Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.0% → 95.8%

Time: 11.5s

Alternatives: 15

Speedup: 0.4×

• 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: 92.0% 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: 95.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + \left(z \cdot b + \left(\frac{x}{a} + \frac{y \cdot z}{a}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 5e+306) t_1 (* a (+ t (+ (* z b) (+ (/ x a) (/ (* y z) a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = a * (t + ((z * b) + ((x / a) + ((y * z) / a))));
	}
	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 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
    if (t_1 <= 5d+306) then
        tmp = t_1
    else
        tmp = a * (t + ((z * b) + ((x / a) + ((y * z) / a))))
    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 + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = a * (t + ((z * b) + ((x / a) + ((y * z) / a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_1 <= 5e+306:
		tmp = t_1
	else:
		tmp = a * (t + ((z * b) + ((x / a) + ((y * z) / a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t + Float64(Float64(z * b) + Float64(Float64(x / a) + Float64(Float64(y * z) / a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = a * (t + ((z * b) + ((x / a) + ((y * z) / a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+306], t$95$1, N[(a * N[(t + N[(N[(z * b), $MachinePrecision] + N[(N[(x / a), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 4.99999999999999993e306

   1. Initial program 100.0%

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

   if 4.99999999999999993e306 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 74.5%

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

      1. associate-+l+ 74.5%

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

      2. associate-*l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 90.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + \left(z \cdot b + \left(\frac{x}{a} + \frac{y \cdot z}{a}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 38.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-99}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-308}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+175}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -4.2e+48)
     t_1
     (if (<= a -1.1e-99)
       (* y z)
       (if (<= a -2.7e-140)
         x
         (if (<= a 3.8e-308)
           (* y z)
           (if (<= a 2.8e-22)
             x
             (if (<= a 2.35e+21)
               t_1
               (if (<= a 3.6e+44) x (if (<= a 3.5e+175) (* t a) t_1))))))))))

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 <= -4.2e+48) {
		tmp = t_1;
	} else if (a <= -1.1e-99) {
		tmp = y * z;
	} else if (a <= -2.7e-140) {
		tmp = x;
	} else if (a <= 3.8e-308) {
		tmp = y * z;
	} else if (a <= 2.8e-22) {
		tmp = x;
	} else if (a <= 2.35e+21) {
		tmp = t_1;
	} else if (a <= 3.6e+44) {
		tmp = x;
	} else if (a <= 3.5e+175) {
		tmp = t * a;
	} 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 = a * (z * b)
    if (a <= (-4.2d+48)) then
        tmp = t_1
    else if (a <= (-1.1d-99)) then
        tmp = y * z
    else if (a <= (-2.7d-140)) then
        tmp = x
    else if (a <= 3.8d-308) then
        tmp = y * z
    else if (a <= 2.8d-22) then
        tmp = x
    else if (a <= 2.35d+21) then
        tmp = t_1
    else if (a <= 3.6d+44) then
        tmp = x
    else if (a <= 3.5d+175) then
        tmp = t * a
    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 = a * (z * b);
	double tmp;
	if (a <= -4.2e+48) {
		tmp = t_1;
	} else if (a <= -1.1e-99) {
		tmp = y * z;
	} else if (a <= -2.7e-140) {
		tmp = x;
	} else if (a <= 3.8e-308) {
		tmp = y * z;
	} else if (a <= 2.8e-22) {
		tmp = x;
	} else if (a <= 2.35e+21) {
		tmp = t_1;
	} else if (a <= 3.6e+44) {
		tmp = x;
	} else if (a <= 3.5e+175) {
		tmp = t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -4.2e+48:
		tmp = t_1
	elif a <= -1.1e-99:
		tmp = y * z
	elif a <= -2.7e-140:
		tmp = x
	elif a <= 3.8e-308:
		tmp = y * z
	elif a <= 2.8e-22:
		tmp = x
	elif a <= 2.35e+21:
		tmp = t_1
	elif a <= 3.6e+44:
		tmp = x
	elif a <= 3.5e+175:
		tmp = t * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -4.2e+48)
		tmp = t_1;
	elseif (a <= -1.1e-99)
		tmp = Float64(y * z);
	elseif (a <= -2.7e-140)
		tmp = x;
	elseif (a <= 3.8e-308)
		tmp = Float64(y * z);
	elseif (a <= 2.8e-22)
		tmp = x;
	elseif (a <= 2.35e+21)
		tmp = t_1;
	elseif (a <= 3.6e+44)
		tmp = x;
	elseif (a <= 3.5e+175)
		tmp = Float64(t * a);
	else
		tmp = t_1;
	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 <= -4.2e+48)
		tmp = t_1;
	elseif (a <= -1.1e-99)
		tmp = y * z;
	elseif (a <= -2.7e-140)
		tmp = x;
	elseif (a <= 3.8e-308)
		tmp = y * z;
	elseif (a <= 2.8e-22)
		tmp = x;
	elseif (a <= 2.35e+21)
		tmp = t_1;
	elseif (a <= 3.6e+44)
		tmp = x;
	elseif (a <= 3.5e+175)
		tmp = t * a;
	else
		tmp = t_1;
	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, -4.2e+48], t$95$1, If[LessEqual[a, -1.1e-99], N[(y * z), $MachinePrecision], If[LessEqual[a, -2.7e-140], x, If[LessEqual[a, 3.8e-308], N[(y * z), $MachinePrecision], If[LessEqual[a, 2.8e-22], x, If[LessEqual[a, 2.35e+21], t$95$1, If[LessEqual[a, 3.6e+44], x, If[LessEqual[a, 3.5e+175], N[(t * a), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.1999999999999997e48 or 2.79999999999999995e-22 < a < 2.35e21 or 3.5000000000000003e175 < a

