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

Percentage Accurate: 99.8% → 99.9%

Time: 11.2s

Alternatives: 21

Speedup: 1.0×

• 25.9% 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: 99.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(y * 5.0 + N[(x * N[(t + N[(N[(y + z), $MachinePrecision] * 2.0), $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. 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-define 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. *-un-lft-identity 100.0%

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

   4. *-un-lft-identity 100.0%

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

   5. associate-+l+ 100.0%

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

   6. *-un-lft-identity 100.0%

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

   7. +-commutative 100.0%

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

   8. *-un-lft-identity 100.0%

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

   9. distribute-rgt-out 100.0%

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

   10. metadata-eval 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 45.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot 2\right)\\ t_2 := y \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+260}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+225}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.58 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (* x 2.0))) (t_2 (* y (* x 2.0))))
   (if (<= x -1.5e+260)
     t_2
     (if (<= x -2.5e+225)
       (* x t)
       (if (<= x -1.2e+115)
         t_2
         (if (<= x -1.58e-68)
           t_1
           (if (<= x 1.12e-207)
             (* y 5.0)
             (if (<= x 3.8e-145)
               t_1
               (if (<= x 5.5e-5)
                 (* y 5.0)
                 (if (<= x 8.5e+28)
                   (* x t)
                   (if (<= x 9.6e+141)
                     t_1
                     (if (<= x 4.4e+207) (* x t) t_2))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x * 2.0);
	double t_2 = y * (x * 2.0);
	double tmp;
	if (x <= -1.5e+260) {
		tmp = t_2;
	} else if (x <= -2.5e+225) {
		tmp = x * t;
	} else if (x <= -1.2e+115) {
		tmp = t_2;
	} else if (x <= -1.58e-68) {
		tmp = t_1;
	} else if (x <= 1.12e-207) {
		tmp = y * 5.0;
	} else if (x <= 3.8e-145) {
		tmp = t_1;
	} else if (x <= 5.5e-5) {
		tmp = y * 5.0;
	} else if (x <= 8.5e+28) {
		tmp = x * t;
	} else if (x <= 9.6e+141) {
		tmp = t_1;
	} else if (x <= 4.4e+207) {
		tmp = x * t;
	} 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 = z * (x * 2.0d0)
    t_2 = y * (x * 2.0d0)
    if (x <= (-1.5d+260)) then
        tmp = t_2
    else if (x <= (-2.5d+225)) then
        tmp = x * t
    else if (x <= (-1.2d+115)) then
        tmp = t_2
    else if (x <= (-1.58d-68)) then
        tmp = t_1
    else if (x <= 1.12d-207) then
        tmp = y * 5.0d0
    else if (x <= 3.8d-145) then
        tmp = t_1
    else if (x <= 5.5d-5) then
        tmp = y * 5.0d0
    else if (x <= 8.5d+28) then
        tmp = x * t
    else if (x <= 9.6d+141) then
        tmp = t_1
    else if (x <= 4.4d+207) then
        tmp = x * t
    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 = z * (x * 2.0);
	double t_2 = y * (x * 2.0);
	double tmp;
	if (x <= -1.5e+260) {
		tmp = t_2;
	} else if (x <= -2.5e+225) {
		tmp = x * t;
	} else if (x <= -1.2e+115) {
		tmp = t_2;
	} else if (x <= -1.58e-68) {
		tmp = t_1;
	} else if (x <= 1.12e-207) {
		tmp = y * 5.0;
	} else if (x <= 3.8e-145) {
		tmp = t_1;
	} else if (x <= 5.5e-5) {
		tmp = y * 5.0;
	} else if (x <= 8.5e+28) {
		tmp = x * t;
	} else if (x <= 9.6e+141) {
		tmp = t_1;
	} else if (x <= 4.4e+207) {
		tmp = x * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x * 2.0)
	t_2 = y * (x * 2.0)
	tmp = 0
	if x <= -1.5e+260:
		tmp = t_2
	elif x <= -2.5e+225:
		tmp = x * t
	elif x <= -1.2e+115:
		tmp = t_2
	elif x <= -1.58e-68:
		tmp = t_1
	elif x <= 1.12e-207:
		tmp = y * 5.0
	elif x <= 3.8e-145:
		tmp = t_1
	elif x <= 5.5e-5:
		tmp = y * 5.0
	elif x <= 8.5e+28:
		tmp = x * t
	elif x <= 9.6e+141:
		tmp = t_1
	elif x <= 4.4e+207:
		tmp = x * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x * 2.0))
	t_2 = Float64(y * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -1.5e+260)
		tmp = t_2;
	elseif (x <= -2.5e+225)
		tmp = Float64(x * t);
	elseif (x <= -1.2e+115)
		tmp = t_2;
	elseif (x <= -1.58e-68)
		tmp = t_1;
	elseif (x <= 1.12e-207)
		tmp = Float64(y * 5.0);
	elseif (x <= 3.8e-145)
		tmp = t_1;
	elseif (x <= 5.5e-5)
		tmp = Float64(y * 5.0);
	elseif (x <= 8.5e+28)
		tmp = Float64(x * t);
	elseif (x <= 9.6e+141)
		tmp = t_1;
	elseif (x <= 4.4e+207)
		tmp = Float64(x * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x * 2.0);
	t_2 = y * (x * 2.0);
	tmp = 0.0;
	if (x <= -1.5e+260)
		tmp = t_2;
	elseif (x <= -2.5e+225)
		tmp = x * t;
	elseif (x <= -1.2e+115)
		tmp = t_2;
	elseif (x <= -1.58e-68)
		tmp = t_1;
	elseif (x <= 1.12e-207)
		tmp = y * 5.0;
	elseif (x <= 3.8e-145)
		tmp = t_1;
	elseif (x <= 5.5e-5)
		tmp = y * 5.0;
	elseif (x <= 8.5e+28)
		tmp = x * t;
	elseif (x <= 9.6e+141)
		tmp = t_1;
	elseif (x <= 4.4e+207)
		tmp = x * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+260], t$95$2, If[LessEqual[x, -2.5e+225], N[(x * t), $MachinePrecision], If[LessEqual[x, -1.2e+115], t$95$2, If[LessEqual[x, -1.58e-68], t$95$1, If[LessEqual[x, 1.12e-207], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 3.8e-145], t$95$1, If[LessEqual[x, 5.5e-5], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 8.5e+28], N[(x * t), $MachinePrecision], If[LessEqual[x, 9.6e+141], t$95$1, If[LessEqual[x, 4.4e+207], N[(x * t), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.4999999999999999e260 or -2.4999999999999999e225 < x < -1.2e115 or 4.40000000000000017e207 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in t around 0 81.4%

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

   5. Taylor expanded in y around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. *-commutative 62.8%

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

      3. associate-*r* 62.8%

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

   7. Simplified 62.8%

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

   if -1.4999999999999999e260 < x < -2.4999999999999999e225 or 5.5000000000000002e-5 < x < 8.49999999999999954e28 or 9.59999999999999989e141 < x < 4.40000000000000017e207

