Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.3% → 99.8%

Time: 15.1s

Alternatives: 16

Speedup: 0.6×

• 32.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+30} \lor \neg \left(z \leq 8 \cdot 10^{+55}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e+30) (not (<= z 8e+55)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ (fma y z x) (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e+30) || !(z <= 8e+55)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = fma(y, z, x) + (a * (t + (z * b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e+30) || !(z <= 8e+55))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(fma(y, z, x) + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e+30], N[Not[LessEqual[z, 8e+55]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z + x), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e30 or 8.00000000000000008e55 < z

   1. Initial program 84.8%

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

      1. associate-+l+ 84.8%

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

      2. associate-*l* 77.1%

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

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 94.5%

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

      1. +-commutative 94.5%

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

      2. associate-+l+ 94.5%

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

      3. +-commutative 94.5%

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

      4. associate-/l* 98.9%

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

      5. distribute-lft-out 99.8%

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

   7. Simplified 99.8%

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

   if -2e30 < z < 8.00000000000000008e55

   1. Initial program 98.6%

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

      1. associate-+l+ 98.6%

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

      2. +-commutative 98.6%

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

      3. fma-define 98.6%

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

      4. associate-*l* 99.3%

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

      5. *-commutative 99.3%

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

      6. *-commutative 99.3%

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

      7. distribute-rgt-out 100.0%

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

      8. *-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+30} \lor \neg \left(z \leq 8 \cdot 10^{+55}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 38.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -0.000135:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-308}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4100000000000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -5.5e+166)
     t_1
     (if (<= a -0.000135)
       (* a t)
       (if (<= a -2.5e-117)
         x
         (if (<= a 2.6e-308)
           (* z y)
           (if (<= a 4.6e-62)
             x
             (if (<= a 4100000000000.0)
               (* z y)
               (if (<= a 1.5e+171) t_1 (* a t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -5.5e+166) {
		tmp = t_1;
	} else if (a <= -0.000135) {
		tmp = a * t;
	} else if (a <= -2.5e-117) {
		tmp = x;
	} else if (a <= 2.6e-308) {
		tmp = z * y;
	} else if (a <= 4.6e-62) {
		tmp = x;
	} else if (a <= 4100000000000.0) {
		tmp = z * y;
	} else if (a <= 1.5e+171) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-5.5d+166)) then
        tmp = t_1
    else if (a <= (-0.000135d0)) then
        tmp = a * t
    else if (a <= (-2.5d-117)) then
        tmp = x
    else if (a <= 2.6d-308) then
        tmp = z * y
    else if (a <= 4.6d-62) then
        tmp = x
    else if (a <= 4100000000000.0d0) then
        tmp = z * y
    else if (a <= 1.5d+171) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -5.5e+166) {
		tmp = t_1;
	} else if (a <= -0.000135) {
		tmp = a * t;
	} else if (a <= -2.5e-117) {
		tmp = x;
	} else if (a <= 2.6e-308) {
		tmp = z * y;
	} else if (a <= 4.6e-62) {
		tmp = x;
	} else if (a <= 4100000000000.0) {
		tmp = z * y;
	} else if (a <= 1.5e+171) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -5.5e+166:
		tmp = t_1
	elif a <= -0.000135:
		tmp = a * t
	elif a <= -2.5e-117:
		tmp = x
	elif a <= 2.6e-308:
		tmp = z * y
	elif a <= 4.6e-62:
		tmp = x
	elif a <= 4100000000000.0:
		tmp = z * y
	elif a <= 1.5e+171:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -5.5e+166)
		tmp = t_1;
	elseif (a <= -0.000135)
		tmp = Float64(a * t);
	elseif (a <= -2.5e-117)
		tmp = x;
	elseif (a <= 2.6e-308)
		tmp = Float64(z * y);
	elseif (a <= 4.6e-62)
		tmp = x;
	elseif (a <= 4100000000000.0)
		tmp = Float64(z * y);
	elseif (a <= 1.5e+171)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -5.5e+166)
		tmp = t_1;
	elseif (a <= -0.000135)
		tmp = a * t;
	elseif (a <= -2.5e-117)
		tmp = x;
	elseif (a <= 2.6e-308)
		tmp = z * y;
	elseif (a <= 4.6e-62)
		tmp = x;
	elseif (a <= 4100000000000.0)
		tmp = z * y;
	elseif (a <= 1.5e+171)
		tmp = t_1;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+166], t$95$1, If[LessEqual[a, -0.000135], N[(a * t), $MachinePrecision], If[LessEqual[a, -2.5e-117], x, If[LessEqual[a, 2.6e-308], N[(z * y), $MachinePrecision], If[LessEqual[a, 4.6e-62], x, If[LessEqual[a, 4100000000000.0], N[(z * y), $MachinePrecision], If[LessEqual[a, 1.5e+171], t$95$1, N[(a * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.50000000000000008e166 or 4.1e12 < a < 1.5e171

