Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.4% → 96.5%

Time: 11.0s

Alternatives: 13

Speedup: 0.6×

• 32.9% 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: 92.4% 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: 96.5% accurate, 0.4× speedup

Math

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

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 (+ x (* 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 = x + (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 = x + (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 = x + (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(x + 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 = x + (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[(x + N[(z * N[(y + N[(a * b), $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)) < +inf.0

   1. Initial program 98.7%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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* 23.5%

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

   3. Simplified 23.5%

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

   5. Taylor expanded in t around 0 18.1%

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

      1. +-commutative 18.1%

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

      2. +-commutative 18.1%

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

      3. associate-*r* 18.1%

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

      4. distribute-rgt-in 71.0%

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

   7. Simplified 71.0%

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

4. Final simplification 96.9%

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

Alternative 2: 40.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+168}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-173}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-262}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+183} \lor \neg \left(a \leq 4.9 \cdot 10^{+235}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -2.9e+168)
     (* t a)
     (if (<= a -4.6e+33)
       t_1
       (if (<= a -2.5e-173)
         (* y z)
         (if (<= a -1.36e-226)
           x
           (if (<= a -5.2e-262)
             (* y z)
             (if (<= a 4.4e-41)
               x
               (if (or (<= a 3.5e+183) (not (<= a 4.9e+235)))
                 t_1
                 (* t a))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (a <= -2.9e+168) {
		tmp = t * a;
	} else if (a <= -4.6e+33) {
		tmp = t_1;
	} else if (a <= -2.5e-173) {
		tmp = y * z;
	} else if (a <= -1.36e-226) {
		tmp = x;
	} else if (a <= -5.2e-262) {
		tmp = y * z;
	} else if (a <= 4.4e-41) {
		tmp = x;
	} else if ((a <= 3.5e+183) || !(a <= 4.9e+235)) {
		tmp = t_1;
	} else {
		tmp = t * 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 = a * (z * b)
    if (a <= (-2.9d+168)) then
        tmp = t * a
    else if (a <= (-4.6d+33)) then
        tmp = t_1
    else if (a <= (-2.5d-173)) then
        tmp = y * z
    else if (a <= (-1.36d-226)) then
        tmp = x
    else if (a <= (-5.2d-262)) then
        tmp = y * z
    else if (a <= 4.4d-41) then
        tmp = x
    else if ((a <= 3.5d+183) .or. (.not. (a <= 4.9d+235))) then
        tmp = t_1
    else
        tmp = t * 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 = a * (z * b);
	double tmp;
	if (a <= -2.9e+168) {
		tmp = t * a;
	} else if (a <= -4.6e+33) {
		tmp = t_1;
	} else if (a <= -2.5e-173) {
		tmp = y * z;
	} else if (a <= -1.36e-226) {
		tmp = x;
	} else if (a <= -5.2e-262) {
		tmp = y * z;
	} else if (a <= 4.4e-41) {
		tmp = x;
	} else if ((a <= 3.5e+183) || !(a <= 4.9e+235)) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -2.9e+168:
		tmp = t * a
	elif a <= -4.6e+33:
		tmp = t_1
	elif a <= -2.5e-173:
		tmp = y * z
	elif a <= -1.36e-226:
		tmp = x
	elif a <= -5.2e-262:
		tmp = y * z
	elif a <= 4.4e-41:
		tmp = x
	elif (a <= 3.5e+183) or not (a <= 4.9e+235):
		tmp = t_1
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (a <= -2.9e+168)
		tmp = Float64(t * a);
	elseif (a <= -4.6e+33)
		tmp = t_1;
	elseif (a <= -2.5e-173)
		tmp = Float64(y * z);
	elseif (a <= -1.36e-226)
		tmp = x;
	elseif (a <= -5.2e-262)
		tmp = Float64(y * z);
	elseif (a <= 4.4e-41)
		tmp = x;
	elseif ((a <= 3.5e+183) || !(a <= 4.9e+235))
		tmp = t_1;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (a <= -2.9e+168)
		tmp = t * a;
	elseif (a <= -4.6e+33)
		tmp = t_1;
	elseif (a <= -2.5e-173)
		tmp = y * z;
	elseif (a <= -1.36e-226)
		tmp = x;
	elseif (a <= -5.2e-262)
		tmp = y * z;
	elseif (a <= 4.4e-41)
		tmp = x;
	elseif ((a <= 3.5e+183) || ~((a <= 4.9e+235)))
		tmp = t_1;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+168], N[(t * a), $MachinePrecision], If[LessEqual[a, -4.6e+33], t$95$1, If[LessEqual[a, -2.5e-173], N[(y * z), $MachinePrecision], If[LessEqual[a, -1.36e-226], x, If[LessEqual[a, -5.2e-262], N[(y * z), $MachinePrecision], If[LessEqual[a, 4.4e-41], x, If[Or[LessEqual[a, 3.5e+183], N[Not[LessEqual[a, 4.9e+235]], $MachinePrecision]], t$95$1, N[(t * a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.9e168 or 3.49999999999999987e183 < a < 4.8999999999999998e235