   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 78.1%

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

   if -1.2e115 < x < -1.58e-68 or 1.12000000000000001e-207 < x < 3.8000000000000002e-145 or 8.49999999999999954e28 < x < 9.59999999999999989e141

   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 48.7%

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

   5. Simplified 48.7%

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

   if -1.58e-68 < x < 1.12000000000000001e-207 or 3.8000000000000002e-145 < x < 5.5000000000000002e-5

   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 70.4%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+260}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+225}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.58 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-207}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+213}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -520000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.00011:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+27} \lor \neg \left(x \leq 1.95 \cdot 10^{+120}\right) \land x \leq 6.5 \cdot 10^{+206}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x 2.0))))
   (if (<= x -2.2e+261)
     t_1
     (if (<= x -1.05e+213)
       (* x t)
       (if (<= x -520000000.0)
         t_1
         (if (<= x -8e-76)
           (* x t)
           (if (<= x 0.00011)
             (* y 5.0)
             (if (or (<= x 8.2e+27)
                     (and (not (<= x 1.95e+120)) (<= x 6.5e+206)))
               (* x t)
               t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * 2.0);
	double tmp;
	if (x <= -2.2e+261) {
		tmp = t_1;
	} else if (x <= -1.05e+213) {
		tmp = x * t;
	} else if (x <= -520000000.0) {
		tmp = t_1;
	} else if (x <= -8e-76) {
		tmp = x * t;
	} else if (x <= 0.00011) {
		tmp = y * 5.0;
	} else if ((x <= 8.2e+27) || (!(x <= 1.95e+120) && (x <= 6.5e+206))) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * 2.0d0)
    if (x <= (-2.2d+261)) then
        tmp = t_1
    else if (x <= (-1.05d+213)) then
        tmp = x * t
    else if (x <= (-520000000.0d0)) then
        tmp = t_1
    else if (x <= (-8d-76)) then
        tmp = x * t
    else if (x <= 0.00011d0) then
        tmp = y * 5.0d0
    else if ((x <= 8.2d+27) .or. (.not. (x <= 1.95d+120)) .and. (x <= 6.5d+206)) 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 * 2.0);
	double tmp;
	if (x <= -2.2e+261) {
		tmp = t_1;
	} else if (x <= -1.05e+213) {
		tmp = x * t;
	} else if (x <= -520000000.0) {
		tmp = t_1;
	} else if (x <= -8e-76) {
		tmp = x * t;
	} else if (x <= 0.00011) {
		tmp = y * 5.0;
	} else if ((x <= 8.2e+27) || (!(x <= 1.95e+120) && (x <= 6.5e+206))) {
		tmp = x * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * 2.0)
	tmp = 0
	if x <= -2.2e+261:
		tmp = t_1
	elif x <= -1.05e+213:
		tmp = x * t
	elif x <= -520000000.0:
		tmp = t_1
	elif x <= -8e-76:
		tmp = x * t
	elif x <= 0.00011:
		tmp = y * 5.0
	elif (x <= 8.2e+27) or (not (x <= 1.95e+120) and (x <= 6.5e+206)):
		tmp = x * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * 2.0))
	tmp = 0.0
	if (x <= -2.2e+261)
		tmp = t_1;
	elseif (x <= -1.05e+213)
		tmp = Float64(x * t);
	elseif (x <= -520000000.0)
		tmp = t_1;
	elseif (x <= -8e-76)
		tmp = Float64(x * t);
	elseif (x <= 0.00011)
		tmp = Float64(y * 5.0);
	elseif ((x <= 8.2e+27) || (!(x <= 1.95e+120) && (x <= 6.5e+206)))
		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 * 2.0);
	tmp = 0.0;
	if (x <= -2.2e+261)
		tmp = t_1;
	elseif (x <= -1.05e+213)
		tmp = x * t;
	elseif (x <= -520000000.0)
		tmp = t_1;
	elseif (x <= -8e-76)
		tmp = x * t;
	elseif (x <= 0.00011)
		tmp = y * 5.0;
	elseif ((x <= 8.2e+27) || (~((x <= 1.95e+120)) && (x <= 6.5e+206)))
		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 * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+261], t$95$1, If[LessEqual[x, -1.05e+213], N[(x * t), $MachinePrecision], If[LessEqual[x, -520000000.0], t$95$1, If[LessEqual[x, -8e-76], N[(x * t), $MachinePrecision], If[LessEqual[x, 0.00011], N[(y * 5.0), $MachinePrecision], If[Or[LessEqual[x, 8.2e+27], And[N[Not[LessEqual[x, 1.95e+120]], $MachinePrecision], LessEqual[x, 6.5e+206]]], N[(x * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.19999999999999984e261 or -1.05e213 < x < -5.2e8 or 8.2000000000000005e27 < x < 1.9499999999999999e120 or 6.4999999999999995e206 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.6%

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

   4. Taylor expanded in t around 0 85.4%

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

   5. Taylor expanded in y around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

      3. associate-*r* 49.2%

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

   7. Simplified 49.2%

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

   if -2.19999999999999984e261 < x < -1.05e213 or -5.2e8 < x < -7.99999999999999942e-76 or 1.10000000000000004e-4 < x < 8.2000000000000005e27 or 1.9499999999999999e120 < x < 6.4999999999999995e206

   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 66.6%

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

   if -7.99999999999999942e-76 < x < 1.10000000000000004e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 64.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+261}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+213}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq -520000000:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-76}:\\ \;\;\;\;x \cdot t\\ \mathbf{elif}\;x \leq 0.00011:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+27} \lor \neg \left(x \leq 1.95 \cdot 10^{+120}\right) \land x \leq 6.5 \cdot 10^{+206}:\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -950000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-208}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* z 2.0)))) (t_2 (* x (+ t (* y 2.0)))))
   (if (<= x -1e+120)
     t_2
     (if (<= x -7e+57)
       t_1
       (if (<= x -950000000.0)
         t_2
         (if (<= x -3.3e-78)
           t_1
           (if (<= x 9.5e-208)
             (* y 5.0)
             (if (<= x 6.5e-145) t_1 (if (<= x 5.5e-5) (* y 5.0) t_2)))))))))