   1. Initial program 84.9%

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

      1. associate-+l+ 85.0%

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

      2. associate-*l* 86.7%

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

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 96.1%

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

   6. Taylor expanded in b around inf 60.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   8. Simplified 60.6%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]

   if -5.50000000000000008e166 < a < -1.35000000000000002e-4 or 1.5e171 < a

   1. Initial program 86.3%

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

      1. associate-+l+ 86.3%

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

      2. associate-*l* 90.7%

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

   3. Simplified 90.7%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 49.7%

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

   if -1.35000000000000002e-4 < a < -2.5e-117 or 2.6e-308 < a < 4.60000000000000001e-62

   1. Initial program 98.8%

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

      1. associate-+l+ 98.8%

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

      2. associate-*l* 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 44.3%

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

   if -2.5e-117 < a < 2.6e-308 or 4.60000000000000001e-62 < a < 4.1e12

   1. Initial program 98.0%

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

      1. associate-+l+ 98.0%

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

      2. associate-*l* 85.1%

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

   3. Simplified 85.1%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 53.1%

      \[\leadsto \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -0.000135:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-308}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4100000000000:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+171}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 39.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+55}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-68}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-268}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-8}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+28}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1e+55)
   (* z y)
   (if (<= z -1.08e-68)
     (* a t)
     (if (<= z -2.55e-300)
       x
       (if (<= z 3.1e-268)
         (* a t)
         (if (<= z 2.5e-151)
           x
           (if (<= z 3.5e-8)
             (* a t)
             (if (<= z 2.95e+28) (* z y) (* z (* a b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e+55) {
		tmp = z * y;
	} else if (z <= -1.08e-68) {
		tmp = a * t;
	} else if (z <= -2.55e-300) {
		tmp = x;
	} else if (z <= 3.1e-268) {
		tmp = a * t;
	} else if (z <= 2.5e-151) {
		tmp = x;
	} else if (z <= 3.5e-8) {
		tmp = a * t;
	} else if (z <= 2.95e+28) {
		tmp = z * y;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1d+55)) then
        tmp = z * y
    else if (z <= (-1.08d-68)) then
        tmp = a * t
    else if (z <= (-2.55d-300)) then
        tmp = x
    else if (z <= 3.1d-268) then
        tmp = a * t
    else if (z <= 2.5d-151) then
        tmp = x
    else if (z <= 3.5d-8) then
        tmp = a * t
    else if (z <= 2.95d+28) then
        tmp = z * y
    else
        tmp = z * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e+55) {
		tmp = z * y;
	} else if (z <= -1.08e-68) {
		tmp = a * t;
	} else if (z <= -2.55e-300) {
		tmp = x;
	} else if (z <= 3.1e-268) {
		tmp = a * t;
	} else if (z <= 2.5e-151) {
		tmp = x;
	} else if (z <= 3.5e-8) {
		tmp = a * t;
	} else if (z <= 2.95e+28) {
		tmp = z * y;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1e+55:
		tmp = z * y
	elif z <= -1.08e-68:
		tmp = a * t
	elif z <= -2.55e-300:
		tmp = x
	elif z <= 3.1e-268:
		tmp = a * t
	elif z <= 2.5e-151:
		tmp = x
	elif z <= 3.5e-8:
		tmp = a * t
	elif z <= 2.95e+28:
		tmp = z * y
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1e+55)
		tmp = Float64(z * y);
	elseif (z <= -1.08e-68)
		tmp = Float64(a * t);
	elseif (z <= -2.55e-300)
		tmp = x;
	elseif (z <= 3.1e-268)
		tmp = Float64(a * t);
	elseif (z <= 2.5e-151)
		tmp = x;
	elseif (z <= 3.5e-8)
		tmp = Float64(a * t);
	elseif (z <= 2.95e+28)
		tmp = Float64(z * y);
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1e+55)
		tmp = z * y;
	elseif (z <= -1.08e-68)
		tmp = a * t;
	elseif (z <= -2.55e-300)
		tmp = x;
	elseif (z <= 3.1e-268)
		tmp = a * t;
	elseif (z <= 2.5e-151)
		tmp = x;
	elseif (z <= 3.5e-8)
		tmp = a * t;
	elseif (z <= 2.95e+28)
		tmp = z * y;
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1e+55], N[(z * y), $MachinePrecision], If[LessEqual[z, -1.08e-68], N[(a * t), $MachinePrecision], If[LessEqual[z, -2.55e-300], x, If[LessEqual[z, 3.1e-268], N[(a * t), $MachinePrecision], If[LessEqual[z, 2.5e-151], x, If[LessEqual[z, 3.5e-8], N[(a * t), $MachinePrecision], If[LessEqual[z, 2.95e+28], N[(z * y), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000001e55 or 3.50000000000000024e-8 < z < 2.9500000000000001e28