   1. Initial program 88.8%

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

      1. associate-+l+ 88.8%

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

      2. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in a around inf 96.5%

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

   6. Taylor expanded in b around inf 63.0%

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

   if -4.1999999999999997e48 < a < -1.10000000000000002e-99 or -2.7e-140 < a < 3.79999999999999975e-308

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if -1.10000000000000002e-99 < a < -2.7e-140 or 3.79999999999999975e-308 < a < 2.79999999999999995e-22 or 2.35e21 < a < 3.6e44

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 55.1%

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

   if 3.6e44 < a < 3.5000000000000003e175

   1. Initial program 88.9%

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

      1. associate-+l+ 88.9%

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

      2. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 53.0%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-99}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-140}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-308}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+175}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-101}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-308}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+175}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= a -1.1e+44)
     t_1
     (if (<= a -1.42e-101)
       (* y z)
       (if (<= a -4.9e-138)
         x
         (if (<= a 3.6e-308)
           (* y z)
           (if (<= a 1.7e-21)
             x
             (if (<= a 5e+22)
               t_1
               (if (<= a 2.7e+44)
                 x
                 (if (<= a 5e+175) (* t a) (* a (* z b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (a <= -1.1e+44) {
		tmp = t_1;
	} else if (a <= -1.42e-101) {
		tmp = y * z;
	} else if (a <= -4.9e-138) {
		tmp = x;
	} else if (a <= 3.6e-308) {
		tmp = y * z;
	} else if (a <= 1.7e-21) {
		tmp = x;
	} else if (a <= 5e+22) {
		tmp = t_1;
	} else if (a <= 2.7e+44) {
		tmp = x;
	} else if (a <= 5e+175) {
		tmp = t * a;
	} else {
		tmp = a * (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) :: t_1
    real(8) :: tmp
    t_1 = (z * a) * b
    if (a <= (-1.1d+44)) then
        tmp = t_1
    else if (a <= (-1.42d-101)) then
        tmp = y * z
    else if (a <= (-4.9d-138)) then
        tmp = x
    else if (a <= 3.6d-308) then
        tmp = y * z
    else if (a <= 1.7d-21) then
        tmp = x
    else if (a <= 5d+22) then
        tmp = t_1
    else if (a <= 2.7d+44) then
        tmp = x
    else if (a <= 5d+175) then
        tmp = t * a
    else
        tmp = a * (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 t_1 = (z * a) * b;
	double tmp;
	if (a <= -1.1e+44) {
		tmp = t_1;
	} else if (a <= -1.42e-101) {
		tmp = y * z;
	} else if (a <= -4.9e-138) {
		tmp = x;
	} else if (a <= 3.6e-308) {
		tmp = y * z;
	} else if (a <= 1.7e-21) {
		tmp = x;
	} else if (a <= 5e+22) {
		tmp = t_1;
	} else if (a <= 2.7e+44) {
		tmp = x;
	} else if (a <= 5e+175) {
		tmp = t * a;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if a <= -1.1e+44:
		tmp = t_1
	elif a <= -1.42e-101:
		tmp = y * z
	elif a <= -4.9e-138:
		tmp = x
	elif a <= 3.6e-308:
		tmp = y * z
	elif a <= 1.7e-21:
		tmp = x
	elif a <= 5e+22:
		tmp = t_1
	elif a <= 2.7e+44:
		tmp = x
	elif a <= 5e+175:
		tmp = t * a
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (a <= -1.1e+44)
		tmp = t_1;
	elseif (a <= -1.42e-101)
		tmp = Float64(y * z);
	elseif (a <= -4.9e-138)
		tmp = x;
	elseif (a <= 3.6e-308)
		tmp = Float64(y * z);
	elseif (a <= 1.7e-21)
		tmp = x;
	elseif (a <= 5e+22)
		tmp = t_1;
	elseif (a <= 2.7e+44)
		tmp = x;
	elseif (a <= 5e+175)
		tmp = Float64(t * a);
	else
		tmp = Float64(a * Float64(z * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (a <= -1.1e+44)
		tmp = t_1;
	elseif (a <= -1.42e-101)
		tmp = y * z;
	elseif (a <= -4.9e-138)
		tmp = x;
	elseif (a <= 3.6e-308)
		tmp = y * z;
	elseif (a <= 1.7e-21)
		tmp = x;
	elseif (a <= 5e+22)
		tmp = t_1;
	elseif (a <= 2.7e+44)
		tmp = x;
	elseif (a <= 5e+175)
		tmp = t * a;
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[a, -1.1e+44], t$95$1, If[LessEqual[a, -1.42e-101], N[(y * z), $MachinePrecision], If[LessEqual[a, -4.9e-138], x, If[LessEqual[a, 3.6e-308], N[(y * z), $MachinePrecision], If[LessEqual[a, 1.7e-21], x, If[LessEqual[a, 5e+22], t$95$1, If[LessEqual[a, 2.7e+44], x, If[LessEqual[a, 5e+175], N[(t * a), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.09999999999999998e44 or 1.7e-21 < a < 4.9999999999999996e22

