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

Percentage Accurate: 99.9% → 100.0%

Time: 8.9s

Alternatives: 13

Speedup: 1.2×

• 27.2% 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: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 100.0%

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

   3. associate-+l+ 100.0%

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

   4. *-un-lft-identity 100.0%

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

   5. +-commutative 100.0%

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

   6. *-un-lft-identity 100.0%

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

   7. distribute-rgt-out 100.0%

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

   8. metadata-eval 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-25} \lor \neg \left(x \leq -1.6 \cdot 10^{-150}\right) \land x \leq 6.8 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* x (+ t (* y 2.0)))))
   (if (<= x -5.4e+30)
     t_2
     (if (<= x -4.2e+15)
       t_1
       (if (<= x -1.8e-7)
         t_2
         (if (or (<= x -5.5e-25) (and (not (<= x -1.6e-150)) (<= x 6.8e-8)))
           (* y 5.0)
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -5.4e+30) {
		tmp = t_2;
	} else if (x <= -4.2e+15) {
		tmp = t_1;
	} else if (x <= -1.8e-7) {
		tmp = t_2;
	} else if ((x <= -5.5e-25) || (!(x <= -1.6e-150) && (x <= 6.8e-8))) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    t_2 = x * (t + (y * 2.0d0))
    if (x <= (-5.4d+30)) then
        tmp = t_2
    else if (x <= (-4.2d+15)) then
        tmp = t_1
    else if (x <= (-1.8d-7)) then
        tmp = t_2
    else if ((x <= (-5.5d-25)) .or. (.not. (x <= (-1.6d-150))) .and. (x <= 6.8d-8)) 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 + (z * 2.0));
	double t_2 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -5.4e+30) {
		tmp = t_2;
	} else if (x <= -4.2e+15) {
		tmp = t_1;
	} else if (x <= -1.8e-7) {
		tmp = t_2;
	} else if ((x <= -5.5e-25) || (!(x <= -1.6e-150) && (x <= 6.8e-8))) {
		tmp = y * 5.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -5.4e+30:
		tmp = t_2
	elif x <= -4.2e+15:
		tmp = t_1
	elif x <= -1.8e-7:
		tmp = t_2
	elif (x <= -5.5e-25) or (not (x <= -1.6e-150) and (x <= 6.8e-8)):
		tmp = y * 5.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -5.4e+30)
		tmp = t_2;
	elseif (x <= -4.2e+15)
		tmp = t_1;
	elseif (x <= -1.8e-7)
		tmp = t_2;
	elseif ((x <= -5.5e-25) || (!(x <= -1.6e-150) && (x <= 6.8e-8)))
		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 + (z * 2.0));
	t_2 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -5.4e+30)
		tmp = t_2;
	elseif (x <= -4.2e+15)
		tmp = t_1;
	elseif (x <= -1.8e-7)
		tmp = t_2;
	elseif ((x <= -5.5e-25) || (~((x <= -1.6e-150)) && (x <= 6.8e-8)))
		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[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+30], t$95$2, If[LessEqual[x, -4.2e+15], t$95$1, If[LessEqual[x, -1.8e-7], t$95$2, If[Or[LessEqual[x, -5.5e-25], And[N[Not[LessEqual[x, -1.6e-150]], $MachinePrecision], LessEqual[x, 6.8e-8]]], N[(y * 5.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.3999999999999997e30 or -4.2e15 < x < -1.79999999999999997e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.6%

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

   3. Taylor expanded in y around 0 78.2%

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

   4. Taylor expanded in x around inf 78.2%

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

      1. *-commutative 78.2%

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

   6. Simplified 78.2%

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

   if -5.3999999999999997e30 < x < -4.2e15 or -5.50000000000000004e-25 < x < -1.5999999999999999e-150 or 6.8e-8 < 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. Taylor expanded in y around 0 74.3%

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

   if -1.79999999999999997e-7 < x < -5.50000000000000004e-25 or -1.5999999999999999e-150 < x < 6.8e-8