   1. Initial program 84.6%

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

      1. associate-+l+ 84.6%

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

      2. associate-*l* 76.8%

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

   3. Simplified 76.8%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 47.6%

      \[\leadsto \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 47.6%

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

   7. Simplified 47.6%

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

   if -1.00000000000000001e55 < z < -1.0799999999999999e-68 or -2.55e-300 < z < 3.0999999999999998e-268 or 2.50000000000000002e-151 < z < 3.50000000000000024e-8

   1. Initial program 95.7%

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

      1. associate-+l+ 95.7%

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

      2. associate-*l* 95.6%

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

   3. Simplified 95.6%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 48.3%

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

   if -1.0799999999999999e-68 < z < -2.55e-300 or 3.0999999999999998e-268 < z < 2.50000000000000002e-151

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.7%

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

   if 2.9500000000000001e28 < z

   1. Initial program 88.0%

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

      1. associate-+l+ 88.0%

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

      2. associate-*l* 82.9%

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

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 83.0%

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

   6. Taylor expanded in b around inf 49.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 50.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]

      2. rem-exp-log 22.3%

         \[\leadsto \color{blue}{e^{\log \left(a \cdot b\right)}} \cdot z \]

      3. rem-exp-log 22.2%

         \[\leadsto e^{\log \left(a \cdot b\right)} \cdot \color{blue}{e^{\log z}} \]

      4. exp-sum 22.2%

         \[\leadsto \color{blue}{e^{\log \left(a \cdot b\right) + \log z}} \]

      5. +-commutative 22.2%

         \[\leadsto e^{\color{blue}{\log z + \log \left(a \cdot b\right)}} \]

      6. exp-sum 22.2%

         \[\leadsto \color{blue}{e^{\log z} \cdot e^{\log \left(a \cdot b\right)}} \]

      7. rem-exp-log 22.3%

         \[\leadsto \color{blue}{z} \cdot e^{\log \left(a \cdot b\right)} \]

      8. rem-exp-log 50.9%

         \[\leadsto z \cdot \color{blue}{\left(a \cdot b\right)} \]

   8. Simplified 50.9%

      \[\leadsto \color{blue}{z \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+55}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-68}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-268}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-8}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+28}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 39.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-68}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-268}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.45e+56)
   (* z y)
   (if (<= z -7e-68)
     (* a t)
     (if (<= z -7.2e-300)
       x
       (if (<= z 6.5e-268) (* a t) (if (<= z 9e-47) x (* z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.45e+56) {
		tmp = z * y;
	} else if (z <= -7e-68) {
		tmp = a * t;
	} else if (z <= -7.2e-300) {
		tmp = x;
	} else if (z <= 6.5e-268) {
		tmp = a * t;
	} else if (z <= 9e-47) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.45d+56)) then
        tmp = z * y
    else if (z <= (-7d-68)) then
        tmp = a * t
    else if (z <= (-7.2d-300)) then
        tmp = x
    else if (z <= 6.5d-268) then
        tmp = a * t
    else if (z <= 9d-47) then
        tmp = x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.45e+56) {
		tmp = z * y;
	} else if (z <= -7e-68) {
		tmp = a * t;
	} else if (z <= -7.2e-300) {
		tmp = x;
	} else if (z <= 6.5e-268) {
		tmp = a * t;
	} else if (z <= 9e-47) {
		tmp = x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.45e+56:
		tmp = z * y
	elif z <= -7e-68:
		tmp = a * t
	elif z <= -7.2e-300:
		tmp = x
	elif z <= 6.5e-268:
		tmp = a * t
	elif z <= 9e-47:
		tmp = x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.45e+56)
		tmp = Float64(z * y);
	elseif (z <= -7e-68)
		tmp = Float64(a * t);
	elseif (z <= -7.2e-300)
		tmp = x;
	elseif (z <= 6.5e-268)
		tmp = Float64(a * t);
	elseif (z <= 9e-47)
		tmp = x;
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.45e+56)
		tmp = z * y;
	elseif (z <= -7e-68)
		tmp = a * t;
	elseif (z <= -7.2e-300)
		tmp = x;
	elseif (z <= 6.5e-268)
		tmp = a * t;
	elseif (z <= 9e-47)
		tmp = x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.45e+56], N[(z * y), $MachinePrecision], If[LessEqual[z, -7e-68], N[(a * t), $MachinePrecision], If[LessEqual[z, -7.2e-300], x, If[LessEqual[z, 6.5e-268], N[(a * t), $MachinePrecision], If[LessEqual[z, 9e-47], x, N[(z * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000004e56 or 9e-47 < z