   1. Initial program 89.3%

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

      1. associate-+l+ 89.3%

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

      2. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 96.9%

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

   6. Taylor expanded in b around inf 55.7%

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

      1. pow1 55.7%

         \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]

   8. Applied egg-rr 55.7%

      \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-*l* 57.3%

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

   10. Simplified 57.3%

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

   if -1.09999999999999998e44 < a < -1.4200000000000001e-101 or -4.90000000000000016e-138 < a < 3.5999999999999999e-308

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if -1.4200000000000001e-101 < a < -4.90000000000000016e-138 or 3.5999999999999999e-308 < a < 1.7e-21 or 4.9999999999999996e22 < a < 2.7e44

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 55.1%

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

   if 2.7e44 < a < 5e175

   1. Initial program 88.9%

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

      1. associate-+l+ 88.9%

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

      2. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 53.0%

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

   if 5e175 < a

   1. Initial program 87.3%

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

      1. associate-+l+ 87.3%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around inf 95.5%

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

   6. Taylor expanded in b around inf 83.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-101}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-308}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+175}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-308}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+178}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= a -4.4e+54)
     t_1
     (if (<= a -4.5e-102)
       (* y z)
       (if (<= a -3.8e-139)
         x
         (if (<= a -1.9e-308)
           (* y z)
           (if (<= a 1.55e-21)
             x
             (if (<= a 1.4e+20)
               t_1
               (if (<= a 4e+45)
                 x
                 (if (<= a 3.8e+178) (* t a) (* z (* a b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (a <= -4.4e+54) {
		tmp = t_1;
	} else if (a <= -4.5e-102) {
		tmp = y * z;
	} else if (a <= -3.8e-139) {
		tmp = x;
	} else if (a <= -1.9e-308) {
		tmp = y * z;
	} else if (a <= 1.55e-21) {
		tmp = x;
	} else if (a <= 1.4e+20) {
		tmp = t_1;
	} else if (a <= 4e+45) {
		tmp = x;
	} else if (a <= 3.8e+178) {
		tmp = t * a;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z * a) * b
    if (a <= (-4.4d+54)) then
        tmp = t_1
    else if (a <= (-4.5d-102)) then
        tmp = y * z
    else if (a <= (-3.8d-139)) then
        tmp = x
    else if (a <= (-1.9d-308)) then
        tmp = y * z
    else if (a <= 1.55d-21) then
        tmp = x
    else if (a <= 1.4d+20) then
        tmp = t_1
    else if (a <= 4d+45) then
        tmp = x
    else if (a <= 3.8d+178) then
        tmp = t * a
    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 t_1 = (z * a) * b;
	double tmp;
	if (a <= -4.4e+54) {
		tmp = t_1;
	} else if (a <= -4.5e-102) {
		tmp = y * z;
	} else if (a <= -3.8e-139) {
		tmp = x;
	} else if (a <= -1.9e-308) {
		tmp = y * z;
	} else if (a <= 1.55e-21) {
		tmp = x;
	} else if (a <= 1.4e+20) {
		tmp = t_1;
	} else if (a <= 4e+45) {
		tmp = x;
	} else if (a <= 3.8e+178) {
		tmp = t * a;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if a <= -4.4e+54:
		tmp = t_1
	elif a <= -4.5e-102:
		tmp = y * z
	elif a <= -3.8e-139:
		tmp = x
	elif a <= -1.9e-308:
		tmp = y * z
	elif a <= 1.55e-21:
		tmp = x
	elif a <= 1.4e+20:
		tmp = t_1
	elif a <= 4e+45:
		tmp = x
	elif a <= 3.8e+178:
		tmp = t * a
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (a <= -4.4e+54)
		tmp = t_1;
	elseif (a <= -4.5e-102)
		tmp = Float64(y * z);
	elseif (a <= -3.8e-139)
		tmp = x;
	elseif (a <= -1.9e-308)
		tmp = Float64(y * z);
	elseif (a <= 1.55e-21)
		tmp = x;
	elseif (a <= 1.4e+20)
		tmp = t_1;
	elseif (a <= 4e+45)
		tmp = x;
	elseif (a <= 3.8e+178)
		tmp = Float64(t * a);
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (a <= -4.4e+54)
		tmp = t_1;
	elseif (a <= -4.5e-102)
		tmp = y * z;
	elseif (a <= -3.8e-139)
		tmp = x;
	elseif (a <= -1.9e-308)
		tmp = y * z;
	elseif (a <= 1.55e-21)
		tmp = x;
	elseif (a <= 1.4e+20)
		tmp = t_1;
	elseif (a <= 4e+45)
		tmp = x;
	elseif (a <= 3.8e+178)
		tmp = t * a;
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[a, -4.4e+54], t$95$1, If[LessEqual[a, -4.5e-102], N[(y * z), $MachinePrecision], If[LessEqual[a, -3.8e-139], x, If[LessEqual[a, -1.9e-308], N[(y * z), $MachinePrecision], If[LessEqual[a, 1.55e-21], x, If[LessEqual[a, 1.4e+20], t$95$1, If[LessEqual[a, 4e+45], x, If[LessEqual[a, 3.8e+178], N[(t * a), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.3999999999999998e54 or 1.5499999999999999e-21 < a < 1.4e20

   1. Initial program 89.3%

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

      1. associate-+l+ 89.3%

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

      2. associate-*l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in a around inf 96.9%

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

   6. Taylor expanded in b around inf 55.7%

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

      1. pow1 55.7%

         \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]

   8. Applied egg-rr 55.7%

      \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 55.7%

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

      2. *-commutative 55.7%

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

      3. associate-*l* 57.3%

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

   10. Simplified 57.3%

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

   if -4.3999999999999998e54 < a < -4.49999999999999999e-102 or -3.80000000000000008e-139 < a < -1.9000000000000001e-308

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   if -4.49999999999999999e-102 < a < -3.80000000000000008e-139 or -1.9000000000000001e-308 < a < 1.5499999999999999e-21 or 1.4e20 < a < 3.9999999999999997e45

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf 55.1%

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

   if 3.9999999999999997e45 < a < 3.79999999999999998e178

   1. Initial program 88.9%

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

      1. associate-+l+ 88.9%

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

      2. associate-*l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 53.0%

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

   if 3.79999999999999998e178 < a

   1. Initial program 87.3%

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

      1. associate-+l+ 87.3%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around inf 95.5%

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

   6. Taylor expanded in b around inf 83.3%

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

      1. associate-*r* 87.6%

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

   8. Simplified 87.6%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+54}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-308}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+178}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 INFINITY) t_1 (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (y + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (y + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(y * z)) + Float64(t * a)) + Float64(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (y + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < +inf.0