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 <= -1e+120) {
		tmp = t_2;
	} else if (x <= -7e+57) {
		tmp = t_1;
	} else if (x <= -950000000.0) {
		tmp = t_2;
	} else if (x <= -3.3e-78) {
		tmp = t_1;
	} else if (x <= 9.5e-208) {
		tmp = y * 5.0;
	} else if (x <= 6.5e-145) {
		tmp = t_1;
	} else if (x <= 5.5e-5) {
		tmp = y * 5.0;
	} 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 = x * (t + (y * 2.0d0))
    if (x <= (-1d+120)) then
        tmp = t_2
    else if (x <= (-7d+57)) then
        tmp = t_1
    else if (x <= (-950000000.0d0)) then
        tmp = t_2
    else if (x <= (-3.3d-78)) then
        tmp = t_1
    else if (x <= 9.5d-208) then
        tmp = y * 5.0d0
    else if (x <= 6.5d-145) then
        tmp = t_1
    else if (x <= 5.5d-5) then
        tmp = y * 5.0d0
    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 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -1e+120) {
		tmp = t_2;
	} else if (x <= -7e+57) {
		tmp = t_1;
	} else if (x <= -950000000.0) {
		tmp = t_2;
	} else if (x <= -3.3e-78) {
		tmp = t_1;
	} else if (x <= 9.5e-208) {
		tmp = y * 5.0;
	} else if (x <= 6.5e-145) {
		tmp = t_1;
	} else if (x <= 5.5e-5) {
		tmp = y * 5.0;
	} else {
		tmp = t_2;
	}
	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 <= -1e+120:
		tmp = t_2
	elif x <= -7e+57:
		tmp = t_1
	elif x <= -950000000.0:
		tmp = t_2
	elif x <= -3.3e-78:
		tmp = t_1
	elif x <= 9.5e-208:
		tmp = y * 5.0
	elif x <= 6.5e-145:
		tmp = t_1
	elif x <= 5.5e-5:
		tmp = y * 5.0
	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(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -1e+120)
		tmp = t_2;
	elseif (x <= -7e+57)
		tmp = t_1;
	elseif (x <= -950000000.0)
		tmp = t_2;
	elseif (x <= -3.3e-78)
		tmp = t_1;
	elseif (x <= 9.5e-208)
		tmp = Float64(y * 5.0);
	elseif (x <= 6.5e-145)
		tmp = t_1;
	elseif (x <= 5.5e-5)
		tmp = Float64(y * 5.0);
	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 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -1e+120)
		tmp = t_2;
	elseif (x <= -7e+57)
		tmp = t_1;
	elseif (x <= -950000000.0)
		tmp = t_2;
	elseif (x <= -3.3e-78)
		tmp = t_1;
	elseif (x <= 9.5e-208)
		tmp = y * 5.0;
	elseif (x <= 6.5e-145)
		tmp = t_1;
	elseif (x <= 5.5e-5)
		tmp = y * 5.0;
	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[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+120], t$95$2, If[LessEqual[x, -7e+57], t$95$1, If[LessEqual[x, -950000000.0], t$95$2, If[LessEqual[x, -3.3e-78], t$95$1, If[LessEqual[x, 9.5e-208], N[(y * 5.0), $MachinePrecision], If[LessEqual[x, 6.5e-145], t$95$1, If[LessEqual[x, 5.5e-5], N[(y * 5.0), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.9999999999999998e119 or -6.9999999999999995e57 < x < -9.5e8 or 5.5000000000000002e-5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.6%

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

   4. Taylor expanded in x around inf 77.2%

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

   if -9.9999999999999998e119 < x < -6.9999999999999995e57 or -9.5e8 < x < -3.29999999999999982e-78 or 9.5000000000000001e-208 < x < 6.5000000000000002e-145

   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 77.5%

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

   if -3.29999999999999982e-78 < x < 9.5000000000000001e-208 or 6.5000000000000002e-145 < x < 5.5000000000000002e-5

   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 72.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq -950000000:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-208}:\\ \;\;\;\;y \cdot 5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-145}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(z \cdot 2 + y \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e+45)
   (* y (+ 5.0 (* x 2.0)))
   (if (<= y -3.5e-43)
     (+ (* y 5.0) (* x t))
     (if (<= y 9.2e-69)
       (* x (+ t (* z 2.0)))
       (if (<= y 2.7e+106)
         (* x (+ (* z 2.0) (* y 2.0)))
         (if (<= y 2.1e+145)
           (* t (+ x (* y (/ 5.0 t))))
           (+ (* y 5.0) (* 2.0 (* y x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+45) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (y <= -3.5e-43) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 9.2e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2.7e+106) {
		tmp = x * ((z * 2.0) + (y * 2.0));
	} else if (y <= 2.1e+145) {
		tmp = t * (x + (y * (5.0 / t)));
	} else {
		tmp = (y * 5.0) + (2.0 * (y * x));
	}
	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 <= (-1.2d+45)) then
        tmp = y * (5.0d0 + (x * 2.0d0))
    else if (y <= (-3.5d-43)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 9.2d-69) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 2.7d+106) then
        tmp = x * ((z * 2.0d0) + (y * 2.0d0))
    else if (y <= 2.1d+145) then
        tmp = t * (x + (y * (5.0d0 / t)))
    else
        tmp = (y * 5.0d0) + (2.0d0 * (y * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+45) {
		tmp = y * (5.0 + (x * 2.0));
	} else if (y <= -3.5e-43) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 9.2e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2.7e+106) {
		tmp = x * ((z * 2.0) + (y * 2.0));
	} else if (y <= 2.1e+145) {
		tmp = t * (x + (y * (5.0 / t)));
	} else {
		tmp = (y * 5.0) + (2.0 * (y * x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e+45:
		tmp = y * (5.0 + (x * 2.0))
	elif y <= -3.5e-43:
		tmp = (y * 5.0) + (x * t)
	elif y <= 9.2e-69:
		tmp = x * (t + (z * 2.0))
	elif y <= 2.7e+106:
		tmp = x * ((z * 2.0) + (y * 2.0))
	elif y <= 2.1e+145:
		tmp = t * (x + (y * (5.0 / t)))
	else:
		tmp = (y * 5.0) + (2.0 * (y * x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e+45)
		tmp = Float64(y * Float64(5.0 + Float64(x * 2.0)));
	elseif (y <= -3.5e-43)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 9.2e-69)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 2.7e+106)
		tmp = Float64(x * Float64(Float64(z * 2.0) + Float64(y * 2.0)));
	elseif (y <= 2.1e+145)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(2.0 * Float64(y * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e+45)
		tmp = y * (5.0 + (x * 2.0));
	elseif (y <= -3.5e-43)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 9.2e-69)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 2.7e+106)
		tmp = x * ((z * 2.0) + (y * 2.0));
	elseif (y <= 2.1e+145)
		tmp = t * (x + (y * (5.0 / t)));
	else
		tmp = (y * 5.0) + (2.0 * (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e+45], N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-43], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-69], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+106], N[(x * N[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+145], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(2.0 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.19999999999999995e45

   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 81.8%

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

   5. Simplified 81.8%

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

   if -1.19999999999999995e45 < y < -3.49999999999999997e-43

   1. Initial program 100.0%

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

      1. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 94.0%

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

   6. Taylor expanded in x around 0 71.4%

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

   7. Taylor expanded in x around 0 77.3%

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

   if -3.49999999999999997e-43 < y < 9.2000000000000003e-69

   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 84.2%

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

   if 9.2000000000000003e-69 < y < 2.70000000000000006e106

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

   4. Taylor expanded in t around 0 69.2%

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

   if 2.70000000000000006e106 < y < 2.09999999999999989e145

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 88.7%

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

   6. Taylor expanded in x around 0 93.0%

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

      1. associate-*r/ 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-/l* 92.8%

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

   8. Simplified 92.8%

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

   if 2.09999999999999989e145 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 97.5%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} + y \cdot 5 \]
3. Recombined 6 regimes into one program.