   1. Initial program 81.1%

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

      1. associate-+l+ 81.1%

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

      2. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 60.9%

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

   if -2.9e168 < a < -4.60000000000000021e33 or 4.4e-41 < a < 3.49999999999999987e183 or 4.8999999999999998e235 < a

   1. Initial program 87.6%

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

      1. associate-+l+ 87.6%

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

      2. associate-*l* 91.7%

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

   3. Simplified 91.7%

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

      1. *-commutative 91.7%

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

      2. distribute-lft-in 93.7%

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

      3. *-commutative 93.7%

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

      4. add-cube-cbrt 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \left(t + z \cdot b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \]

      5. associate-*r* 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(t + z \cdot b\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}} \]

      6. +-commutative 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\left(z \cdot b + t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      7. fma-def 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\mathsf{fma}\left(z, b, t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      8. pow2 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\mathsf{fma}\left(z, b, t\right) \cdot \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}\right) \cdot \sqrt[3]{a} \]

   6. Applied egg-rr 93.1%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\mathsf{fma}\left(z, b, t\right) \cdot {\left(\sqrt[3]{a}\right)}^{2}\right) \cdot \sqrt[3]{a}} \]

   7. Taylor expanded in b around inf 49.8%

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

   if -4.60000000000000021e33 < a < -2.5000000000000001e-173 or -1.35999999999999992e-226 < a < -5.1999999999999998e-262

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around inf 50.3%

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

      1. *-commutative 50.3%

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

   7. Simplified 50.3%

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

   if -2.5000000000000001e-173 < a < -1.35999999999999992e-226 or -5.1999999999999998e-262 < a < 4.4e-41