   1. Initial program 98.4%

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

   if +inf.0 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-*l* 20.0%

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

   3. Simplified 20.0%

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

   5. Taylor expanded in z around inf 80.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq \infty:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-247}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 20000000000:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.8e-42)
   x
   (if (<= x 4.3e-247)
     (* y z)
     (if (<= x 20000000000.0)
       (* t a)
       (if (<= x 5.5e+63) (* y z) (if (<= x 6.8e+72) (* t a) x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.8e-42) {
		tmp = x;
	} else if (x <= 4.3e-247) {
		tmp = y * z;
	} else if (x <= 20000000000.0) {
		tmp = t * a;
	} else if (x <= 5.5e+63) {
		tmp = y * z;
	} else if (x <= 6.8e+72) {
		tmp = t * a;
	} 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 (x <= (-6.8d-42)) then
        tmp = x
    else if (x <= 4.3d-247) then
        tmp = y * z
    else if (x <= 20000000000.0d0) then
        tmp = t * a
    else if (x <= 5.5d+63) then
        tmp = y * z
    else if (x <= 6.8d+72) then
        tmp = t * a
    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 (x <= -6.8e-42) {
		tmp = x;
	} else if (x <= 4.3e-247) {
		tmp = y * z;
	} else if (x <= 20000000000.0) {
		tmp = t * a;
	} else if (x <= 5.5e+63) {
		tmp = y * z;
	} else if (x <= 6.8e+72) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.8e-42:
		tmp = x
	elif x <= 4.3e-247:
		tmp = y * z
	elif x <= 20000000000.0:
		tmp = t * a
	elif x <= 5.5e+63:
		tmp = y * z
	elif x <= 6.8e+72:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.8e-42)
		tmp = x;
	elseif (x <= 4.3e-247)
		tmp = Float64(y * z);
	elseif (x <= 20000000000.0)
		tmp = Float64(t * a);
	elseif (x <= 5.5e+63)
		tmp = Float64(y * z);
	elseif (x <= 6.8e+72)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.8e-42)
		tmp = x;
	elseif (x <= 4.3e-247)
		tmp = y * z;
	elseif (x <= 20000000000.0)
		tmp = t * a;
	elseif (x <= 5.5e+63)
		tmp = y * z;
	elseif (x <= 6.8e+72)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.8e-42], x, If[LessEqual[x, 4.3e-247], N[(y * z), $MachinePrecision], If[LessEqual[x, 20000000000.0], N[(t * a), $MachinePrecision], If[LessEqual[x, 5.5e+63], N[(y * z), $MachinePrecision], If[LessEqual[x, 6.8e+72], N[(t * a), $MachinePrecision], x]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.80000000000000045e-42 or 6.7999999999999997e72 < x

   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 49.5%

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

   if -6.80000000000000045e-42 < x < 4.30000000000000005e-247 or 2e10 < x < 5.50000000000000004e63

   1. Initial program 95.8%

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

      1. associate-+l+ 95.8%

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

      2. associate-*l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 47.3%

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

      1. *-commutative 47.3%

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

   7. Simplified 47.3%

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

   if 4.30000000000000005e-247 < x < 2e10 or 5.50000000000000004e63 < x < 6.7999999999999997e72

   1. Initial program 96.4%

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

      1. associate-+l+ 96.4%

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

      2. associate-*l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 45.7%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-247}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 20000000000:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+63}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+72}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t + z \cdot b\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 10^{-21}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;a \leq 23500000000000:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (+ t (* z b)))))
   (if (<= a -8e-13)
     t_1
     (if (<= a 1.18e-94)
       (+ x (* y z))
       (if (<= a 1e-21)
         (+ x (* t a))
         (if (<= a 23500000000000.0) (* z (+ y (* a b))) t_1))))))