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(z \cdot 2 + y \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+145}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + 2 \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(z \cdot 2 + y \cdot 2\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -2.35e+45)
     t_1
     (if (<= y -2.8e-43)
       (+ (* y 5.0) (* x t))
       (if (<= y 9.2e-69)
         (* x (+ t (* z 2.0)))
         (if (<= y 1.15e+106)
           (* x (+ (* z 2.0) (* y 2.0)))
           (if (<= y 8.5e+144) (* t (+ x (* y (/ 5.0 t)))) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.35e+45) {
		tmp = t_1;
	} else if (y <= -2.8e-43) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 9.2e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 1.15e+106) {
		tmp = x * ((z * 2.0) + (y * 2.0));
	} else if (y <= 8.5e+144) {
		tmp = t * (x + (y * (5.0 / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-2.35d+45)) then
        tmp = t_1
    else if (y <= (-2.8d-43)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 9.2d-69) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 1.15d+106) then
        tmp = x * ((z * 2.0d0) + (y * 2.0d0))
    else if (y <= 8.5d+144) then
        tmp = t * (x + (y * (5.0d0 / 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 * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -2.35e+45) {
		tmp = t_1;
	} else if (y <= -2.8e-43) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 9.2e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 1.15e+106) {
		tmp = x * ((z * 2.0) + (y * 2.0));
	} else if (y <= 8.5e+144) {
		tmp = t * (x + (y * (5.0 / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -2.35e+45:
		tmp = t_1
	elif y <= -2.8e-43:
		tmp = (y * 5.0) + (x * t)
	elif y <= 9.2e-69:
		tmp = x * (t + (z * 2.0))
	elif y <= 1.15e+106:
		tmp = x * ((z * 2.0) + (y * 2.0))
	elif y <= 8.5e+144:
		tmp = t * (x + (y * (5.0 / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -2.35e+45)
		tmp = t_1;
	elseif (y <= -2.8e-43)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 9.2e-69)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 1.15e+106)
		tmp = Float64(x * Float64(Float64(z * 2.0) + Float64(y * 2.0)));
	elseif (y <= 8.5e+144)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -2.35e+45)
		tmp = t_1;
	elseif (y <= -2.8e-43)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 9.2e-69)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 1.15e+106)
		tmp = x * ((z * 2.0) + (y * 2.0));
	elseif (y <= 8.5e+144)
		tmp = t * (x + (y * (5.0 / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.35e+45], t$95$1, If[LessEqual[y, -2.8e-43], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-69], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+106], N[(x * N[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+144], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.35000000000000001e45 or 8.4999999999999998e144 < 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 88.2%

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

   5. Simplified 88.2%

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

   if -2.35000000000000001e45 < y < -2.7999999999999998e-43

   1. Initial program 100.0%

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

      1. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 94.0%

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

   6. Taylor expanded in x around 0 71.4%

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

   7. Taylor expanded in x around 0 77.3%

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

   if -2.7999999999999998e-43 < y < 9.2000000000000003e-69

   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 84.2%

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

   if 9.2000000000000003e-69 < y < 1.1500000000000001e106

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

   4. Taylor expanded in t around 0 69.2%

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

   if 1.1500000000000001e106 < y < 8.4999999999999998e144

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 88.7%

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

   6. Taylor expanded in x around 0 93.0%

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

      1. associate-*r/ 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-/l* 92.8%

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

   8. Simplified 92.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(z \cdot 2 + y \cdot 2\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -8.2e+44)
     t_1
     (if (<= y -2.3e-43)
       (+ (* y 5.0) (* x t))
       (if (<= y 9.2e-69)
         (* x (+ t (* z 2.0)))
         (if (<= y 2.8e+105)
           (* (+ y z) (* x 2.0))
           (if (<= y 1.5e+148) (* t (+ x (* y (/ 5.0 t)))) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.2e+44) {
		tmp = t_1;
	} else if (y <= -2.3e-43) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 9.2e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2.8e+105) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= 1.5e+148) {
		tmp = t * (x + (y * (5.0 / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-8.2d+44)) then
        tmp = t_1
    else if (y <= (-2.3d-43)) then
        tmp = (y * 5.0d0) + (x * t)
    else if (y <= 9.2d-69) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 2.8d+105) then
        tmp = (y + z) * (x * 2.0d0)
    else if (y <= 1.5d+148) then
        tmp = t * (x + (y * (5.0d0 / 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 * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -8.2e+44) {
		tmp = t_1;
	} else if (y <= -2.3e-43) {
		tmp = (y * 5.0) + (x * t);
	} else if (y <= 9.2e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 2.8e+105) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= 1.5e+148) {
		tmp = t * (x + (y * (5.0 / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -8.2e+44:
		tmp = t_1
	elif y <= -2.3e-43:
		tmp = (y * 5.0) + (x * t)
	elif y <= 9.2e-69:
		tmp = x * (t + (z * 2.0))
	elif y <= 2.8e+105:
		tmp = (y + z) * (x * 2.0)
	elif y <= 1.5e+148:
		tmp = t * (x + (y * (5.0 / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -8.2e+44)
		tmp = t_1;
	elseif (y <= -2.3e-43)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (y <= 9.2e-69)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 2.8e+105)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	elseif (y <= 1.5e+148)
		tmp = Float64(t * Float64(x + Float64(y * Float64(5.0 / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -8.2e+44)
		tmp = t_1;
	elseif (y <= -2.3e-43)
		tmp = (y * 5.0) + (x * t);
	elseif (y <= 9.2e-69)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 2.8e+105)
		tmp = (y + z) * (x * 2.0);
	elseif (y <= 1.5e+148)
		tmp = t * (x + (y * (5.0 / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+44], t$95$1, If[LessEqual[y, -2.3e-43], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-69], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+105], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+148], N[(t * N[(x + N[(y * N[(5.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.1999999999999993e44 or 1.50000000000000007e148 < 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 88.2%

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

   5. Simplified 88.2%

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

   if -8.1999999999999993e44 < y < -2.2999999999999999e-43

   1. Initial program 100.0%

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

      1. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 94.0%

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

   6. Taylor expanded in x around 0 71.4%

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

   7. Taylor expanded in x around 0 77.3%

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

   if -2.2999999999999999e-43 < y < 9.2000000000000003e-69

   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 84.2%

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

   if 9.2000000000000003e-69 < y < 2.8000000000000001e105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