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 70.4%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-25} \lor \neg \left(x \leq -1.6 \cdot 10^{-150}\right) \land x \leq 6.8 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 3: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+76} \lor \neg \left(t \leq 4.3 \cdot 10^{+73}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))))
   (if (<= t -2.9e+232)
     t_1
     (if (<= t -3.05e+159)
       (* x (+ t (* z 2.0)))
       (if (or (<= t -4.1e+76) (not (<= t 4.3e+73)))
         t_1
         (+ (* 2.0 (* x (+ y z))) (* y 5.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double tmp;
	if (t <= -2.9e+232) {
		tmp = t_1;
	} else if (t <= -3.05e+159) {
		tmp = x * (t + (z * 2.0));
	} else if ((t <= -4.1e+76) || !(t <= 4.3e+73)) {
		tmp = t_1;
	} else {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * 5.0d0) + (x * t)
    if (t <= (-2.9d+232)) then
        tmp = t_1
    else if (t <= (-3.05d+159)) then
        tmp = x * (t + (z * 2.0d0))
    else if ((t <= (-4.1d+76)) .or. (.not. (t <= 4.3d+73))) then
        tmp = t_1
    else
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double tmp;
	if (t <= -2.9e+232) {
		tmp = t_1;
	} else if (t <= -3.05e+159) {
		tmp = x * (t + (z * 2.0));
	} else if ((t <= -4.1e+76) || !(t <= 4.3e+73)) {
		tmp = t_1;
	} else {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	tmp = 0
	if t <= -2.9e+232:
		tmp = t_1
	elif t <= -3.05e+159:
		tmp = x * (t + (z * 2.0))
	elif (t <= -4.1e+76) or not (t <= 4.3e+73):
		tmp = t_1
	else:
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	tmp = 0.0
	if (t <= -2.9e+232)
		tmp = t_1;
	elseif (t <= -3.05e+159)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif ((t <= -4.1e+76) || !(t <= 4.3e+73))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	tmp = 0.0;
	if (t <= -2.9e+232)
		tmp = t_1;
	elseif (t <= -3.05e+159)
		tmp = x * (t + (z * 2.0));
	elseif ((t <= -4.1e+76) || ~((t <= 4.3e+73)))
		tmp = t_1;
	else
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+232], t$95$1, If[LessEqual[t, -3.05e+159], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -4.1e+76], N[Not[LessEqual[t, 4.3e+73]], $MachinePrecision]], t$95$1, N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000023e232 or -3.05e159 < t < -4.0999999999999998e76 or 4.30000000000000013e73 < 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. Step-by-step derivation

      1. distribute-rgt-in 95.0%

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

      2. fma-def 98.7%

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

      3. associate-+l+ 98.7%

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

      4. *-un-lft-identity 98.7%

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

      5. +-commutative 98.7%

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

      6. *-un-lft-identity 98.7%

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

      7. distribute-rgt-out 98.7%

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

      8. metadata-eval 98.7%

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

      9. *-commutative 98.7%

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

   3. Applied egg-rr 98.7%

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

   4. Taylor expanded in t around inf 85.8%

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

      1. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   if -2.90000000000000023e232 < t < -3.05e159

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.1%

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

   if -4.0999999999999998e76 < t < 4.30000000000000013e73

   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. +-commutative 99.9%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. +-commutative 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around 0 93.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+232}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+76} \lor \neg \left(t \leq 4.3 \cdot 10^{+73}\right):\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \end{array} \]