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 <= -8e-13) {
		tmp = t_1;
	} else if (a <= 1.18e-94) {
		tmp = x + (y * z);
	} else if (a <= 1e-21) {
		tmp = x + (t * a);
	} else if (a <= 23500000000000.0) {
		tmp = z * (y + (a * b));
	} 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 = a * (t + (z * b))
    if (a <= (-8d-13)) then
        tmp = t_1
    else if (a <= 1.18d-94) then
        tmp = x + (y * z)
    else if (a <= 1d-21) then
        tmp = x + (t * a)
    else if (a <= 23500000000000.0d0) then
        tmp = z * (y + (a * b))
    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 = a * (t + (z * b));
	double tmp;
	if (a <= -8e-13) {
		tmp = t_1;
	} else if (a <= 1.18e-94) {
		tmp = x + (y * z);
	} else if (a <= 1e-21) {
		tmp = x + (t * a);
	} else if (a <= 23500000000000.0) {
		tmp = z * (y + (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (t + (z * b))
	tmp = 0
	if a <= -8e-13:
		tmp = t_1
	elif a <= 1.18e-94:
		tmp = x + (y * z)
	elif a <= 1e-21:
		tmp = x + (t * a)
	elif a <= 23500000000000.0:
		tmp = z * (y + (a * b))
	else:
		tmp = t_1
	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 <= -8e-13)
		tmp = t_1;
	elseif (a <= 1.18e-94)
		tmp = Float64(x + Float64(y * z));
	elseif (a <= 1e-21)
		tmp = Float64(x + Float64(t * a));
	elseif (a <= 23500000000000.0)
		tmp = Float64(z * Float64(y + Float64(a * b)));
	else
		tmp = t_1;
	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 <= -8e-13)
		tmp = t_1;
	elseif (a <= 1.18e-94)
		tmp = x + (y * z);
	elseif (a <= 1e-21)
		tmp = x + (t * a);
	elseif (a <= 23500000000000.0)
		tmp = z * (y + (a * b));
	else
		tmp = t_1;
	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, -8e-13], t$95$1, If[LessEqual[a, 1.18e-94], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-21], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 23500000000000.0], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.0000000000000002e-13 or 2.35e13 < a

   1. Initial program 89.6%

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

      1. associate-+l+ 89.6%

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

      2. associate-*l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in a around inf 78.8%

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

   if -8.0000000000000002e-13 < a < 1.18e-94

   1. Initial program 99.0%

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

      1. associate-+l+ 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* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in a around 0 83.6%

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

   if 1.18e-94 < a < 9.99999999999999908e-22

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around 0 83.6%

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

      1. +-commutative 83.6%

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

   7. Simplified 83.6%

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

   if 9.99999999999999908e-22 < a < 2.35e13

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-*l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 86.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.18 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 10^{-21}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;a \leq 23500000000000:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+115}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+121}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+177}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -2.7e+115)
   (* (* z a) b)
   (if (<= a 2e+121)
     (+ x (* y z))
     (if (<= a 1.4e+177) (* t a) (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -2.7e+115) {
		tmp = (z * a) * b;
	} else if (a <= 2e+121) {
		tmp = x + (y * z);
	} else if (a <= 1.4e+177) {
		tmp = t * a;
	} 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 (a <= (-2.7d+115)) then
        tmp = (z * a) * b
    else if (a <= 2d+121) then
        tmp = x + (y * z)
    else if (a <= 1.4d+177) then
        tmp = t * a
    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 (a <= -2.7e+115) {
		tmp = (z * a) * b;
	} else if (a <= 2e+121) {
		tmp = x + (y * z);
	} else if (a <= 1.4e+177) {
		tmp = t * a;
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -2.7e+115:
		tmp = (z * a) * b
	elif a <= 2e+121:
		tmp = x + (y * z)
	elif a <= 1.4e+177:
		tmp = t * a
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -2.7e+115)
		tmp = Float64(Float64(z * a) * b);
	elseif (a <= 2e+121)
		tmp = Float64(x + Float64(y * z));
	elseif (a <= 1.4e+177)
		tmp = Float64(t * a);
	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 (a <= -2.7e+115)
		tmp = (z * a) * b;
	elseif (a <= 2e+121)
		tmp = x + (y * z);
	elseif (a <= 1.4e+177)
		tmp = t * a;
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -2.7e+115], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 2e+121], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e+177], N[(t * a), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.70000000000000004e115

   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* 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 a around inf 95.3%

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

   6. Taylor expanded in b around inf 58.4%

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

      1. pow1 58.4%

         \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]

   8. Applied egg-rr 58.4%

      \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*l* 60.7%

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

   10. Simplified 60.7%

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

   if -2.70000000000000004e115 < a < 2.00000000000000007e121

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. associate-*l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in a around 0 68.9%

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

   if 2.00000000000000007e121 < a < 1.40000000000000001e177

   1. Initial program 90.9%

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

      1. associate-+l+ 90.9%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around inf 73.7%