   4. Taylor expanded in t around 0 69.2%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. associate-*r* 69.2%

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

      2. associate-*r* 69.2%

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

      3. distribute-lft-in 69.2%

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

      4. *-commutative 69.2%

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

      5. *-commutative 69.2%

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

   7. Simplified 69.2%

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

   if 2.8000000000000001e105 < y < 1.50000000000000007e148

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around inf 88.7%

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

   6. Taylor expanded in x around 0 93.0%

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

      1. associate-*r/ 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-/l* 92.8%

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

   8. Simplified 92.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(x + y \cdot \frac{5}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 5 + x \cdot t\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* y 5.0) (* x t))) (t_2 (* y (+ 5.0 (* x 2.0)))))
   (if (<= y -5.4e+44)
     t_2
     (if (<= y -4e-43)
       t_1
       (if (<= y 5.6e-69)
         (* x (+ t (* z 2.0)))
         (if (<= y 4.1e+105)
           (* (+ y z) (* x 2.0))
           (if (<= y 1.05e+145) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -5.4e+44) {
		tmp = t_2;
	} else if (y <= -4e-43) {
		tmp = t_1;
	} else if (y <= 5.6e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 4.1e+105) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= 1.05e+145) {
		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 = (y * 5.0d0) + (x * t)
    t_2 = y * (5.0d0 + (x * 2.0d0))
    if (y <= (-5.4d+44)) then
        tmp = t_2
    else if (y <= (-4d-43)) then
        tmp = t_1
    else if (y <= 5.6d-69) then
        tmp = x * (t + (z * 2.0d0))
    else if (y <= 4.1d+105) then
        tmp = (y + z) * (x * 2.0d0)
    else if (y <= 1.05d+145) 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 = (y * 5.0) + (x * t);
	double t_2 = y * (5.0 + (x * 2.0));
	double tmp;
	if (y <= -5.4e+44) {
		tmp = t_2;
	} else if (y <= -4e-43) {
		tmp = t_1;
	} else if (y <= 5.6e-69) {
		tmp = x * (t + (z * 2.0));
	} else if (y <= 4.1e+105) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= 1.05e+145) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * 5.0) + (x * t)
	t_2 = y * (5.0 + (x * 2.0))
	tmp = 0
	if y <= -5.4e+44:
		tmp = t_2
	elif y <= -4e-43:
		tmp = t_1
	elif y <= 5.6e-69:
		tmp = x * (t + (z * 2.0))
	elif y <= 4.1e+105:
		tmp = (y + z) * (x * 2.0)
	elif y <= 1.05e+145:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * 5.0) + Float64(x * t))
	t_2 = Float64(y * Float64(5.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (y <= -5.4e+44)
		tmp = t_2;
	elseif (y <= -4e-43)
		tmp = t_1;
	elseif (y <= 5.6e-69)
		tmp = Float64(x * Float64(t + Float64(z * 2.0)));
	elseif (y <= 4.1e+105)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	elseif (y <= 1.05e+145)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * 5.0) + (x * t);
	t_2 = y * (5.0 + (x * 2.0));
	tmp = 0.0;
	if (y <= -5.4e+44)
		tmp = t_2;
	elseif (y <= -4e-43)
		tmp = t_1;
	elseif (y <= 5.6e-69)
		tmp = x * (t + (z * 2.0));
	elseif (y <= 4.1e+105)
		tmp = (y + z) * (x * 2.0);
	elseif (y <= 1.05e+145)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+44], t$95$2, If[LessEqual[y, -4e-43], t$95$1, If[LessEqual[y, 5.6e-69], N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+105], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+145], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4e44 or 1.04999999999999995e145 < 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 88.2%

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

   5. Simplified 88.2%

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

   if -5.4e44 < y < -4.00000000000000031e-43 or 4.1000000000000002e105 < y < 1.04999999999999995e145

   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. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 88.7%

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

   6. Taylor expanded in x around 0 71.5%

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

   7. Taylor expanded in x around 0 82.7%

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

   if -4.00000000000000031e-43 < y < 5.59999999999999959e-69

   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 84.2%

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

   if 5.59999999999999959e-69 < y < 4.1000000000000002e105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

   4. Taylor expanded in t around 0 69.2%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. associate-*r* 69.2%

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

      2. associate-*r* 69.2%

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

      3. distribute-lft-in 69.2%

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

      4. *-commutative 69.2%

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

      5. *-commutative 69.2%

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

   7. Simplified 69.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-43}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+105}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+145}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-68} \lor \neg \left(x \leq 1.12 \cdot 10^{-207} \lor \neg \left(x \leq 3.8 \cdot 10^{-145}\right) \land x \leq 11200000000\right):\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.25e-68)
         (not
          (or (<= x 1.12e-207)
              (and (not (<= x 3.8e-145)) (<= x 11200000000.0)))))
   (* x (+ t (+ (* z 2.0) (* y 2.0))))
   (+ (* y 5.0) (* x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.25e-68) || !((x <= 1.12e-207) || (!(x <= 3.8e-145) && (x <= 11200000000.0)))) {
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.25d-68)) .or. (.not. (x <= 1.12d-207) .or. (.not. (x <= 3.8d-145)) .and. (x <= 11200000000.0d0))) then
        tmp = x * (t + ((z * 2.0d0) + (y * 2.0d0)))
    else
        tmp = (y * 5.0d0) + (x * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.25e-68) || !((x <= 1.12e-207) || (!(x <= 3.8e-145) && (x <= 11200000000.0)))) {
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	} else {
		tmp = (y * 5.0) + (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.25e-68) or not ((x <= 1.12e-207) or (not (x <= 3.8e-145) and (x <= 11200000000.0))):
		tmp = x * (t + ((z * 2.0) + (y * 2.0)))
	else:
		tmp = (y * 5.0) + (x * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.25e-68) || !((x <= 1.12e-207) || (!(x <= 3.8e-145) && (x <= 11200000000.0))))
		tmp = Float64(x * Float64(t + Float64(Float64(z * 2.0) + Float64(y * 2.0))));
	else
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.25e-68) || ~(((x <= 1.12e-207) || (~((x <= 3.8e-145)) && (x <= 11200000000.0)))))
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	else
		tmp = (y * 5.0) + (x * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.25e-68], N[Not[Or[LessEqual[x, 1.12e-207], And[N[Not[LessEqual[x, 3.8e-145]], $MachinePrecision], LessEqual[x, 11200000000.0]]]], $MachinePrecision]], N[(x * N[(t + N[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e-68 or 1.12000000000000001e-207 < x < 3.8000000000000002e-145 or 1.12e10 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 95.9%

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

   if -2.25e-68 < x < 1.12000000000000001e-207 or 3.8000000000000002e-145 < x < 1.12e10

   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. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 71.9%

