else if (y <= 3.6e-213) {
		tmp = t_2;
	} else if (y <= 5e-34) {
		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) :: t_2
    real(8) :: tmp
    t_1 = y * (x + 5.0d0)
    t_2 = 2.0d0 * (x * z)
    if (y <= (-1.3d+130)) then
        tmp = t_1
    else if (y <= (-2.9d+62)) then
        tmp = t_2
    else if (y <= (-3.6d-20)) then
        tmp = t_1
    else if (y <= 3.6d-285) then
        tmp = x * t
    else if (y <= 3.6d-213) then
        tmp = t_2
    else if (y <= 5d-34) 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 = y * (x + 5.0);
	double t_2 = 2.0 * (x * z);
	double tmp;
	if (y <= -1.3e+130) {
		tmp = t_1;
	} else if (y <= -2.9e+62) {
		tmp = t_2;
	} else if (y <= -3.6e-20) {
		tmp = t_1;
	} else if (y <= 3.6e-285) {
		tmp = x * t;
	} else if (y <= 3.6e-213) {
		tmp = t_2;
	} else if (y <= 5e-34) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x + 5.0)
	t_2 = 2.0 * (x * z)
	tmp = 0
	if y <= -1.3e+130:
		tmp = t_1
	elif y <= -2.9e+62:
		tmp = t_2
	elif y <= -3.6e-20:
		tmp = t_1
	elif y <= 3.6e-285:
		tmp = x * t
	elif y <= 3.6e-213:
		tmp = t_2
	elif y <= 5e-34:
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x + 5.0))
	t_2 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (y <= -1.3e+130)
		tmp = t_1;
	elseif (y <= -2.9e+62)
		tmp = t_2;
	elseif (y <= -3.6e-20)
		tmp = t_1;
	elseif (y <= 3.6e-285)
		tmp = Float64(x * t);
	elseif (y <= 3.6e-213)
		tmp = t_2;
	elseif (y <= 5e-34)
		tmp = Float64(x * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x + 5.0);
	t_2 = 2.0 * (x * z);
	tmp = 0.0;
	if (y <= -1.3e+130)
		tmp = t_1;
	elseif (y <= -2.9e+62)
		tmp = t_2;
	elseif (y <= -3.6e-20)
		tmp = t_1;
	elseif (y <= 3.6e-285)
		tmp = x * t;
	elseif (y <= 3.6e-213)
		tmp = t_2;
	elseif (y <= 5e-34)
		tmp = x * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+130], t$95$1, If[LessEqual[y, -2.9e+62], t$95$2, If[LessEqual[y, -3.6e-20], t$95$1, If[LessEqual[y, 3.6e-285], N[(x * t), $MachinePrecision], If[LessEqual[y, 3.6e-213], t$95$2, If[LessEqual[y, 5e-34], N[(x * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e130 or -2.89999999999999984e62 < y < -3.59999999999999974e-20 or 5.0000000000000003e-34 < 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 0 91.0%

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

   4. Taylor expanded in y around inf 65.6%

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

   if -1.2999999999999999e130 < y < -2.89999999999999984e62 or 3.60000000000000004e-285 < y < 3.6000000000000001e-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 z around inf 66.2%

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

   if -3.59999999999999974e-20 < y < 3.60000000000000004e-285 or 3.6000000000000001e-213 < y < 5.0000000000000003e-34