   1. Initial program 87.0%

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

      1. associate-+l+ 87.0%

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

      2. associate-*l* 80.8%

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

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 44.3%

      \[\leadsto \color{blue}{y \cdot z} \]
   6. Step-by-step derivation

      1. *-commutative 44.3%

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

   7. Simplified 44.3%

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

   if -1.45000000000000004e56 < z < -7.00000000000000026e-68 or -7.20000000000000031e-300 < z < 6.5000000000000003e-268

   1. Initial program 94.6%

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

      1. associate-+l+ 94.6%

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

      2. associate-*l* 91.9%

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

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 53.2%

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

   if -7.00000000000000026e-68 < z < -7.20000000000000031e-300 or 6.5000000000000003e-268 < z < 9e-47

   1. Initial program 98.9%

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

      1. associate-+l+ 99.0%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 50.3%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-68}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-268}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot t + z \cdot y\\ t_2 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+27}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+164}:\\ \;\;\;\;t\_1 + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* a t) (* z y))) (t_2 (* z (+ y (* a b)))))
   (if (<= z -9.6e+116)
     t_2
     (if (<= z 7e+27)
       (+ x t_1)
       (if (<= z 6.4e+164) (+ t_1 (* b (* z a))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * t) + (z * y);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -9.6e+116) {
		tmp = t_2;
	} else if (z <= 7e+27) {
		tmp = x + t_1;
	} else if (z <= 6.4e+164) {
		tmp = t_1 + (b * (z * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * t) + (z * y)
    t_2 = z * (y + (a * b))
    if (z <= (-9.6d+116)) then
        tmp = t_2
    else if (z <= 7d+27) then
        tmp = x + t_1
    else if (z <= 6.4d+164) then
        tmp = t_1 + (b * (z * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * t) + (z * y);
	double t_2 = z * (y + (a * b));
	double tmp;
	if (z <= -9.6e+116) {
		tmp = t_2;
	} else if (z <= 7e+27) {
		tmp = x + t_1;
	} else if (z <= 6.4e+164) {
		tmp = t_1 + (b * (z * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a * t) + (z * y)
	t_2 = z * (y + (a * b))
	tmp = 0
	if z <= -9.6e+116:
		tmp = t_2
	elif z <= 7e+27:
		tmp = x + t_1
	elif z <= 6.4e+164:
		tmp = t_1 + (b * (z * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * t) + Float64(z * y))
	t_2 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (z <= -9.6e+116)
		tmp = t_2;
	elseif (z <= 7e+27)
		tmp = Float64(x + t_1);
	elseif (z <= 6.4e+164)
		tmp = Float64(t_1 + Float64(b * Float64(z * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * t) + (z * y);
	t_2 = z * (y + (a * b));
	tmp = 0.0;
	if (z <= -9.6e+116)
		tmp = t_2;
	elseif (z <= 7e+27)
		tmp = x + t_1;
	elseif (z <= 6.4e+164)
		tmp = t_1 + (b * (z * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+116], t$95$2, If[LessEqual[z, 7e+27], N[(x + t$95$1), $MachinePrecision], If[LessEqual[z, 6.4e+164], N[(t$95$1 + N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.6000000000000001e116 or 6.3999999999999996e164 < z

   1. Initial program 80.7%

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

      1. associate-+l+ 80.7%

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

      2. associate-*l* 74.4%

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

   3. Simplified 74.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 93.2%

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

   if -9.6000000000000001e116 < z < 7.0000000000000004e27

   1. Initial program 97.5%

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

      1. associate-+l+ 97.5%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 90.0%

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

   if 7.0000000000000004e27 < z < 6.3999999999999996e164

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0 88.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+27}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+164}:\\ \;\;\;\;\left(a \cdot t + z \cdot y\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.42 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+130}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq -0.00034 \lor \neg \left(a \leq 22500000000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.42e+169)
     t_1
     (if (<= a -1.15e+130)
       (+ x (* a t))
       (if (or (<= a -0.00034) (not (<= a 22500000000000.0)))
         t_1
         (+ x (* z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.42e+169) {
		tmp = t_1;
	} else if (a <= -1.15e+130) {
		tmp = x + (a * t);
	} else if ((a <= -0.00034) || !(a <= 22500000000000.0)) {
		tmp = t_1;
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    if (a <= (-1.42d+169)) then
        tmp = t_1
    else if (a <= (-1.15d+130)) then
        tmp = x + (a * t)
    else if ((a <= (-0.00034d0)) .or. (.not. (a <= 22500000000000.0d0))) then
        tmp = t_1
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.42e+169) {
		tmp = t_1;
	} else if (a <= -1.15e+130) {
		tmp = x + (a * t);
	} else if ((a <= -0.00034) || !(a <= 22500000000000.0)) {
		tmp = t_1;
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -1.42e+169:
		tmp = t_1
	elif a <= -1.15e+130:
		tmp = x + (a * t)
	elif (a <= -0.00034) or not (a <= 22500000000000.0):
		tmp = t_1
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -1.42e+169)
		tmp = t_1;
	elseif (a <= -1.15e+130)
		tmp = Float64(x + Float64(a * t));
	elseif ((a <= -0.00034) || !(a <= 22500000000000.0))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -1.42e+169)
		tmp = t_1;
	elseif (a <= -1.15e+130)
		tmp = x + (a * t);
	elseif ((a <= -0.00034) || ~((a <= 22500000000000.0)))
		tmp = t_1;
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.42e+169], t$95$1, If[LessEqual[a, -1.15e+130], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -0.00034], N[Not[LessEqual[a, 22500000000000.0]], $MachinePrecision]], t$95$1, N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.42000000000000002e169 or -1.15000000000000011e130 < a < -3.4e-4 or 2.25e13 < a