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

   6. Taylor expanded in x around 0 59.6%

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

   7. Taylor expanded in x around 0 87.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-68} \lor \neg \left(x \leq 1.12 \cdot 10^{-207} \lor \neg \left(x \leq 3.8 \cdot 10^{-145}\right) \land x \leq 11200000000\right):\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + y \cdot 2\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-28} \lor \neg \left(x \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (* y 2.0)))))
   (if (<= x -2.2e+103)
     t_1
     (if (<= x -3e+59)
       (* z (* x 2.0))
       (if (or (<= x -2.9e-28) (not (<= x 5.5e-5))) t_1 (* y 5.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -2.2e+103) {
		tmp = t_1;
	} else if (x <= -3e+59) {
		tmp = z * (x * 2.0);
	} else if ((x <= -2.9e-28) || !(x <= 5.5e-5)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + (y * 2.0d0))
    if (x <= (-2.2d+103)) then
        tmp = t_1
    else if (x <= (-3d+59)) then
        tmp = z * (x * 2.0d0)
    else if ((x <= (-2.9d-28)) .or. (.not. (x <= 5.5d-5))) then
        tmp = t_1
    else
        tmp = y * 5.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t + (y * 2.0));
	double tmp;
	if (x <= -2.2e+103) {
		tmp = t_1;
	} else if (x <= -3e+59) {
		tmp = z * (x * 2.0);
	} else if ((x <= -2.9e-28) || !(x <= 5.5e-5)) {
		tmp = t_1;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + (y * 2.0))
	tmp = 0
	if x <= -2.2e+103:
		tmp = t_1
	elif x <= -3e+59:
		tmp = z * (x * 2.0)
	elif (x <= -2.9e-28) or not (x <= 5.5e-5):
		tmp = t_1
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(y * 2.0)))
	tmp = 0.0
	if (x <= -2.2e+103)
		tmp = t_1;
	elseif (x <= -3e+59)
		tmp = Float64(z * Float64(x * 2.0));
	elseif ((x <= -2.9e-28) || !(x <= 5.5e-5))
		tmp = t_1;
	else
		tmp = Float64(y * 5.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t + (y * 2.0));
	tmp = 0.0;
	if (x <= -2.2e+103)
		tmp = t_1;
	elseif (x <= -3e+59)
		tmp = z * (x * 2.0);
	elseif ((x <= -2.9e-28) || ~((x <= 5.5e-5)))
		tmp = t_1;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+103], t$95$1, If[LessEqual[x, -3e+59], N[(z * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.9e-28], N[Not[LessEqual[x, 5.5e-5]], $MachinePrecision]], t$95$1, N[(y * 5.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.19999999999999992e103 or -3e59 < x < -2.90000000000000013e-28 or 5.5000000000000002e-5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.1%

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

   4. Taylor expanded in x around inf 74.8%

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

   if -2.19999999999999992e103 < x < -3e59

   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 70.9%

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

   5. Simplified 70.9%

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

   if -2.90000000000000013e-28 < x < 5.5000000000000002e-5

   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 62.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+59}:\\ \;\;\;\;z \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-28} \lor \neg \left(x \leq 5.5 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(t + y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + z \cdot 2\right)\\ t_2 := y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+107}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -3e-31)
     t_2
     (if (<= y 9.2e-69)
       t_1
       (if (<= y 2e+107)
         (* (+ y z) (* x 2.0))
         (if (<= y 1.25e+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 <= -3e-31) {
		tmp = t_2;
	} else if (y <= 9.2e-69) {
		tmp = t_1;
	} else if (y <= 2e+107) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= 1.25e+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 <= (-3d-31)) then
        tmp = t_2
    else if (y <= 9.2d-69) then
        tmp = t_1
    else if (y <= 2d+107) then
        tmp = (y + z) * (x * 2.0d0)
    else if (y <= 1.25d+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 <= -3e-31) {
		tmp = t_2;
	} else if (y <= 9.2e-69) {
		tmp = t_1;
	} else if (y <= 2e+107) {
		tmp = (y + z) * (x * 2.0);
	} else if (y <= 1.25e+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 <= -3e-31:
		tmp = t_2
	elif y <= 9.2e-69:
		tmp = t_1
	elif y <= 2e+107:
		tmp = (y + z) * (x * 2.0)
	elif y <= 1.25e+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 <= -3e-31)
		tmp = t_2;
	elseif (y <= 9.2e-69)
		tmp = t_1;
	elseif (y <= 2e+107)
		tmp = Float64(Float64(y + z) * Float64(x * 2.0));
	elseif (y <= 1.25e+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 <= -3e-31)
		tmp = t_2;
	elseif (y <= 9.2e-69)
		tmp = t_1;
	elseif (y <= 2e+107)
		tmp = (y + z) * (x * 2.0);
	elseif (y <= 1.25e+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, -3e-31], t$95$2, If[LessEqual[y, 9.2e-69], t$95$1, If[LessEqual[y, 2e+107], N[(N[(y + z), $MachinePrecision] * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+124], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999981e-31 or 1.2499999999999999e124 < 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 84.0%

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

   5. Simplified 84.0%

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

   if -2.99999999999999981e-31 < y < 9.2000000000000003e-69 or 1.9999999999999999e107 < y < 1.2499999999999999e124

   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 82.8%

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

   if 9.2000000000000003e-69 < y < 1.9999999999999999e107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.6%

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

   4. Taylor expanded in t around 0 69.2%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. associate-*r* 69.2%

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

      2. associate-*r* 69.2%

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

      3. distribute-lft-in 69.2%

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

      4. *-commutative 69.2%

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

      5. *-commutative 69.2%

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

   7. Simplified 69.2%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+107}:\\ \;\;\;\;\left(y + z\right) \cdot \left(x \cdot 2\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 0.00079:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (+ (* z 2.0) (* y 2.0))))))
   (if (<= x -2.25e-68)
     t_1
     (if (<= x 2.15e-172)
       (+ (* x (+ t (+ y y))) (* y 5.0))
       (if (<= x 0.00079) (+ (* 2.0 (* x (+ y z))) (* y 5.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((z * 2.0) + (y * 2.0)));
	double tmp;
	if (x <= -2.25e-68) {
		tmp = t_1;
	} else if (x <= 2.15e-172) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else if (x <= 0.00079) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + ((z * 2.0d0) + (y * 2.0d0)))
    if (x <= (-2.25d-68)) then
        tmp = t_1
    else if (x <= 2.15d-172) then
        tmp = (x * (t + (y + y))) + (y * 5.0d0)
    else if (x <= 0.00079d0) then
        tmp = (2.0d0 * (x * (y + z))) + (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) + (y * 2.0)));
	double tmp;
	if (x <= -2.25e-68) {
		tmp = t_1;
	} else if (x <= 2.15e-172) {
		tmp = (x * (t + (y + y))) + (y * 5.0);
	} else if (x <= 0.00079) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((z * 2.0) + (y * 2.0)))
	tmp = 0
	if x <= -2.25e-68:
		tmp = t_1
	elif x <= 2.15e-172:
		tmp = (x * (t + (y + y))) + (y * 5.0)
	elif x <= 0.00079:
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(z * 2.0) + Float64(y * 2.0))))
	tmp = 0.0
	if (x <= -2.25e-68)
		tmp = t_1;
	elseif (x <= 2.15e-172)
		tmp = Float64(Float64(x * Float64(t + Float64(y + y))) + Float64(y * 5.0));
	elseif (x <= 0.00079)
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + 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) + (y * 2.0)));
	tmp = 0.0;
	if (x <= -2.25e-68)
		tmp = t_1;
	elseif (x <= 2.15e-172)
		tmp = (x * (t + (y + y))) + (y * 5.0);
	elseif (x <= 0.00079)
		tmp = (2.0 * (x * (y + z))) + (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[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e-68], t$95$1, If[LessEqual[x, 2.15e-172], N[(N[(x * N[(t + N[(y + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00079], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e-68 or 7.90000000000000012e-4 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.6%