   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 54.1%

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

   5. Simplified 54.1%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+130}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-285}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-213}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-34}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+161} \lor \neg \left(y \leq -2.05 \cdot 10^{+62} \lor \neg \left(y \leq -1.2 \cdot 10^{-13}\right) \land y \leq 7 \cdot 10^{+99}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.08e+161)
         (not (or (<= y -2.05e+62) (and (not (<= y -1.2e-13)) (<= y 7e+99)))))
   (* 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 <= -1.08e+161) || !((y <= -2.05e+62) || (!(y <= -1.2e-13) && (y <= 7e+99)))) {
		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 <= (-1.08d+161)) .or. (.not. (y <= (-2.05d+62)) .or. (.not. (y <= (-1.2d-13))) .and. (y <= 7d+99))) 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 <= -1.08e+161) || !((y <= -2.05e+62) || (!(y <= -1.2e-13) && (y <= 7e+99)))) {
		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 <= -1.08e+161) or not ((y <= -2.05e+62) or (not (y <= -1.2e-13) and (y <= 7e+99))):
		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 <= -1.08e+161) || !((y <= -2.05e+62) || (!(y <= -1.2e-13) && (y <= 7e+99))))
		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 <= -1.08e+161) || ~(((y <= -2.05e+62) || (~((y <= -1.2e-13)) && (y <= 7e+99)))))
		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, -1.08e+161], N[Not[Or[LessEqual[y, -2.05e+62], And[N[Not[LessEqual[y, -1.2e-13]], $MachinePrecision], LessEqual[y, 7e+99]]]], $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 < -1.08e161 or -2.04999999999999992e62 < y < -1.1999999999999999e-13 or 6.9999999999999995e99 < 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 86.3%

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

   5. Simplified 86.3%

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

   if -1.08e161 < y < -2.04999999999999992e62 or -1.1999999999999999e-13 < y < 6.9999999999999995e99

   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 81.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+161} \lor \neg \left(y \leq -2.05 \cdot 10^{+62} \lor \neg \left(y \leq -1.2 \cdot 10^{-13}\right) \land y \leq 7 \cdot 10^{+99}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x z))))
   (if (<= t -3.7e+72)
     (* x t)
     (if (<= t 3.7e-51)
       t_1
       (if (<= t 1.35e-11) (* y 5.0) (if (<= t 5.6e+31) t_1 (* x t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * (x * z);
	double tmp;
	if (t <= -3.7e+72) {
		tmp = x * t;
	} else if (t <= 3.7e-51) {
		tmp = t_1;
	} else if (t <= 1.35e-11) {
		tmp = y * 5.0;
	} else if (t <= 5.6e+31) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (x * z)
    if (t <= (-3.7d+72)) then
        tmp = x * t
    else if (t <= 3.7d-51) then
        tmp = t_1
    else if (t <= 1.35d-11) then
        tmp = y * 5.0d0
    else if (t <= 5.6d+31) then
        tmp = t_1
    else
        tmp = x * t
    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 (t <= -3.7e+72) {
		tmp = x * t;
	} else if (t <= 3.7e-51) {
		tmp = t_1;
	} else if (t <= 1.35e-11) {
		tmp = y * 5.0;
	} else if (t <= 5.6e+31) {
		tmp = t_1;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * (x * z)
	tmp = 0
	if t <= -3.7e+72:
		tmp = x * t
	elif t <= 3.7e-51:
		tmp = t_1
	elif t <= 1.35e-11:
		tmp = y * 5.0
	elif t <= 5.6e+31:
		tmp = t_1
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(x * z))
	tmp = 0.0
	if (t <= -3.7e+72)
		tmp = Float64(x * t);
	elseif (t <= 3.7e-51)
		tmp = t_1;
	elseif (t <= 1.35e-11)
		tmp = Float64(y * 5.0);
	elseif (t <= 5.6e+31)
		tmp = t_1;
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * (x * z);
	tmp = 0.0;
	if (t <= -3.7e+72)
		tmp = x * t;
	elseif (t <= 3.7e-51)
		tmp = t_1;
	elseif (t <= 1.35e-11)
		tmp = y * 5.0;
	elseif (t <= 5.6e+31)
		tmp = t_1;
	else
		tmp = x * t;
	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[t, -3.7e+72], N[(x * t), $MachinePrecision], If[LessEqual[t, 3.7e-51], t$95$1, If[LessEqual[t, 1.35e-11], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 5.6e+31], t$95$1, N[(x * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000002e72 or 5.60000000000000034e31 < t

   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 62.7%

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

   5. Simplified 62.7%

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

   if -3.7000000000000002e72 < t < 3.69999999999999973e-51 or 1.35000000000000002e-11 < t < 5.60000000000000034e31