Alternative 4: 64.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-9} \lor \neg \left(x \leq -6.5 \cdot 10^{-25}\right) \land \left(x \leq -1.55 \cdot 10^{-150} \lor \neg \left(x \leq 6.8 \cdot 10^{-8}\right)\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.36e-9)
         (and (not (<= x -6.5e-25))
              (or (<= x -1.55e-150) (not (<= x 6.8e-8)))))
   (* x (+ t (* z 2.0)))
   (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.36e-9) || (!(x <= -6.5e-25) && ((x <= -1.55e-150) || !(x <= 6.8e-8)))) {
		tmp = x * (t + (z * 2.0));
	} 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 <= (-1.36d-9)) .or. (.not. (x <= (-6.5d-25))) .and. (x <= (-1.55d-150)) .or. (.not. (x <= 6.8d-8))) then
        tmp = x * (t + (z * 2.0d0))
    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 <= -1.36e-9) || (!(x <= -6.5e-25) && ((x <= -1.55e-150) || !(x <= 6.8e-8)))) {
		tmp = x * (t + (z * 2.0));
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.36e-9) or (not (x <= -6.5e-25) and ((x <= -1.55e-150) or not (x <= 6.8e-8))):
		tmp = x * (t + (z * 2.0))
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.36e-9) || (!(x <= -6.5e-25) && ((x <= -1.55e-150) || !(x <= 6.8e-8))))
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.36e-9) || (~((x <= -6.5e-25)) && ((x <= -1.55e-150) || ~((x <= 6.8e-8)))))
		tmp = x * (t + (z * 2.0));
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.36e-9], And[N[Not[LessEqual[x, -6.5e-25]], $MachinePrecision], Or[LessEqual[x, -1.55e-150], N[Not[LessEqual[x, 6.8e-8]], $MachinePrecision]]]], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.36000000000000006e-9 or -6.5e-25 < x < -1.54999999999999999e-150 or 6.8e-8 < 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. Taylor expanded in y around 0 71.2%

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

   if -1.36000000000000006e-9 < x < -6.5e-25 or -1.54999999999999999e-150 < x < 6.8e-8

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 70.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-9} \lor \neg \left(x \leq -6.5 \cdot 10^{-25}\right) \land \left(x \leq -1.55 \cdot 10^{-150} \lor \neg \left(x \leq 6.8 \cdot 10^{-8}\right)\right):\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 5: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+15} \lor \neg \left(y \leq 2 \cdot 10^{-45} \lor \neg \left(y \leq 2.8 \cdot 10^{-17}\right) \land y \leq 1.9 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+15)
         (not (or (<= y 2e-45) (and (not (<= y 2.8e-17)) (<= y 1.9e+124)))))
   (* y (+ 5.0 (* x 2.0)))
   (* x (+ t (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+15) || !((y <= 2e-45) || (!(y <= 2.8e-17) && (y <= 1.9e+124)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 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 ((y <= (-7.5d+15)) .or. (.not. (y <= 2d-45) .or. (.not. (y <= 2.8d-17)) .and. (y <= 1.9d+124))) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else
        tmp = x * (t + (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+15) || !((y <= 2e-45) || (!(y <= 2.8e-17) && (y <= 1.9e+124)))) {
		tmp = y * (5.0 + (x * 2.0));
	} else {
		tmp = x * (t + (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+15) or not ((y <= 2e-45) or (not (y <= 2.8e-17) and (y <= 1.9e+124))):
		tmp = y * (5.0 + (x * 2.0))
	else:
		tmp = x * (t + (z * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+15) || !((y <= 2e-45) || (!(y <= 2.8e-17) && (y <= 1.9e+124))))
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	else
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e+15) || ~(((y <= 2e-45) || (~((y <= 2.8e-17)) && (y <= 1.9e+124)))))
		tmp = y * (5.0 + (x * 2.0));
	else
		tmp = x * (t + (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+15], N[Not[Or[LessEqual[y, 2e-45], And[N[Not[LessEqual[y, 2.8e-17]], $MachinePrecision], LessEqual[y, 1.9e+124]]]], $MachinePrecision]], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e15 or 1.99999999999999997e-45 < y < 2.7999999999999999e-17 or 1.8999999999999999e124 < 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. Taylor expanded in y around inf 90.0%

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

   4. Simplified 90.0%

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

   if -7.5e15 < y < 1.99999999999999997e-45 or 2.7999999999999999e-17 < y < 1.8999999999999999e124

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+15} \lor \neg \left(y \leq 2 \cdot 10^{-45} \lor \neg \left(y \leq 2.8 \cdot 10^{-17}\right) \land y \leq 1.9 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]