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

   if -2.25e-68 < x < 2.1499999999999999e-172

   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 87.0%

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

   if 2.1499999999999999e-172 < x < 7.90000000000000012e-4

   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. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 93.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(t + \left(y + y\right)\right) + y \cdot 5\\ \mathbf{elif}\;x \leq 0.00079:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 0.00064:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ t (+ (* z 2.0) (* y 2.0))))))
   (if (<= x -2.25e-68)
     t_1
     (if (<= x 1.8e-172)
       (+ (* y 5.0) (* x t))
       (if (<= x 0.00064) (+ (* 2.0 (* x (+ y z))) (* y 5.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t + ((z * 2.0) + (y * 2.0)));
	double tmp;
	if (x <= -2.25e-68) {
		tmp = t_1;
	} else if (x <= 1.8e-172) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 0.00064) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t + ((z * 2.0d0) + (y * 2.0d0)))
    if (x <= (-2.25d-68)) then
        tmp = t_1
    else if (x <= 1.8d-172) then
        tmp = (y * 5.0d0) + (x * t)
    else if (x <= 0.00064d0) then
        tmp = (2.0d0 * (x * (y + z))) + (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) + (y * 2.0)));
	double tmp;
	if (x <= -2.25e-68) {
		tmp = t_1;
	} else if (x <= 1.8e-172) {
		tmp = (y * 5.0) + (x * t);
	} else if (x <= 0.00064) {
		tmp = (2.0 * (x * (y + z))) + (y * 5.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t + ((z * 2.0) + (y * 2.0)))
	tmp = 0
	if x <= -2.25e-68:
		tmp = t_1
	elif x <= 1.8e-172:
		tmp = (y * 5.0) + (x * t)
	elif x <= 0.00064:
		tmp = (2.0 * (x * (y + z))) + (y * 5.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t + Float64(Float64(z * 2.0) + Float64(y * 2.0))))
	tmp = 0.0
	if (x <= -2.25e-68)
		tmp = t_1;
	elseif (x <= 1.8e-172)
		tmp = Float64(Float64(y * 5.0) + Float64(x * t));
	elseif (x <= 0.00064)
		tmp = Float64(Float64(2.0 * Float64(x * Float64(y + z))) + 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) + (y * 2.0)));
	tmp = 0.0;
	if (x <= -2.25e-68)
		tmp = t_1;
	elseif (x <= 1.8e-172)
		tmp = (y * 5.0) + (x * t);
	elseif (x <= 0.00064)
		tmp = (2.0 * (x * (y + z))) + (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[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e-68], t$95$1, If[LessEqual[x, 1.8e-172], N[(N[(y * 5.0), $MachinePrecision] + N[(x * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00064], N[(N[(2.0 * N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e-68 or 6.40000000000000052e-4 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.6%

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

   if -2.25e-68 < x < 1.80000000000000007e-172

   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. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 67.4%

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

   6. Taylor expanded in x around 0 54.6%

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

   7. Taylor expanded in x around 0 87.0%

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

   if 1.80000000000000007e-172 < x < 6.40000000000000052e-4

   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. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0 93.3%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;y \cdot 5 + x \cdot t\\ \mathbf{elif}\;x \leq 0.00064:\\ \;\;\;\;2 \cdot \left(x \cdot \left(y + z\right)\right) + y \cdot 5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-10} \lor \neg \left(x \leq 1.7 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(t + \left(\left(y + z\right) \cdot 2 + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-10) (not (<= x 1.7e-13)))
   (* x (+ t (+ (* (+ y z) 2.0) (* 5.0 (/ y x)))))
   (+ (* x (+ t (+ y (* z 2.0)))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-10) || !(x <= 1.7e-13)) {
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))));
	} else {
		tmp = (x * (t + (y + (z * 2.0)))) + (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 <= (-3.1d-10)) .or. (.not. (x <= 1.7d-13))) then
        tmp = x * (t + (((y + z) * 2.0d0) + (5.0d0 * (y / x))))
    else
        tmp = (x * (t + (y + (z * 2.0d0)))) + (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 <= -3.1e-10) || !(x <= 1.7e-13)) {
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))));
	} else {
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-10) or not (x <= 1.7e-13):
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))))
	else:
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-10) || !(x <= 1.7e-13))
		tmp = Float64(x * Float64(t + Float64(Float64(Float64(y + z) * 2.0) + Float64(5.0 * Float64(y / x)))));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(y + Float64(z * 2.0)))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.1e-10) || ~((x <= 1.7e-13)))
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))));
	else
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-10], N[Not[LessEqual[x, 1.7e-13]], $MachinePrecision]], N[(x * N[(t + N[(N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.10000000000000015e-10 or 1.70000000000000008e-13 < x

   1. Initial program 100.0%

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

      1. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

   if -3.10000000000000015e-10 < x < 1.70000000000000008e-13

   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 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-10} \lor \neg \left(x \leq 1.7 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \left(t + \left(\left(y + z\right) \cdot 2 + 5 \cdot \frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9} \lor \neg \left(x \leq 11200000000\right):\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.55e-9) (not (<= x 11200000000.0)))
   (* x (+ t (+ (* z 2.0) (* y 2.0))))
   (+ (* x (+ t (+ y (* z 2.0)))) (* y 5.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.55e-9) || !(x <= 11200000000.0)) {
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	} else {
		tmp = (x * (t + (y + (z * 2.0)))) + (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 <= (-1.55d-9)) .or. (.not. (x <= 11200000000.0d0))) then
        tmp = x * (t + ((z * 2.0d0) + (y * 2.0d0)))
    else
        tmp = (x * (t + (y + (z * 2.0d0)))) + (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 <= -1.55e-9) || !(x <= 11200000000.0)) {
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	} else {
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.55e-9) or not (x <= 11200000000.0):
		tmp = x * (t + ((z * 2.0) + (y * 2.0)))
	else:
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.55e-9) || !(x <= 11200000000.0))
		tmp = Float64(x * Float64(t + Float64(Float64(z * 2.0) + Float64(y * 2.0))));
	else
		tmp = Float64(Float64(x * Float64(t + Float64(y + Float64(z * 2.0)))) + Float64(y * 5.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.55e-9) || ~((x <= 11200000000.0)))
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	else
		tmp = (x * (t + (y + (z * 2.0)))) + (y * 5.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.55e-9], N[Not[LessEqual[x, 11200000000.0]], $MachinePrecision]], N[(x * N[(t + N[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t + N[(y + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 5.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000002e-9 or 1.12e10 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.6%