   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 inf 45.9%

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

   if 3.69999999999999973e-51 < t < 1.35000000000000002e-11

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 65.1%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-11}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+31} \lor \neg \left(x \leq 4.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e+31) (not (<= x 4.7e-7)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* x (+ t (+ y (* 2.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e+31) || !(x <= 4.7e-7)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (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 <= (-4d+31)) .or. (.not. (x <= 4.7d-7))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + (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 <= -4e+31) || !(x <= 4.7e-7)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4e+31) or not (x <= 4.7e-7):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4e+31) || !(x <= 4.7e-7))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + Float64(2.0 * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4e+31) || ~((x <= 4.7e-7)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (x * (t + (y + (2.0 * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4e+31], N[Not[LessEqual[x, 4.7e-7]], $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 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999999e31 or 4.7e-7 < 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-def 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 99.5%

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

   if -3.9999999999999999e31 < x < 4.7e-7

   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 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+31} \lor \neg \left(x \leq 4.7 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + 2 \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -102000000000:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;t \leq 10^{+35}:\\ \;\;\;\;y \cdot 5 + \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -102000000000.0)
   (* x (+ (* 2.0 (+ y z)) t))
   (if (<= t 1e+35)
     (+ (* y 5.0) (* (+ y z) (* x 2.0)))
     (+ (* x t) (* y (+ 5.0 (* x 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -102000000000.0) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else if (t <= 1e+35) {
		tmp = (y * 5.0) + ((y + z) * (x * 2.0));
	} else {
		tmp = (x * t) + (y * (5.0 + (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 (t <= (-102000000000.0d0)) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else if (t <= 1d+35) then
        tmp = (y * 5.0d0) + ((y + z) * (x * 2.0d0))
    else
        tmp = (x * t) + (y * (5.0d0 + (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 (t <= -102000000000.0) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else if (t <= 1e+35) {
		tmp = (y * 5.0) + ((y + z) * (x * 2.0));
	} else {
		tmp = (x * t) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -102000000000.0:
		tmp = x * ((2.0 * (y + z)) + t)
	elif t <= 1e+35:
		tmp = (y * 5.0) + ((y + z) * (x * 2.0))
	else:
		tmp = (x * t) + (y * (5.0 + (x * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -102000000000.0)
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	elseif (t <= 1e+35)
		tmp = Float64(Float64(y * 5.0) + Float64(Float64(y + z) * Float64(x * 2.0)));
	else
		tmp = Float64(Float64(x * t) + Float64(y * Float64(5.0 + Float64(x * 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -102000000000.0)
		tmp = x * ((2.0 * (y + z)) + t);
	elseif (t <= 1e+35)
		tmp = (y * 5.0) + ((y + z) * (x * 2.0));
	else
		tmp = (x * t) + (y * (5.0 + (x * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -102000000000.0], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+35], N[(N[(y * 5.0), $MachinePrecision] + N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] + N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.02e11

   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-def 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 88.2%

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

   if -1.02e11 < t < 9.9999999999999997e34

   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 0 93.8%

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

   5. Simplified 93.8%

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

   if 9.9999999999999997e34 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 87.7%

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

   4. Taylor expanded in y around 0 87.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -102000000000:\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{elif}\;t \leq 10^{+35}:\\ \;\;\;\;y \cdot 5 + \left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-15} \lor \neg \left(x \leq 2.7 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e-15) (not (<= x 2.7e-38)))
   (* 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 <= -8.5e-15) || !(x <= 2.7e-38)) {
		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 <= (-8.5d-15)) .or. (.not. (x <= 2.7d-38))) 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 <= -8.5e-15) || !(x <= 2.7e-38)) {
		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 <= -8.5e-15) or not (x <= 2.7e-38):
		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 <= -8.5e-15) || !(x <= 2.7e-38))
		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 <= -8.5e-15) || ~((x <= 2.7e-38)))
		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, -8.5e-15], N[Not[LessEqual[x, 2.7e-38]], $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 < -8.50000000000000007e-15 or 2.70000000000000005e-38 < 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-def 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 98.3%

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

   if -8.50000000000000007e-15 < x < 2.70000000000000005e-38

   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. distribute-rgt-in 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. *-commutative 99.9%