   1. Initial program 85.0%

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

      1. associate-+l+ 85.1%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 76.9%

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

   if -1.42000000000000002e169 < a < -1.15000000000000011e130

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 83.7%

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

      1. +-commutative 83.7%

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

   7. Simplified 83.7%

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

   if -3.4e-4 < a < 2.25e13

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 90.3%

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

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 74.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+130}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq -0.00034 \lor \neg \left(a \leq 22500000000000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -1.16 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t + \frac{x}{a}\right)\\ \mathbf{elif}\;a \leq -0.00036 \lor \neg \left(a \leq 920000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -1.16e+169)
     t_1
     (if (<= a -1.6e+129)
       (* a (+ t (/ x a)))
       (if (or (<= a -0.00036) (not (<= a 920000000.0))) t_1 (+ x (* z y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.16e+169) {
		tmp = t_1;
	} else if (a <= -1.6e+129) {
		tmp = a * (t + (x / a));
	} else if ((a <= -0.00036) || !(a <= 920000000.0)) {
		tmp = t_1;
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t + (z * b))
    if (a <= (-1.16d+169)) then
        tmp = t_1
    else if (a <= (-1.6d+129)) then
        tmp = a * (t + (x / a))
    else if ((a <= (-0.00036d0)) .or. (.not. (a <= 920000000.0d0))) then
        tmp = t_1
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (t + (z * b));
	double tmp;
	if (a <= -1.16e+169) {
		tmp = t_1;
	} else if (a <= -1.6e+129) {
		tmp = a * (t + (x / a));
	} else if ((a <= -0.00036) || !(a <= 920000000.0)) {
		tmp = t_1;
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -1.16e+169:
		tmp = t_1
	elif a <= -1.6e+129:
		tmp = a * (t + (x / a))
	elif (a <= -0.00036) or not (a <= 920000000.0):
		tmp = t_1
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(t + Float64(z * b)))
	tmp = 0.0
	if (a <= -1.16e+169)
		tmp = t_1;
	elseif (a <= -1.6e+129)
		tmp = Float64(a * Float64(t + Float64(x / a)));
	elseif ((a <= -0.00036) || !(a <= 920000000.0))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (t + (z * b));
	tmp = 0.0;
	if (a <= -1.16e+169)
		tmp = t_1;
	elseif (a <= -1.6e+129)
		tmp = a * (t + (x / a));
	elseif ((a <= -0.00036) || ~((a <= 920000000.0)))
		tmp = t_1;
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.16e+169], t$95$1, If[LessEqual[a, -1.6e+129], N[(a * N[(t + N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -0.00036], N[Not[LessEqual[a, 920000000.0]], $MachinePrecision]], t$95$1, N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.16e169 or -1.6000000000000001e129 < a < -3.60000000000000023e-4 or 9.2e8 < a