   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* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 56.5%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+168}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-173}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -1.36 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-262}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+183} \lor \neg \left(a \leq 4.9 \cdot 10^{+235}\right):\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 40.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+168}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-172}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-255}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+235}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= a -2.6e+168)
     (* t a)
     (if (<= a -2.65e+33)
       t_1
       (if (<= a -1.75e-172)
         (* y z)
         (if (<= a -8.6e-223)
           x
           (if (<= a -3.5e-255)
             (* y z)
             (if (<= a 1.9e-47)
               x
               (if (<= a 3.35e+184)
                 t_1
                 (if (<= a 9.2e+235) (* 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 <= -2.6e+168) {
		tmp = t * a;
	} else if (a <= -2.65e+33) {
		tmp = t_1;
	} else if (a <= -1.75e-172) {
		tmp = y * z;
	} else if (a <= -8.6e-223) {
		tmp = x;
	} else if (a <= -3.5e-255) {
		tmp = y * z;
	} else if (a <= 1.9e-47) {
		tmp = x;
	} else if (a <= 3.35e+184) {
		tmp = t_1;
	} else if (a <= 9.2e+235) {
		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 <= (-2.6d+168)) then
        tmp = t * a
    else if (a <= (-2.65d+33)) then
        tmp = t_1
    else if (a <= (-1.75d-172)) then
        tmp = y * z
    else if (a <= (-8.6d-223)) then
        tmp = x
    else if (a <= (-3.5d-255)) then
        tmp = y * z
    else if (a <= 1.9d-47) then
        tmp = x
    else if (a <= 3.35d+184) then
        tmp = t_1
    else if (a <= 9.2d+235) 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 <= -2.6e+168) {
		tmp = t * a;
	} else if (a <= -2.65e+33) {
		tmp = t_1;
	} else if (a <= -1.75e-172) {
		tmp = y * z;
	} else if (a <= -8.6e-223) {
		tmp = x;
	} else if (a <= -3.5e-255) {
		tmp = y * z;
	} else if (a <= 1.9e-47) {
		tmp = x;
	} else if (a <= 3.35e+184) {
		tmp = t_1;
	} else if (a <= 9.2e+235) {
		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 <= -2.6e+168:
		tmp = t * a
	elif a <= -2.65e+33:
		tmp = t_1
	elif a <= -1.75e-172:
		tmp = y * z
	elif a <= -8.6e-223:
		tmp = x
	elif a <= -3.5e-255:
		tmp = y * z
	elif a <= 1.9e-47:
		tmp = x
	elif a <= 3.35e+184:
		tmp = t_1
	elif a <= 9.2e+235:
		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 <= -2.6e+168)
		tmp = Float64(t * a);
	elseif (a <= -2.65e+33)
		tmp = t_1;
	elseif (a <= -1.75e-172)
		tmp = Float64(y * z);
	elseif (a <= -8.6e-223)
		tmp = x;
	elseif (a <= -3.5e-255)
		tmp = Float64(y * z);
	elseif (a <= 1.9e-47)
		tmp = x;
	elseif (a <= 3.35e+184)
		tmp = t_1;
	elseif (a <= 9.2e+235)
		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 <= -2.6e+168)
		tmp = t * a;
	elseif (a <= -2.65e+33)
		tmp = t_1;
	elseif (a <= -1.75e-172)
		tmp = y * z;
	elseif (a <= -8.6e-223)
		tmp = x;
	elseif (a <= -3.5e-255)
		tmp = y * z;
	elseif (a <= 1.9e-47)
		tmp = x;
	elseif (a <= 3.35e+184)
		tmp = t_1;
	elseif (a <= 9.2e+235)
		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, -2.6e+168], N[(t * a), $MachinePrecision], If[LessEqual[a, -2.65e+33], t$95$1, If[LessEqual[a, -1.75e-172], N[(y * z), $MachinePrecision], If[LessEqual[a, -8.6e-223], x, If[LessEqual[a, -3.5e-255], N[(y * z), $MachinePrecision], If[LessEqual[a, 1.9e-47], x, If[LessEqual[a, 3.35e+184], t$95$1, If[LessEqual[a, 9.2e+235], N[(t * a), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.6e168 or 3.35e184 < a < 9.2e235

   1. Initial program 81.1%

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

      1. associate-+l+ 81.1%

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

      2. associate-*l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 60.9%

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

   if -2.6e168 < a < -2.65000000000000012e33 or 1.90000000000000007e-47 < a < 3.35e184

   1. Initial program 89.1%

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

      1. associate-+l+ 89.1%

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

      2. associate-*l* 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. Step-by-step derivation

      1. *-commutative 92.6%

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

      2. distribute-lft-in 93.8%

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

      3. *-commutative 93.8%

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

      4. add-cube-cbrt 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \left(t + z \cdot b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \]

      5. associate-*r* 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(t + z \cdot b\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}} \]

      6. +-commutative 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\left(z \cdot b + t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      7. fma-def 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\mathsf{fma}\left(z, b, t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      8. pow2 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\mathsf{fma}\left(z, b, t\right) \cdot \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}\right) \cdot \sqrt[3]{a} \]

   6. Applied egg-rr 93.1%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\mathsf{fma}\left(z, b, t\right) \cdot {\left(\sqrt[3]{a}\right)}^{2}\right) \cdot \sqrt[3]{a}} \]

   7. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. associate-*l* 48.9%

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

   9. Simplified 48.9%

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

   if -2.65000000000000012e33 < a < -1.75000000000000014e-172 or -8.5999999999999998e-223 < a < -3.49999999999999979e-255

   1. Initial program 98.1%

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

      1. associate-+l+ 98.1%

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

      2. associate-*l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in y around inf 50.3%

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

      1. *-commutative 50.3%

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

   7. Simplified 50.3%

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

   if -1.75000000000000014e-172 < a < -8.5999999999999998e-223 or -3.49999999999999979e-255 < a < 1.90000000000000007e-47

   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* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 56.5%

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

   if 9.2e235 < a

   1. Initial program 79.9%

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

      1. associate-+l+ 79.9%

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

      2. associate-*l* 86.6%

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

   3. Simplified 86.6%

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

      1. *-commutative 86.6%

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

      2. distribute-lft-in 93.2%

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

      3. *-commutative 93.2%

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

      4. add-cube-cbrt 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \left(t + z \cdot b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \]