Alternative 6: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-18}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -3.3e+28)
     t_2
     (if (<= y 2.6e-55)
       t_1
       (if (<= y 1.45e-18)
         (+ (* y 5.0) (* x t))
         (if (<= y 1.9e+124) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -3.3e+28) {
		tmp = t_2;
	} else if (y <= 2.6e-55) {
		tmp = t_1;
	} else if (y <= 1.45e-18) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.9e+124) {
		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 + (z * 2.0d0))
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-3.3d+28)) then
        tmp = t_2
    else if (y <= 2.6d-55) then
        tmp = t_1
    else if (y <= 1.45d-18) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 1.9d+124) 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 + (z * 2.0));
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -3.3e+28) {
		tmp = t_2;
	} else if (y <= 2.6e-55) {
		tmp = t_1;
	} else if (y <= 1.45e-18) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.9e+124) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -3.3e+28:
		tmp = t_2
	elif y <= 2.6e-55:
		tmp = t_1
	elif y <= 1.45e-18:
		tmp = (y * 5.0) + (x * t)
	elif y <= 1.9e+124:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -3.3e+28)
		tmp = t_2;
	elseif (y <= 2.6e-55)
		tmp = t_1;
	elseif (y <= 1.45e-18)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 1.9e+124)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -3.3e+28)
		tmp = t_2;
	elseif (y <= 2.6e-55)
		tmp = t_1;
	elseif (y <= 1.45e-18)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 1.9e+124)
		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[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+28], t$95$2, If[LessEqual[y, 2.6e-55], t$95$1, If[LessEqual[y, 1.45e-18], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+124], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3e28 or 1.8999999999999999e124 < 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. Taylor expanded in y around inf 89.9%

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

   4. Simplified 89.9%

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

   if -3.3e28 < y < 2.5999999999999999e-55 or 1.45e-18 < y < 1.8999999999999999e124

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.9%

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

   if 2.5999999999999999e-55 < y < 1.45e-18

   1. Initial program 99.8%

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

      1. distribute-rgt-in 99.8%

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

      2. fma-def 99.8%

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

      3. associate-+l+ 99.8%

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

      4. *-un-lft-identity 99.8%

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

      5. +-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. distribute-rgt-out 99.8%

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

      8. metadata-eval 99.8%

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

      9. *-commutative 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around inf 98.4%

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

      1. *-commutative 98.4%

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

   6. Simplified 98.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-18}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 7: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))))
   (if (<= y -5.2e+19)
     (+ (* y 5.0) (* 2.0 (* y x)))
     (if (<= y 6.8e-55)
       t_1
       (if (<= y 1.15e-16)
         (+ (* y 5.0) (* x t))
         (if (<= y 1.9e+124) t_1 (* y (+ 5.0 (* x 2.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (z * 2.0));
	double tmp;
	if (y <= -5.2e+19) {
		tmp = (y * 5.0) + (2.0 * (y * x));
	} else if (y <= 6.8e-55) {
		tmp = t_1;
	} else if (y <= 1.15e-16) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.9e+124) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (z * 2.0d0))
    if (y <= (-5.2d+19)) then
        tmp = (y * 5.0d0) + (2.0d0 * (y * x))
    else if (y <= 6.8d-55) then
        tmp = t_1
    else if (y <= 1.15d-16) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 1.9d+124) then
        tmp = t_1
    else
        tmp = 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 t_1 = x * (t + (z * 2.0));
	double tmp;
	if (y <= -5.2e+19) {
		tmp = (y * 5.0) + (2.0 * (y * x));
	} else if (y <= 6.8e-55) {
		tmp = t_1;
	} else if (y <= 1.15e-16) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 1.9e+124) {
		tmp = t_1;
	} else {
		tmp = y * (5.0 + (x * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (z * 2.0))
	tmp = 0
	if y <= -5.2e+19:
		tmp = (y * 5.0) + (2.0 * (y * x))
	elif y <= 6.8e-55:
		tmp = t_1
	elif y <= 1.15e-16:
		tmp = (y * 5.0) + (x * t)
	elif y <= 1.9e+124:
		tmp = t_1
	else:
		tmp = y * (5.0 + (x * 2.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(z * 2.0)))
	tmp = 0.0
	if (y <= -5.2e+19)
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(y * x)));
	elseif (y <= 6.8e-55)
		tmp = t_1;
	elseif (y <= 1.15e-16)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 1.9e+124)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (z * 2.0));
	tmp = 0.0;
	if (y <= -5.2e+19)
		tmp = (y * 5.0) + (2.0 * (y * x));
	elseif (y <= 6.8e-55)
		tmp = t_1;
	elseif (y <= 1.15e-16)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 1.9e+124)
		tmp = t_1;
	else
		tmp = y * (5.0 + (x * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+19], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-55], t$95$1, If[LessEqual[y, 1.15e-16], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+124], t$95$1, N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2e19