   1. Initial program 85.0%

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

      1. associate-+l+ 85.1%

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

      2. associate-*l* 87.7%

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

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 76.9%

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

   if -1.16e169 < a < -1.6000000000000001e129

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 100.0%

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

   6. Taylor expanded in z around 0 83.8%

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

   if -3.60000000000000023e-4 < a < 9.2e8

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 90.3%

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

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 74.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.16 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t + \frac{x}{a}\right)\\ \mathbf{elif}\;a \leq -0.00036 \lor \neg \left(a \leq 920000000\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+66}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 4000000000000:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+168}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -2.35e+166)
     t_1
     (if (<= a -7.2e+66)
       (* a t)
       (if (<= a 4000000000000.0)
         (+ x (* z y))
         (if (<= a 2.6e+168) t_1 (* a t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -2.35e+166) {
		tmp = t_1;
	} else if (a <= -7.2e+66) {
		tmp = a * t;
	} else if (a <= 4000000000000.0) {
		tmp = x + (z * y);
	} else if (a <= 2.6e+168) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (a <= (-2.35d+166)) then
        tmp = t_1
    else if (a <= (-7.2d+66)) then
        tmp = a * t
    else if (a <= 4000000000000.0d0) then
        tmp = x + (z * y)
    else if (a <= 2.6d+168) then
        tmp = t_1
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -2.35e+166) {
		tmp = t_1;
	} else if (a <= -7.2e+66) {
		tmp = a * t;
	} else if (a <= 4000000000000.0) {
		tmp = x + (z * y);
	} else if (a <= 2.6e+168) {
		tmp = t_1;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -2.35e+166:
		tmp = t_1
	elif a <= -7.2e+66:
		tmp = a * t
	elif a <= 4000000000000.0:
		tmp = x + (z * y)
	elif a <= 2.6e+168:
		tmp = t_1
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -2.35e+166)
		tmp = t_1;
	elseif (a <= -7.2e+66)
		tmp = Float64(a * t);
	elseif (a <= 4000000000000.0)
		tmp = Float64(x + Float64(z * y));
	elseif (a <= 2.6e+168)
		tmp = t_1;
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -2.35e+166)
		tmp = t_1;
	elseif (a <= -7.2e+66)
		tmp = a * t;
	elseif (a <= 4000000000000.0)
		tmp = x + (z * y);
	elseif (a <= 2.6e+168)
		tmp = t_1;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.35e+166], t$95$1, If[LessEqual[a, -7.2e+66], N[(a * t), $MachinePrecision], If[LessEqual[a, 4000000000000.0], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+168], t$95$1, N[(a * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.35e166 or 4e12 < a < 2.6e168

   1. Initial program 84.9%

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

      1. associate-+l+ 85.0%

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

      2. associate-*l* 86.7%

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

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 96.1%

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

   6. Taylor expanded in b around inf 60.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   8. Simplified 60.6%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]

   if -2.35e166 < a < -7.2e66 or 2.6e168 < a

   1. Initial program 82.0%

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

      1. associate-+l+ 82.0%

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

      2. associate-*l* 86.3%

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

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 56.7%

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

   if -7.2e66 < a < 4e12

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 71.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.35 \cdot 10^{+166}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{+66}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;a \leq 4000000000000:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+168}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot t\\ t_2 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -1.52 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 90000000000:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a t))) (t_2 (* a (* z b))))
   (if (<= a -1.52e+172)
     t_2
     (if (<= a -6.8e+52)
       t_1
       (if (<= a 90000000000.0) (+ x (* z y)) (if (<= a 2.4e+155) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double t_2 = a * (z * b);
	double tmp;
	if (a <= -1.52e+172) {
		tmp = t_2;
	} else if (a <= -6.8e+52) {
		tmp = t_1;
	} else if (a <= 90000000000.0) {
		tmp = x + (z * y);
	} else if (a <= 2.4e+155) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * t)
    t_2 = a * (z * b)
    if (a <= (-1.52d+172)) then
        tmp = t_2
    else if (a <= (-6.8d+52)) then
        tmp = t_1
    else if (a <= 90000000000.0d0) then
        tmp = x + (z * y)
    else if (a <= 2.4d+155) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * t);
	double t_2 = a * (z * b);
	double tmp;
	if (a <= -1.52e+172) {
		tmp = t_2;
	} else if (a <= -6.8e+52) {
		tmp = t_1;
	} else if (a <= 90000000000.0) {
		tmp = x + (z * y);
	} else if (a <= 2.4e+155) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * t)
	t_2 = a * (z * b)
	tmp = 0
	if a <= -1.52e+172:
		tmp = t_2
	elif a <= -6.8e+52:
		tmp = t_1
	elif a <= 90000000000.0:
		tmp = x + (z * y)
	elif a <= 2.4e+155:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * t))
	t_2 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -1.52e+172)
		tmp = t_2;
	elseif (a <= -6.8e+52)
		tmp = t_1;
	elseif (a <= 90000000000.0)
		tmp = Float64(x + Float64(z * y));
	elseif (a <= 2.4e+155)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * t);
	t_2 = a * (z * b);
	tmp = 0.0;
	if (a <= -1.52e+172)
		tmp = t_2;
	elseif (a <= -6.8e+52)
		tmp = t_1;
	elseif (a <= 90000000000.0)
		tmp = x + (z * y);
	elseif (a <= 2.4e+155)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.52e+172], t$95$2, If[LessEqual[a, -6.8e+52], t$95$1, If[LessEqual[a, 90000000000.0], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+155], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5200000000000001e172 or 9e10 < a < 2.40000000000000021e155

   1. Initial program 84.6%

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

      1. associate-+l+ 84.7%

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

      2. associate-*l* 86.5%

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

   3. Simplified 86.5%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 96.1%

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

   6. Taylor expanded in b around inf 61.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 61.6%

         \[\leadsto a \cdot \color{blue}{\left(z \cdot b\right)} \]