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

      7. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around inf 79.7%

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

   7. Simplified 79.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-15} \lor \neg \left(x \leq 2.7 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-106} \lor \neg \left(x \leq 1.1 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.1e-106) (not (<= x 1.1e-29)))
   (* x (+ (* 2.0 (+ y z)) t))
   (+ (* y 5.0) (* 2.0 (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1e-106) || !(x <= 1.1e-29)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (2.0 * (x * 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 <= (-1.1d-106)) .or. (.not. (x <= 1.1d-29))) then
        tmp = x * ((2.0d0 * (y + z)) + t)
    else
        tmp = (y * 5.0d0) + (2.0d0 * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1e-106) || !(x <= 1.1e-29)) {
		tmp = x * ((2.0 * (y + z)) + t);
	} else {
		tmp = (y * 5.0) + (2.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.1e-106) or not (x <= 1.1e-29):
		tmp = x * ((2.0 * (y + z)) + t)
	else:
		tmp = (y * 5.0) + (2.0 * (x * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.1e-106) || !(x <= 1.1e-29))
		tmp = Float64(x * Float64(Float64(2.0 * Float64(y + z)) + t));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.1e-106) || ~((x <= 1.1e-29)))
		tmp = x * ((2.0 * (y + z)) + t);
	else
		tmp = (y * 5.0) + (2.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.1e-106], N[Not[LessEqual[x, 1.1e-29]], $MachinePrecision]], N[(x * N[(N[(2.0 * N[(y + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.09999999999999997e-106 or 1.09999999999999995e-29 < 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-def 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 95.4%

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

   if -1.09999999999999997e-106 < x < 1.09999999999999995e-29

   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. distribute-rgt-in 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. count-2 99.9%

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

      6. *-commutative 99.9%

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

      7. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 82.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-106} \lor \neg \left(x \leq 1.1 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \left(y + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+161} \lor \neg \left(y \leq 1.08 \cdot 10^{+136}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.08e+161) (not (<= y 1.08e+136)))
   (* y (+ x 5.0))
   (* x (+ t (* 2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.08e+161) || !(y <= 1.08e+136)) {
		tmp = y * (x + 5.0);
	} 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 <= (-1.08d+161)) .or. (.not. (y <= 1.08d+136))) then
        tmp = y * (x + 5.0d0)
    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 <= -1.08e+161) || !(y <= 1.08e+136)) {
		tmp = y * (x + 5.0);
	} else {
		tmp = x * (t + (2.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.08e+161) or not (y <= 1.08e+136):
		tmp = y * (x + 5.0)
	else:
		tmp = x * (t + (2.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.08e+161) || !(y <= 1.08e+136))
		tmp = Float64(y * Float64(x + 5.0));
	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 <= -1.08e+161) || ~((y <= 1.08e+136)))
		tmp = y * (x + 5.0);
	else
		tmp = x * (t + (2.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.08e+161], N[Not[LessEqual[y, 1.08e+136]], $MachinePrecision]], N[(y * N[(x + 5.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(2.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08e161 or 1.07999999999999994e136 < 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 0 95.0%

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

   4. Taylor expanded in y around inf 85.9%

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

   if -1.08e161 < y < 1.07999999999999994e136

   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 77.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+161} \lor \neg \left(y \leq 1.08 \cdot 10^{+136}\right):\\ \;\;\;\;y \cdot \left(x + 5\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + 2 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * (t + (y + (z + (y + z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + N[(z + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. Final simplification 99.9%

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

Alternative 13: 47.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-107} \lor \neg \left(x \leq 3.1 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e-107) (not (<= x 3.1e-39))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e-107) || !(x <= 3.1e-39)) {
		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 <= (-9.5d-107)) .or. (.not. (x <= 3.1d-39))) 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 <= -9.5e-107) || !(x <= 3.1e-39)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.5e-107) or not (x <= 3.1e-39):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.5e-107) || !(x <= 3.1e-39))
		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 <= -9.5e-107) || ~((x <= 3.1e-39)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.5e-107], N[Not[LessEqual[x, 3.1e-39]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999999e-107 or 3.0999999999999997e-39 < 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 t around inf 39.1%

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

   5. Simplified 39.1%

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

   if -9.4999999999999999e-107 < x < 3.0999999999999997e-39

   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 63.8%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-107} \lor \neg \left(x \leq 3.1 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.2% 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 25.6%

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

4. Final simplification 25.6%

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

Reproduce

herbie shell --seed 2024017 
(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)))