      5. associate-*r* 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(t + z \cdot b\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}} \]

      6. +-commutative 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\left(z \cdot b + t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      7. fma-def 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\mathsf{fma}\left(z, b, t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      8. pow2 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \left(\mathsf{fma}\left(z, b, t\right) \cdot \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}\right) \cdot \sqrt[3]{a} \]

   6. Applied egg-rr 93.0%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\mathsf{fma}\left(z, b, t\right) \cdot {\left(\sqrt[3]{a}\right)}^{2}\right) \cdot \sqrt[3]{a}} \]

   7. Taylor expanded in b around inf 61.2%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+168}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+33}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-172}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-255}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.35 \cdot 10^{+184}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+235}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ t_2 := a \cdot \left(t + z \cdot b\right)\\ t_3 := z \cdot \left(y + a \cdot b\right)\\ \mathbf{if}\;a \leq -3.7 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-85}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z)))
        (t_2 (* a (+ t (* z b))))
        (t_3 (* z (+ y (* a b)))))
   (if (<= a -3.7e+58)
     t_2
     (if (<= a -8e-28)
       t_1
       (if (<= a -3.1e-46)
         t_2
         (if (<= a -4.3e-85)
           t_3
           (if (<= a 1.45e-48)
             t_1
             (if (<= a 3.3e+31)
               t_3
               (if (<= a 4.2e+88) (+ x (* t a)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = a * (t + (z * b));
	double t_3 = z * (y + (a * b));
	double tmp;
	if (a <= -3.7e+58) {
		tmp = t_2;
	} else if (a <= -8e-28) {
		tmp = t_1;
	} else if (a <= -3.1e-46) {
		tmp = t_2;
	} else if (a <= -4.3e-85) {
		tmp = t_3;
	} else if (a <= 1.45e-48) {
		tmp = t_1;
	} else if (a <= 3.3e+31) {
		tmp = t_3;
	} else if (a <= 4.2e+88) {
		tmp = x + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (y * z)
    t_2 = a * (t + (z * b))
    t_3 = z * (y + (a * b))
    if (a <= (-3.7d+58)) then
        tmp = t_2
    else if (a <= (-8d-28)) then
        tmp = t_1
    else if (a <= (-3.1d-46)) then
        tmp = t_2
    else if (a <= (-4.3d-85)) then
        tmp = t_3
    else if (a <= 1.45d-48) then
        tmp = t_1
    else if (a <= 3.3d+31) then
        tmp = t_3
    else if (a <= 4.2d+88) then
        tmp = x + (t * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double t_2 = a * (t + (z * b));
	double t_3 = z * (y + (a * b));
	double tmp;
	if (a <= -3.7e+58) {
		tmp = t_2;
	} else if (a <= -8e-28) {
		tmp = t_1;
	} else if (a <= -3.1e-46) {
		tmp = t_2;
	} else if (a <= -4.3e-85) {
		tmp = t_3;
	} else if (a <= 1.45e-48) {
		tmp = t_1;
	} else if (a <= 3.3e+31) {
		tmp = t_3;
	} else if (a <= 4.2e+88) {
		tmp = x + (t * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	t_2 = a * (t + (z * b))
	t_3 = z * (y + (a * b))
	tmp = 0
	if a <= -3.7e+58:
		tmp = t_2
	elif a <= -8e-28:
		tmp = t_1
	elif a <= -3.1e-46:
		tmp = t_2
	elif a <= -4.3e-85:
		tmp = t_3
	elif a <= 1.45e-48:
		tmp = t_1
	elif a <= 3.3e+31:
		tmp = t_3
	elif a <= 4.2e+88:
		tmp = x + (t * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	t_2 = Float64(a * Float64(t + Float64(z * b)))
	t_3 = Float64(z * Float64(y + Float64(a * b)))
	tmp = 0.0
	if (a <= -3.7e+58)
		tmp = t_2;
	elseif (a <= -8e-28)
		tmp = t_1;
	elseif (a <= -3.1e-46)
		tmp = t_2;
	elseif (a <= -4.3e-85)
		tmp = t_3;
	elseif (a <= 1.45e-48)
		tmp = t_1;
	elseif (a <= 3.3e+31)
		tmp = t_3;
	elseif (a <= 4.2e+88)
		tmp = Float64(x + Float64(t * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	t_2 = a * (t + (z * b));
	t_3 = z * (y + (a * b));
	tmp = 0.0;
	if (a <= -3.7e+58)
		tmp = t_2;
	elseif (a <= -8e-28)
		tmp = t_1;
	elseif (a <= -3.1e-46)
		tmp = t_2;
	elseif (a <= -4.3e-85)
		tmp = t_3;
	elseif (a <= 1.45e-48)
		tmp = t_1;
	elseif (a <= 3.3e+31)
		tmp = t_3;
	elseif (a <= 4.2e+88)
		tmp = x + (t * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.7e+58], t$95$2, If[LessEqual[a, -8e-28], t$95$1, If[LessEqual[a, -3.1e-46], t$95$2, If[LessEqual[a, -4.3e-85], t$95$3, If[LessEqual[a, 1.45e-48], t$95$1, If[LessEqual[a, 3.3e+31], t$95$3, If[LessEqual[a, 4.2e+88], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.7000000000000002e58 or -7.99999999999999977e-28 < a < -3.1000000000000001e-46 or 4.2e88 < a