   8. Simplified 61.6%

      \[\leadsto \color{blue}{a \cdot \left(z \cdot b\right)} \]

   if -1.5200000000000001e172 < a < -6.8e52 or 2.40000000000000021e155 < a

   1. Initial program 84.1%

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

      1. associate-+l+ 84.1%

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

      2. associate-*l* 87.9%

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

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 72.4%

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

      1. +-commutative 72.4%

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

   7. Simplified 72.4%

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

   if -6.8e52 < a < 9e10

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 91.3%

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

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 72.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.52 \cdot 10^{+172}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{+52}:\\ \;\;\;\;x + a \cdot t\\ \mathbf{elif}\;a \leq 90000000000:\\ \;\;\;\;x + z \cdot y\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+155}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-53} \lor \neg \left(z \leq 4 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-53) (not (<= z 4e+26)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ x (+ (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-53) || !(z <= 4e+26)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6d-53)) .or. (.not. (z <= 4d+26))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    else
        tmp = x + ((a * t) + (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-53) || !(z <= 4e+26)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-53) or not (z <= 4e+26):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	else:
		tmp = x + ((a * t) + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-53) || !(z <= 4e+26))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-53) || ~((z <= 4e+26)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	else
		tmp = x + ((a * t) + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-53], N[Not[LessEqual[z, 4e+26]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000004e-53 or 4.00000000000000019e26 < z

   1. Initial program 86.5%

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

      1. associate-+l+ 86.5%

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

      2. associate-*l* 80.2%

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

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-+l+ 94.6%

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

      3. +-commutative 94.6%

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

      4. associate-/l* 98.3%

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

      5. distribute-lft-out 99.8%

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

   7. Simplified 99.8%

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

   if -6.0000000000000004e-53 < z < 4.00000000000000019e26

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 93.4%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-53} \lor \neg \left(z \leq 4 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-31} \lor \neg \left(z \leq 2.6 \cdot 10^{+49}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e-31) (not (<= z 2.6e+49)))
   (* z (+ y (+ (/ x z) (* a (+ b (/ t z))))))
   (+ (+ x (* z y)) (+ (* a (* z b)) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-31) || !(z <= 2.6e+49)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = (x + (z * y)) + ((a * (z * b)) + (a * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.5d-31)) .or. (.not. (z <= 2.6d+49))) then
        tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
    else
        tmp = (x + (z * y)) + ((a * (z * b)) + (a * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-31) || !(z <= 2.6e+49)) {
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	} else {
		tmp = (x + (z * y)) + ((a * (z * b)) + (a * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.5e-31) or not (z <= 2.6e+49):
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))))
	else:
		tmp = (x + (z * y)) + ((a * (z * b)) + (a * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e-31) || !(z <= 2.6e+49))
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * Float64(b + Float64(t / z))))));
	else
		tmp = Float64(Float64(x + Float64(z * y)) + Float64(Float64(a * Float64(z * b)) + Float64(a * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.5e-31) || ~((z <= 2.6e+49)))
		tmp = z * (y + ((x / z) + (a * (b + (t / z)))));
	else
		tmp = (x + (z * y)) + ((a * (z * b)) + (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e-31], N[Not[LessEqual[z, 2.6e+49]], $MachinePrecision]], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000004e-31 or 2.59999999999999989e49 < z

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. associate-*l* 78.9%

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

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-+l+ 94.3%

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

      3. +-commutative 94.3%

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

      4. associate-/l* 98.3%

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

      5. distribute-lft-out 99.8%

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

   7. Simplified 99.8%

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

   if -4.5000000000000004e-31 < z < 2.59999999999999989e49

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-31} \lor \neg \left(z \leq 2.6 \cdot 10^{+49}\right):\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot \left(b + \frac{t}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot y\right) + \left(a \cdot \left(z \cdot b\right) + a \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -225000000000 \lor \neg \left(t \leq 26000000\right) \land \left(t \leq 1.85 \cdot 10^{+173} \lor \neg \left(t \leq 1.6 \cdot 10^{+213}\right)\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -225000000000.0)
         (and (not (<= t 26000000.0))
              (or (<= t 1.85e+173) (not (<= t 1.6e+213)))))
   (* a t)
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -225000000000.0) || (!(t <= 26000000.0) && ((t <= 1.85e+173) || !(t <= 1.6e+213)))) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-225000000000.0d0)) .or. (.not. (t <= 26000000.0d0)) .and. (t <= 1.85d+173) .or. (.not. (t <= 1.6d+213))) then
        tmp = a * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -225000000000.0) || (!(t <= 26000000.0) && ((t <= 1.85e+173) || !(t <= 1.6e+213)))) {
		tmp = a * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -225000000000.0) or (not (t <= 26000000.0) and ((t <= 1.85e+173) or not (t <= 1.6e+213))):
		tmp = a * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -225000000000.0) || (!(t <= 26000000.0) && ((t <= 1.85e+173) || !(t <= 1.6e+213))))
		tmp = Float64(a * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -225000000000.0) || (~((t <= 26000000.0)) && ((t <= 1.85e+173) || ~((t <= 1.6e+213)))))
		tmp = a * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -225000000000.0], And[N[Not[LessEqual[t, 26000000.0]], $MachinePrecision], Or[LessEqual[t, 1.85e+173], N[Not[LessEqual[t, 1.6e+213]], $MachinePrecision]]]], N[(a * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.25e11 or 2.6e7 < t < 1.84999999999999993e173 or 1.5999999999999999e213 < t