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

   if -1.55000000000000002e-9 < x < 1.12e10

   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 99.1%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-9} \lor \neg \left(x \leq 11200000000\right):\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + \left(y + z \cdot 2\right)\right) + y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 95.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-28} \lor \neg \left(x \leq 8800\right):\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + \frac{x \cdot \left(t + z \cdot 2\right)}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.9e-28) (not (<= x 8800.0)))
   (* x (+ t (+ (* z 2.0) (* y 2.0))))
   (* y (+ 5.0 (/ (* x (+ t (* z 2.0))) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.9e-28) || !(x <= 8800.0)) {
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	} else {
		tmp = y * (5.0 + ((x * (t + (z * 2.0))) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.9d-28)) .or. (.not. (x <= 8800.0d0))) then
        tmp = x * (t + ((z * 2.0d0) + (y * 2.0d0)))
    else
        tmp = y * (5.0d0 + ((x * (t + (z * 2.0d0))) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.9e-28) || !(x <= 8800.0)) {
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	} else {
		tmp = y * (5.0 + ((x * (t + (z * 2.0))) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.9e-28) or not (x <= 8800.0):
		tmp = x * (t + ((z * 2.0) + (y * 2.0)))
	else:
		tmp = y * (5.0 + ((x * (t + (z * 2.0))) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.9e-28) || !(x <= 8800.0))
		tmp = Float64(x * Float64(t + Float64(Float64(z * 2.0) + Float64(y * 2.0))));
	else
		tmp = Float64(y * Float64(5.0 + Float64(Float64(x * Float64(t + Float64(z * 2.0))) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.9e-28) || ~((x <= 8800.0)))
		tmp = x * (t + ((z * 2.0) + (y * 2.0)));
	else
		tmp = y * (5.0 + ((x * (t + (z * 2.0))) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.9e-28], N[Not[LessEqual[x, 8800.0]], $MachinePrecision]], N[(x * N[(t + N[(N[(z * 2.0), $MachinePrecision] + N[(y * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(5.0 + N[(N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.90000000000000013e-28 or 8800 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.9%

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

   if -2.90000000000000013e-28 < x < 8800

   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 94.3%

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

   4. Taylor expanded in y around 0 93.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-28} \lor \neg \left(x \leq 8800\right):\\ \;\;\;\;x \cdot \left(t + \left(z \cdot 2 + y \cdot 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(5 + \frac{x \cdot \left(t + z \cdot 2\right)}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 98.2% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 2e+15)
   (+ (* x (+ t (* z 2.0))) (* y (+ 5.0 (* x 2.0))))
   (* x (+ t (+ (* (+ y z) 2.0) (* 5.0 (/ y x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2e+15) {
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	} else {
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))));
	}
	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 <= 2d+15) then
        tmp = (x * (t + (z * 2.0d0))) + (y * (5.0d0 + (x * 2.0d0)))
    else
        tmp = x * (t + (((y + z) * 2.0d0) + (5.0d0 * (y / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2e+15) {
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	} else {
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 2e+15:
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)))
	else:
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 2e+15)
		tmp = Float64(Float64(x * Float64(t + Float64(z * 2.0))) + Float64(y * Float64(5.0 + Float64(x * 2.0))));
	else
		tmp = Float64(x * Float64(t + Float64(Float64(Float64(y + z) * 2.0) + Float64(5.0 * Float64(y / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 2e+15)
		tmp = (x * (t + (z * 2.0))) + (y * (5.0 + (x * 2.0)));
	else
		tmp = x * (t + (((y + z) * 2.0) + (5.0 * (y / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 2e+15], N[(N[(x * N[(t + N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(5.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t + N[(N[(N[(y + z), $MachinePrecision] * 2.0), $MachinePrecision] + N[(5.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2e15

   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 99.4%

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

   if 2e15 < x

   1. Initial program 100.0%

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

      1. +-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-define 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. *-un-lft-identity 100.0%

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

      4. *-un-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. *-un-lft-identity 100.0%

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

      7. +-commutative 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. distribute-rgt-out 100.0%

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

      10. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 18: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-31} \lor \neg \left(y \leq 1.16 \cdot 10^{+123}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-31) (not (<= y 1.16e+123)))
   (* 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 <= -2.6e-31) || !(y <= 1.16e+123)) {
		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 <= (-2.6d-31)) .or. (.not. (y <= 1.16d+123))) 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 <= -2.6e-31) || !(y <= 1.16e+123)) {
		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 <= -2.6e-31) or not (y <= 1.16e+123):
		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 <= -2.6e-31) || !(y <= 1.16e+123))
		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 <= -2.6e-31) || ~((y <= 1.16e+123)))
		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, -2.6e-31], N[Not[LessEqual[y, 1.16e+123]], $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 < -2.59999999999999995e-31 or 1.16e123 < 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 84.0%

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

   5. Simplified 84.0%

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

   if -2.59999999999999995e-31 < y < 1.16e123

   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 77.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-31} \lor \neg \left(y \leq 1.16 \cdot 10^{+123}\right):\\ \;\;\;\;y \cdot \left(5 + x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t + z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 20: 47.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-76} \lor \neg \left(x \leq 0.00022\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.2e-76) (not (<= x 0.00022))) (* x t) (* y 5.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.2e-76) || !(x <= 0.00022)) {
		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 <= (-1.2d-76)) .or. (.not. (x <= 0.00022d0))) 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 <= -1.2e-76) || !(x <= 0.00022)) {
		tmp = x * t;
	} else {
		tmp = y * 5.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.2e-76) or not (x <= 0.00022):
		tmp = x * t
	else:
		tmp = y * 5.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.2e-76) || !(x <= 0.00022))
		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 <= -1.2e-76) || ~((x <= 0.00022)))
		tmp = x * t;
	else
		tmp = y * 5.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.2e-76], N[Not[LessEqual[x, 0.00022]], $MachinePrecision]], N[(x * t), $MachinePrecision], N[(y * 5.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000007e-76 or 2.20000000000000008e-4 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 33.7%

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

   if -1.20000000000000007e-76 < x < 2.20000000000000008e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 64.9%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-76} \lor \neg \left(x \leq 0.00022\right):\\ \;\;\;\;x \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot 5\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.5% 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 30.9%

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

4. Final simplification 30.9%

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

Reproduce

herbie shell --seed 2024103 
(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)))