   1. Initial program 84.5%

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

      1. associate-+l+ 84.5%

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

      2. associate-*l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in a around inf 83.2%

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

   if -3.7000000000000002e58 < a < -7.99999999999999977e-28 or -4.29999999999999999e-85 < a < 1.4500000000000001e-48

   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* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in a around 0 80.5%

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

   if -3.1000000000000001e-46 < a < -4.29999999999999999e-85 or 1.4500000000000001e-48 < a < 3.29999999999999992e31

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 80.2%

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

   if 3.29999999999999992e31 < a < 4.2e88

   1. Initial program 83.3%

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

      1. associate-+l+ 83.3%

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

      2. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-28}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+88}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+58}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-255}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.2e+58)
   (* t a)
   (if (<= a -5e-177)
     (* y z)
     (if (<= a -3.35e-226)
       x
       (if (<= a -2.6e-255) (* y z) (if (<= a 6.4e+37) x (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e+58) {
		tmp = t * a;
	} else if (a <= -5e-177) {
		tmp = y * z;
	} else if (a <= -3.35e-226) {
		tmp = x;
	} else if (a <= -2.6e-255) {
		tmp = y * z;
	} else if (a <= 6.4e+37) {
		tmp = x;
	} else {
		tmp = t * 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) :: tmp
    if (a <= (-4.2d+58)) then
        tmp = t * a
    else if (a <= (-5d-177)) then
        tmp = y * z
    else if (a <= (-3.35d-226)) then
        tmp = x
    else if (a <= (-2.6d-255)) then
        tmp = y * z
    else if (a <= 6.4d+37) then
        tmp = x
    else
        tmp = t * 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 tmp;
	if (a <= -4.2e+58) {
		tmp = t * a;
	} else if (a <= -5e-177) {
		tmp = y * z;
	} else if (a <= -3.35e-226) {
		tmp = x;
	} else if (a <= -2.6e-255) {
		tmp = y * z;
	} else if (a <= 6.4e+37) {
		tmp = x;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.2e+58:
		tmp = t * a
	elif a <= -5e-177:
		tmp = y * z
	elif a <= -3.35e-226:
		tmp = x
	elif a <= -2.6e-255:
		tmp = y * z
	elif a <= 6.4e+37:
		tmp = x
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.2e+58)
		tmp = Float64(t * a);
	elseif (a <= -5e-177)
		tmp = Float64(y * z);
	elseif (a <= -3.35e-226)
		tmp = x;
	elseif (a <= -2.6e-255)
		tmp = Float64(y * z);
	elseif (a <= 6.4e+37)
		tmp = x;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.2e+58)
		tmp = t * a;
	elseif (a <= -5e-177)
		tmp = y * z;
	elseif (a <= -3.35e-226)
		tmp = x;
	elseif (a <= -2.6e-255)
		tmp = y * z;
	elseif (a <= 6.4e+37)
		tmp = x;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.2e+58], N[(t * a), $MachinePrecision], If[LessEqual[a, -5e-177], N[(y * z), $MachinePrecision], If[LessEqual[a, -3.35e-226], x, If[LessEqual[a, -2.6e-255], N[(y * z), $MachinePrecision], If[LessEqual[a, 6.4e+37], x, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.20000000000000024e58 or 6.40000000000000027e37 < a