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 85.0%

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

   if -5.2e19 < y < 6.79999999999999946e-55 or 1.15e-16 < y < 1.8999999999999999e124

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.9%

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

   if 6.79999999999999946e-55 < y < 1.15e-16

   1. Initial program 99.8%

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

      1. distribute-rgt-in 99.8%

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

      2. fma-def 99.8%

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

      3. associate-+l+ 99.8%

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

      4. *-un-lft-identity 99.8%

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

      5. +-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. distribute-rgt-out 99.8%

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

      8. metadata-eval 99.8%

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

      9. *-commutative 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in t around inf 98.4%

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

      1. *-commutative 98.4%

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

   6. Simplified 98.4%

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

   if 1.8999999999999999e124 < 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. Taylor expanded in y around inf 99.9%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{y \cdot \left(5 + x \cdot 2\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 8: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+96} \lor \neg \left(z \leq 6.8 \cdot 10^{+25}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e+96) (not (<= z 6.8e+25)))
   (+ (* 2.0 (* x (+ y z))) (* y 5.0))
   (+ (* x t) (* y (+ 5.0 (* x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+96) || !(z <= 6.8e+25)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} 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 ((z <= (-3.9d+96)) .or. (.not. (z <= 6.8d+25))) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    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 ((z <= -3.9e+96) || !(z <= 6.8e+25)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (x * t) + (y * (5.0 + (x * 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e+96) or not (z <= 6.8e+25):
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = (x * t) + (y * (5.0 + (x * 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e+96) || !(z <= 6.8e+25))
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	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 ((z <= -3.9e+96) || ~((z <= 6.8e+25)))
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = (x * t) + (y * (5.0 + (x * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e+96], N[Not[LessEqual[z, 6.8e+25]], $MachinePrecision]], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $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 2 regimes

2. if z < -3.9e96 or 6.79999999999999967e25 < 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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. +-commutative 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around 0 90.5%

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

   if -3.9e96 < z < 6.79999999999999967e25

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 93.7%

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

   3. Taylor expanded in y around 0 91.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+96} \lor \neg \left(z \leq 6.8 \cdot 10^{+25}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t + y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]

Alternative 9: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+97} \lor \neg \left(z \leq 5.6 \cdot 10^{+25}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e+97) (not (<= z 5.6e+25)))
   (+ (* 2.0 (* x (+ y z))) (* y 5.0))
   (+ (* y 5.0) (* x (+ t (+ y y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+97) || !(z <= 5.6e+25)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.4d+97)) .or. (.not. (z <= 5.6d+25))) then
        tmp = (2.0d0 * (x * (y + z))) + (y * 5.0d0)
    else
        tmp = (y * 5.0d0) + (x * (t + (y + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+97) || !(z <= 5.6e+25)) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = (y * 5.0) + (x * (t + (y + y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e+97) or not (z <= 5.6e+25):
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = (y * 5.0) + (x * (t + (y + y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+97) || !(z <= 5.6e+25))
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + Float64(y * 5.0));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * Float64(t + Float64(y + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e+97) || ~((z <= 5.6e+25)))
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	else
		tmp = (y * 5.0) + (x * (t + (y + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e+97], N[Not[LessEqual[z, 5.6e+25]], $MachinePrecision]], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e97 or 5.6000000000000003e25 < 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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. +-commutative 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. metadata-eval 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around 0 90.5%

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

   if -1.4e97 < z < 5.6000000000000003e25

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 93.7%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+97} \lor \neg \left(z \leq 5.6 \cdot 10^{+25}\right):\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot \left(t + \left(y + y\right)\right)\\ \end{array} \]

Alternative 10: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[(N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision] + t), $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. Step-by-step derivation