   1. Initial program 92.0%

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

      1. associate-+l+ 92.0%

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

      2. associate-*l* 85.4%

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

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 48.1%

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

   if -2.25e11 < t < 2.6e7 or 1.84999999999999993e173 < t < 1.5999999999999999e213

   1. Initial program 93.1%

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

      1. associate-+l+ 93.1%

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

      2. associate-*l* 93.1%

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

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 39.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -225000000000 \lor \neg \left(t \leq 26000000\right) \land \left(t \leq 1.85 \cdot 10^{+173} \lor \neg \left(t \leq 1.6 \cdot 10^{+213}\right)\right):\\ \;\;\;\;a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+120} \lor \neg \left(z \leq 60\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.6e+120) (not (<= z 60.0)))
   (* z (+ y (* a b)))
   (+ x (* a (+ t (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.6e+120) || !(z <= 60.0)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.6d+120)) .or. (.not. (z <= 60.0d0))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * (t + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.6e+120) || !(z <= 60.0)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.6e+120) or not (z <= 60.0):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.6e+120) || !(z <= 60.0))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.6e+120) || ~((z <= 60.0)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.6e+120], N[Not[LessEqual[z, 60.0]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.60000000000000004e120 or 60 < z

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 87.8%

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

   if -9.60000000000000004e120 < z < 60

   1. Initial program 96.8%

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

      1. associate-+l+ 96.8%

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

      2. +-commutative 96.8%

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

      3. fma-define 96.9%

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

      4. associate-*l* 96.8%

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

      5. *-commutative 96.8%

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

      6. *-commutative 96.8%

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

      7. distribute-rgt-out 98.1%

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

      8. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 82.4%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+120} \lor \neg \left(z \leq 60\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+117} \lor \neg \left(z \leq 1.48 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.5e+117) (not (<= z 1.48e+29)))
   (* z (+ y (* a b)))
   (+ x (+ (* a t) (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e+117) || !(z <= 1.48e+29)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.5d+117)) .or. (.not. (z <= 1.48d+29))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + ((a * t) + (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e+117) || !(z <= 1.48e+29)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + ((a * t) + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.5e+117) or not (z <= 1.48e+29):
		tmp = z * (y + (a * b))
	else:
		tmp = x + ((a * t) + (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.5e+117) || !(z <= 1.48e+29))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(Float64(a * t) + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.5e+117) || ~((z <= 1.48e+29)))
		tmp = z * (y + (a * b));
	else
		tmp = x + ((a * t) + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.5e+117], N[Not[LessEqual[z, 1.48e+29]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * t), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e117 or 1.48e29 < z

   1. Initial program 84.7%

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

      1. associate-+l+ 84.7%

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

      2. associate-*l* 76.9%

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

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 87.8%

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

   if -1.5e117 < z < 1.48e29

   1. Initial program 97.5%

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

      1. associate-+l+ 97.5%

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

      2. associate-*l* 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 90.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+117} \lor \neg \left(z \leq 1.48 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot t + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+18} \lor \neg \left(z \leq 245\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e+18) (not (<= z 245.0)))
   (* z (+ y (* a b)))
   (+ x (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e+18) || !(z <= 245.0)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.1d+18)) .or. (.not. (z <= 245.0d0))) then
        tmp = z * (y + (a * b))
    else
        tmp = x + (a * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.1e+18) || !(z <= 245.0)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (a * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.1e+18) or not (z <= 245.0):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (a * t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.1e+18) || !(z <= 245.0))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = Float64(x + Float64(a * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.1e+18) || ~((z <= 245.0)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (a * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.1e+18], N[Not[LessEqual[z, 245.0]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e18 or 245 < z

   1. Initial program 86.1%

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

      1. associate-+l+ 86.1%

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

      2. associate-*l* 79.2%

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

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 82.9%

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

   if -2.1e18 < z < 245

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+18} \lor \neg \left(z \leq 245\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.2% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 92.6%

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

   1. associate-+l+ 92.6%

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

   2. associate-*l* 89.7%

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

3. Simplified 89.7%

   \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 27.0%

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

6. Final simplification 27.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (if (< z -11820553527347888000.0) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))