   1. Initial program 83.5%

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

      1. associate-+l+ 83.5%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 45.2%

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

   if -4.20000000000000024e58 < a < -5e-177 or -3.3500000000000001e-226 < a < -2.60000000000000021e-255

   1. Initial program 98.2%

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

      1. associate-+l+ 98.2%

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

      2. associate-*l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in y around inf 48.7%

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

      1. *-commutative 48.7%

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

   7. Simplified 48.7%

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

   if -5e-177 < a < -3.3500000000000001e-226 or -2.60000000000000021e-255 < a < 6.40000000000000027e37

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 49.0%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+58}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-226}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-255}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+179}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-47} \lor \neg \left(x \leq 7.5 \cdot 10^{-19}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a + y \cdot z\right) + \left(z \cdot a\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.5e+179)
   (+ x (* t a))
   (if (or (<= x -5.8e-47) (not (<= x 7.5e-19)))
     (+ x (* z (+ y (* a b))))
     (+ (+ (* t a) (* y z)) (* (* z a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.5e+179) {
		tmp = x + (t * a);
	} else if ((x <= -5.8e-47) || !(x <= 7.5e-19)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = ((t * a) + (y * z)) + ((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 (x <= (-5.5d+179)) then
        tmp = x + (t * a)
    else if ((x <= (-5.8d-47)) .or. (.not. (x <= 7.5d-19))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = ((t * a) + (y * z)) + ((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 (x <= -5.5e+179) {
		tmp = x + (t * a);
	} else if ((x <= -5.8e-47) || !(x <= 7.5e-19)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = ((t * a) + (y * z)) + ((z * a) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.5e+179:
		tmp = x + (t * a)
	elif (x <= -5.8e-47) or not (x <= 7.5e-19):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = ((t * a) + (y * z)) + ((z * a) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.5e+179)
		tmp = Float64(x + Float64(t * a));
	elseif ((x <= -5.8e-47) || !(x <= 7.5e-19))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(Float64(t * a) + Float64(y * z)) + Float64(Float64(z * a) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.5e+179)
		tmp = x + (t * a);
	elseif ((x <= -5.8e-47) || ~((x <= 7.5e-19)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = ((t * a) + (y * z)) + ((z * a) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.5e+179], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.8e-47], N[Not[LessEqual[x, 7.5e-19]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4999999999999998e179

   1. Initial program 90.6%

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

      1. associate-+l+ 90.6%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around 0 84.9%

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

      1. +-commutative 84.9%

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

   7. Simplified 84.9%

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

   if -5.4999999999999998e179 < x < -5.8000000000000001e-47 or 7.49999999999999957e-19 < x

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in t around 0 77.7%

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

      1. +-commutative 77.7%

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

      2. +-commutative 77.7%

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

      3. associate-*r* 81.8%

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

      4. distribute-rgt-in 84.5%

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

   7. Simplified 84.5%

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

   if -5.8000000000000001e-47 < x < 7.49999999999999957e-19

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 89.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+179}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-47} \lor \neg \left(x \leq 7.5 \cdot 10^{-19}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a + y \cdot z\right) + \left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+182} \lor \neg \left(z \leq 1.2 \cdot 10^{+158}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.6e+182) (not (<= z 1.2e+158)))
   (+ x (* z (+ y (* a b))))
   (+ (+ x (* y z)) (+ (* t a) (* a (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e+182) || !(z <= 1.2e+158)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + ((t * a) + (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) :: tmp
    if ((z <= (-7.6d+182)) .or. (.not. (z <= 1.2d+158))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (x + (y * z)) + ((t * a) + (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 tmp;
	if ((z <= -7.6e+182) || !(z <= 1.2e+158)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.6e+182) or not (z <= 1.2e+158):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.6e+182) || !(z <= 1.2e+158))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(Float64(t * a) + Float64(a * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.6e+182) || ~((z <= 1.2e+158)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (x + (y * z)) + ((t * a) + (a * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.6e+182], N[Not[LessEqual[z, 1.2e+158]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] + N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000025e182 or 1.20000000000000004e158 < z

   1. Initial program 80.4%

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

      1. associate-+l+ 80.4%

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

      2. associate-*l* 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in t around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. +-commutative 80.9%