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

   if 1.40000000000000001e177 < a

   1. Initial program 87.3%

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

      1. associate-+l+ 87.3%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around inf 95.5%

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

   6. Taylor expanded in b around inf 83.3%

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

      1. associate-*r* 87.6%

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

   8. Simplified 87.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+115}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+121}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+177}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+118}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-95}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+178}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.9e+118)
   (* (* z a) b)
   (if (<= a 5.2e-95)
     (+ x (* y z))
     (if (<= a 4.1e+178) (+ x (* t a)) (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.9e+118) {
		tmp = (z * a) * b;
	} else if (a <= 5.2e-95) {
		tmp = x + (y * z);
	} else if (a <= 4.1e+178) {
		tmp = x + (t * a);
	} 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 (a <= (-3.9d+118)) then
        tmp = (z * a) * b
    else if (a <= 5.2d-95) then
        tmp = x + (y * z)
    else if (a <= 4.1d+178) then
        tmp = x + (t * a)
    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 (a <= -3.9e+118) {
		tmp = (z * a) * b;
	} else if (a <= 5.2e-95) {
		tmp = x + (y * z);
	} else if (a <= 4.1e+178) {
		tmp = x + (t * a);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.9e+118:
		tmp = (z * a) * b
	elif a <= 5.2e-95:
		tmp = x + (y * z)
	elif a <= 4.1e+178:
		tmp = x + (t * a)
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.9e+118)
		tmp = Float64(Float64(z * a) * b);
	elseif (a <= 5.2e-95)
		tmp = Float64(x + Float64(y * z));
	elseif (a <= 4.1e+178)
		tmp = Float64(x + Float64(t * a));
	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 (a <= -3.9e+118)
		tmp = (z * a) * b;
	elseif (a <= 5.2e-95)
		tmp = x + (y * z);
	elseif (a <= 4.1e+178)
		tmp = x + (t * a);
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.9e+118], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 5.2e-95], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e+178], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.9e118

   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* 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 a around inf 95.3%

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

   6. Taylor expanded in b around inf 58.4%

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

      1. pow1 58.4%

         \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]

   8. Applied egg-rr 58.4%

      \[\leadsto \color{blue}{{\left(a \cdot \left(b \cdot z\right)\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*l* 60.7%

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

   10. Simplified 60.7%

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

   if -3.9e118 < a < 5.20000000000000001e-95

   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* 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 a around 0 76.9%

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

   if 5.20000000000000001e-95 < a < 4.09999999999999996e178

   1. Initial program 95.0%

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

      1. associate-+l+ 95.0%

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

      2. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around 0 69.7%

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

      1. +-commutative 69.7%

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

   7. Simplified 69.7%

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

   if 4.09999999999999996e178 < a

   1. Initial program 87.3%

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

      1. associate-+l+ 87.3%

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

      2. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around inf 95.5%

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

   6. Taylor expanded in b around inf 83.3%

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

      1. associate-*r* 87.6%

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

   8. Simplified 87.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+118}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-95}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+178}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+111} \lor \neg \left(a \leq 2.05 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.8e+111) (not (<= a 2.05e+118)))
   (* a (+ t (* z b)))
   (+ x (+ (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -5.8e+111) || !(a <= 2.05e+118)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	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 ((a <= (-5.8d+111)) .or. (.not. (a <= 2.05d+118))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + ((t * a) + (y * z))
    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 ((a <= -5.8e+111) || !(a <= 2.05e+118)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + ((t * a) + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -5.8e+111) or not (a <= 2.05e+118):
		tmp = a * (t + (z * b))
	else:
		tmp = x + ((t * a) + (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -5.8e+111) || !(a <= 2.05e+118))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -5.8e+111) || ~((a <= 2.05e+118)))
		tmp = a * (t + (z * b));
	else
		tmp = x + ((t * a) + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -5.8e+111], N[Not[LessEqual[a, 2.05e+118]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.7999999999999999e111 or 2.0499999999999999e118 < a

   1. Initial program 85.3%

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

      1. associate-+l+ 85.3%

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

      2. associate-*l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in a around inf 91.4%