   1. associate-+l+ 99.9%

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

   2. *-un-lft-identity 99.9%

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

   3. +-commutative 99.9%

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

   4. *-un-lft-identity 99.9%

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

   5. distribute-rgt-out 99.9%

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

   6. metadata-eval 99.9%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

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

Alternative 11: 46.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-277}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{-141}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.75e+48)
   (* x t)
   (if (<= t 5.8e-277)
     (* y 5.0)
     (if (<= t 1.04e-141)
       (* 2.0 (* x z))
       (if (<= t 1.8e-9) (* y 5.0) (* x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.75e+48) {
		tmp = x * t;
	} else if (t <= 5.8e-277) {
		tmp = y * 5.0;
	} else if (t <= 1.04e-141) {
		tmp = 2.0 * (x * z);
	} else if (t <= 1.8e-9) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.75d+48)) then
        tmp = x * t
    else if (t <= 5.8d-277) then
        tmp = y * 5.0d0
    else if (t <= 1.04d-141) then
        tmp = 2.0d0 * (x * z)
    else if (t <= 1.8d-9) then
        tmp = y * 5.0d0
    else
        tmp = x * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.75e+48) {
		tmp = x * t;
	} else if (t <= 5.8e-277) {
		tmp = y * 5.0;
	} else if (t <= 1.04e-141) {
		tmp = 2.0 * (x * z);
	} else if (t <= 1.8e-9) {
		tmp = y * 5.0;
	} else {
		tmp = x * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.75e+48:
		tmp = x * t
	elif t <= 5.8e-277:
		tmp = y * 5.0
	elif t <= 1.04e-141:
		tmp = 2.0 * (x * z)
	elif t <= 1.8e-9:
		tmp = y * 5.0
	else:
		tmp = x * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.75e+48)
		tmp = Float64(x * t);
	elseif (t <= 5.8e-277)
		tmp = Float64(y * 5.0);
	elseif (t <= 1.04e-141)
		tmp = Float64(2.0 * Float64(x * z));
	elseif (t <= 1.8e-9)
		tmp = Float64(y * 5.0);
	else
		tmp = Float64(x * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.75e+48)
		tmp = x * t;
	elseif (t <= 5.8e-277)
		tmp = y * 5.0;
	elseif (t <= 1.04e-141)
		tmp = 2.0 * (x * z);
	elseif (t <= 1.8e-9)
		tmp = y * 5.0;
	else
		tmp = x * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.75e+48], N[(x * t), $MachinePrecision], If[LessEqual[t, 5.8e-277], N[(y * 5.0), $MachinePrecision], If[LessEqual[t, 1.04e-141], N[(2.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-9], N[(y * 5.0), $MachinePrecision], N[(x * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7500000000000001e48 or 1.8e-9 < 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. Taylor expanded in t around inf 58.1%

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

   if -2.7500000000000001e48 < t < 5.79999999999999955e-277 or 1.04e-141 < t < 1.8e-9

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 52.3%

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

   if 5.79999999999999955e-277 < t < 1.04e-141

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 57.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-277}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{-141}:\\ \;\;\;\;2 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\\ \end{array} \]

Alternative 12: 45.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+51} \lor \neg \left(t \leq 1.25 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.55e+51) (not (<= t 1.25e-8))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.55e+51) || !(t <= 1.25e-8)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.55d+51)) .or. (.not. (t <= 1.25d-8))) then
        tmp = x * t
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.55e+51) || !(t <= 1.25e-8)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.55e+51) or not (t <= 1.25e-8):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.55e+51) || !(t <= 1.25e-8))
		tmp = Float64(x * t);
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.55e+51) || ~((t <= 1.25e-8)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.55e+51], N[Not[LessEqual[t, 1.25e-8]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.55000000000000005e51 or 1.2499999999999999e-8 < 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. Taylor expanded in t around inf 58.1%

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

   if -2.55000000000000005e51 < t < 1.2499999999999999e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 44.7%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+51} \lor \neg \left(t \leq 1.25 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]

Alternative 13: 29.4% 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. Taylor expanded in x around 0 32.6%

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

3. Final simplification 32.6%

   \[\leadsto y \cdot 5 \]

Reproduce

herbie shell --seed 2023320 
(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)))