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

      3. associate-*r* 86.8%

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

      4. distribute-rgt-in 98.3%

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

   7. Simplified 98.3%

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

   if -7.60000000000000025e182 < z < 1.20000000000000004e158

   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* 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
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+182} \lor \neg \left(z \leq 1.2 \cdot 10^{+158}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+168}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+34} \lor \neg \left(a \leq 1.7 \cdot 10^{+110}\right):\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.2e+168)
   (* t a)
   (if (or (<= a -3.2e+34) (not (<= a 1.7e+110)))
     (* (* z a) b)
     (+ x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e+168) {
		tmp = t * a;
	} else if ((a <= -3.2e+34) || !(a <= 1.7e+110)) {
		tmp = (z * a) * 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 <= (-4.2d+168)) then
        tmp = t * a
    else if ((a <= (-3.2d+34)) .or. (.not. (a <= 1.7d+110))) then
        tmp = (z * a) * 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 <= -4.2e+168) {
		tmp = t * a;
	} else if ((a <= -3.2e+34) || !(a <= 1.7e+110)) {
		tmp = (z * a) * b;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.2e+168:
		tmp = t * a
	elif (a <= -3.2e+34) or not (a <= 1.7e+110):
		tmp = (z * a) * b
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.2e+168)
		tmp = Float64(t * a);
	elseif ((a <= -3.2e+34) || !(a <= 1.7e+110))
		tmp = Float64(Float64(z * a) * 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 <= -4.2e+168)
		tmp = t * a;
	elseif ((a <= -3.2e+34) || ~((a <= 1.7e+110)))
		tmp = (z * a) * b;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.2e+168], N[(t * a), $MachinePrecision], If[Or[LessEqual[a, -3.2e+34], N[Not[LessEqual[a, 1.7e+110]], $MachinePrecision]], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.20000000000000006e168

   1. Initial program 84.6%

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

      1. associate-+l+ 84.6%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 59.2%

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

   if -4.20000000000000006e168 < a < -3.1999999999999998e34 or 1.7000000000000001e110 < a

   1. Initial program 85.0%

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

      1. associate-+l+ 85.0%

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

      2. associate-*l* 89.9%

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

   3. Simplified 89.9%

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

      1. *-commutative 89.9%

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

      2. distribute-lft-in 93.7%

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

      3. *-commutative 93.7%

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

      4. add-cube-cbrt 93.0%

         \[\leadsto \left(x + y \cdot z\right) + \left(t + z \cdot b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \]

      5. associate-*r* 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\left(t + z \cdot b\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}} \]

      6. +-commutative 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\left(z \cdot b + t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      7. fma-def 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\color{blue}{\mathsf{fma}\left(z, b, t\right)} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a} \]

      8. pow2 93.1%

         \[\leadsto \left(x + y \cdot z\right) + \left(\mathsf{fma}\left(z, b, t\right) \cdot \color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}\right) \cdot \sqrt[3]{a} \]

   6. Applied egg-rr 93.1%

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{\left(\mathsf{fma}\left(z, b, t\right) \cdot {\left(\sqrt[3]{a}\right)}^{2}\right) \cdot \sqrt[3]{a}} \]

   7. Taylor expanded in b around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-*l* 51.3%

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

   9. Simplified 51.3%

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

   if -3.1999999999999998e34 < a < 1.7000000000000001e110

   1. Initial program 97.3%

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

      1. associate-+l+ 97.3%

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

      2. associate-*l* 93.1%

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

   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 a around 0 70.1%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+168}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+34} \lor \neg \left(a \leq 1.7 \cdot 10^{+110}\right):\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+58} \lor \neg \left(a \leq 1.1 \cdot 10^{+42}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -9.5e+58) (not (<= a 1.1e+42)))
   (* a (+ t (* z b)))
   (+ x (* z (+ y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.5e+58) || !(a <= 1.1e+42)) {
		tmp = a * (t + (z * b));
	} 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 ((a <= (-9.5d+58)) .or. (.not. (a <= 1.1d+42))) then
        tmp = a * (t + (z * b))
    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 ((a <= -9.5e+58) || !(a <= 1.1e+42)) {
		tmp = a * (t + (z * b));
	} else {
		tmp = x + (z * (y + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -9.5e+58) or not (a <= 1.1e+42):
		tmp = a * (t + (z * b))
	else:
		tmp = x + (z * (y + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -9.5e+58) || !(a <= 1.1e+42))
		tmp = Float64(a * Float64(t + Float64(z * b)));
	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 ((a <= -9.5e+58) || ~((a <= 1.1e+42)))
		tmp = a * (t + (z * b));
	else
		tmp = x + (z * (y + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -9.5e+58], N[Not[LessEqual[a, 1.1e+42]], $MachinePrecision]], N[(a * N[(t + N[(z * b), $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 a < -9.5000000000000002e58 or 1.1000000000000001e42 < a