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

   if -5.7999999999999999e111 < a < 2.0499999999999999e118

   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* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in b around 0 86.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+111} \lor \neg \left(a \leq 2.05 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+106} \lor \neg \left(t \leq 2.1 \cdot 10^{+81}\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.9e+106) (not (<= t 2.1e+81)))
   (+ x (+ (* t a) (* y z)))
   (+ x (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.9e+106) || !(t <= 2.1e+81)) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (z * (y + (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 ((t <= (-1.9d+106)) .or. (.not. (t <= 2.1d+81))) then
        tmp = x + ((t * a) + (y * z))
    else
        tmp = x + (z * (y + (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 ((t <= -1.9e+106) || !(t <= 2.1e+81)) {
		tmp = x + ((t * a) + (y * z));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.9e+106) or not (t <= 2.1e+81):
		tmp = x + ((t * a) + (y * z))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.9e+106) || !(t <= 2.1e+81))
		tmp = Float64(x + Float64(Float64(t * a) + Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.9e+106) || ~((t <= 2.1e+81)))
		tmp = x + ((t * a) + (y * z));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.9e+106], N[Not[LessEqual[t, 2.1e+81]], $MachinePrecision]], N[(x + N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8999999999999999e106 or 2.0999999999999999e81 < t

   1. Initial program 94.0%

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

      1. associate-+l+ 94.0%

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

      2. associate-*l* 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 b around 0 91.1%

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

   if -1.8999999999999999e106 < t < 2.0999999999999999e81

   1. Initial program 95.0%

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

      1. associate-+l+ 95.0%

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

      2. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in t around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. +-commutative 90.9%

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

      3. associate-*r* 91.9%

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

      4. distribute-rgt-in 93.2%

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

   7. Simplified 93.2%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+106} \lor \neg \left(t \leq 2.1 \cdot 10^{+81}\right):\\ \;\;\;\;x + \left(t \cdot a + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-14} \lor \neg \left(a \leq 2.9 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.2e-14) (not (<= a 2.9e-52)))
   (* a (+ t (* z b)))
   (+ x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.2e-14) || !(a <= 2.9e-52)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	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 ((a <= (-6.2d-14)) .or. (.not. (a <= 2.9d-52))) then
        tmp = a * (t + (z * b))
    else
        tmp = x + (y * z)
    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 ((a <= -6.2e-14) || !(a <= 2.9e-52)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.2e-14) or not (a <= 2.9e-52):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.2e-14) || !(a <= 2.9e-52))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6.2e-14) || ~((a <= 2.9e-52)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.2e-14], N[Not[LessEqual[a, 2.9e-52]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.20000000000000009e-14 or 2.9000000000000002e-52 < a

   1. Initial program 90.7%

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

      1. associate-+l+ 90.7%

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

      2. associate-*l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in a around inf 77.5%

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

   if -6.20000000000000009e-14 < a < 2.9000000000000002e-52

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in a around 0 81.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-14} \lor \neg \left(a \leq 2.9 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 91.9% accurate, 1.0× speedup

Math

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

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(x + Float64(y * z)) + Float64(Float64(t * a) + Float64(a * Float64(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[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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* 94.6%

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

3. Simplified 94.6%

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

5. Final simplification 94.6%

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

Alternative 14: 39.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+73}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.3e-9) x (if (<= x 7e+73) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e-9) {
		tmp = x;
	} else if (x <= 7e+73) {
		tmp = t * a;
	} 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 (x <= (-3.3d-9)) then
        tmp = x
    else if (x <= 7d+73) then
        tmp = t * a
    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 (x <= -3.3e-9) {
		tmp = x;
	} else if (x <= 7e+73) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.3e-9:
		tmp = x
	elif x <= 7e+73:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.3e-9)
		tmp = x;
	elseif (x <= 7e+73)
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.3e-9)
		tmp = x;
	elseif (x <= 7e+73)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.3e-9], x, If[LessEqual[x, 7e+73], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.30000000000000018e-9 or 7.00000000000000004e73 < x

   1. Initial program 93.6%

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

      1. associate-+l+ 93.6%

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

      2. associate-*l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 51.0%

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

   if -3.30000000000000018e-9 < x < 7.00000000000000004e73

   1. Initial program 95.5%

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

      1. associate-+l+ 95.5%

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

      2. associate-*l* 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 34.7%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+73}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.4% 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 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* 94.6%

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

3. Simplified 94.6%

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

5. Taylor expanded in x around inf 28.7%

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

6. Final simplification 28.7%

   \[\leadsto x \]
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 2024060 
(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)))