   1. Initial program 83.5%

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

      1. associate-+l+ 83.5%

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

      2. associate-*l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 82.2%

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

   if -9.5000000000000002e58 < a < 1.1000000000000001e42

   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* 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 t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. +-commutative 79.9%

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

      3. associate-*r* 85.0%

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

      4. distribute-rgt-in 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+58} \lor \neg \left(a \leq 1.1 \cdot 10^{+42}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+58} \lor \neg \left(a \leq 5.2 \cdot 10^{-45}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.7e+58) (not (<= a 5.2e-45)))
   (* 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 <= -3.7e+58) || !(a <= 5.2e-45)) {
		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 <= (-3.7d+58)) .or. (.not. (a <= 5.2d-45))) 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 <= -3.7e+58) || !(a <= 5.2e-45)) {
		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 <= -3.7e+58) or not (a <= 5.2e-45):
		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 <= -3.7e+58) || !(a <= 5.2e-45))
		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 <= -3.7e+58) || ~((a <= 5.2e-45)))
		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, -3.7e+58], N[Not[LessEqual[a, 5.2e-45]], $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 < -3.7000000000000002e58 or 5.19999999999999973e-45 < a

   1. Initial program 85.6%

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

      1. associate-+l+ 85.6%

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

      2. associate-*l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in a around inf 78.7%

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

   if -3.7000000000000002e58 < a < 5.19999999999999973e-45

   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* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around 0 76.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+58} \lor \neg \left(a \leq 5.2 \cdot 10^{-45}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+61} \lor \neg \left(y \leq 9.6 \cdot 10^{+57}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e+61) (not (<= y 9.6e+57))) (+ x (* y z)) (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+61) || !(y <= 9.6e+57)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * 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) :: tmp
    if ((y <= (-8d+61)) .or. (.not. (y <= 9.6d+57))) then
        tmp = x + (y * z)
    else
        tmp = x + (t * 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 tmp;
	if ((y <= -8e+61) || !(y <= 9.6e+57)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8e+61) or not (y <= 9.6e+57):
		tmp = x + (y * z)
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8e+61) || !(y <= 9.6e+57))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8e+61) || ~((y <= 9.6e+57)))
		tmp = x + (y * z);
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8e+61], N[Not[LessEqual[y, 9.6e+57]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999996e61 or 9.60000000000000019e57 < y

   1. Initial program 87.7%

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

      1. associate-+l+ 87.7%

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

      2. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in a around 0 67.8%

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

   if -7.9999999999999996e61 < y < 9.60000000000000019e57

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around 0 62.2%

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

      1. +-commutative 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+61} \lor \neg \left(y \leq 9.6 \cdot 10^{+57}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 60000000000000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.7e+58) x (if (<= x 60000000000000.0) (* t a) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.7e+58) {
		tmp = x;
	} else if (x <= 60000000000000.0) {
		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 <= (-4.7d+58)) then
        tmp = x
    else if (x <= 60000000000000.0d0) 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 <= -4.7e+58) {
		tmp = x;
	} else if (x <= 60000000000000.0) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.7e+58:
		tmp = x
	elif x <= 60000000000000.0:
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.7e+58)
		tmp = x;
	elseif (x <= 60000000000000.0)
		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 <= -4.7e+58)
		tmp = x;
	elseif (x <= 60000000000000.0)
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.7e+58], x, If[LessEqual[x, 60000000000000.0], N[(t * a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.69999999999999972e58 or 6e13 < x

   1. Initial program 94.4%

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

      1. associate-+l+ 94.4%

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

      2. associate-*l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in x around inf 52.0%

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

   if -4.69999999999999972e58 < x < 6e13

   1. Initial program 90.5%

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

      1. associate-+l+ 90.5%

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

      2. associate-*l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in t around inf 35.5%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 60000000000000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-+l+ 92.2%

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

   2. associate-*l* 92.0%

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

3. Simplified 92.0%

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

5. Taylor expanded in x around inf 25.6%

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

6. Final simplification 25.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.2% 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 2024027 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (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)))