Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.8% → 95.7%

Time: 10.5s

Alternatives: 13

Speedup: 0.6×

• 31.8% 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: 92.8% 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: 95.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+130} \lor \neg \left(z \leq 2.5 \cdot 10^{+67}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.6e+130) (not (<= z 2.5e+67)))
   (+ 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 <= -9.6e+130) || !(z <= 2.5e+67)) {
		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 <= (-9.6d+130)) .or. (.not. (z <= 2.5d+67))) 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 <= -9.6e+130) || !(z <= 2.5e+67)) {
		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 <= -9.6e+130) or not (z <= 2.5e+67):
		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 <= -9.6e+130) || !(z <= 2.5e+67))
		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 <= -9.6e+130) || ~((z <= 2.5e+67)))
		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, -9.6e+130], N[Not[LessEqual[z, 2.5e+67]], $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 < -9.60000000000000097e130 or 2.49999999999999988e67 < z

   1. Initial program 78.7%

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

      1. associate-+l+ 78.7%

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

      2. associate-*l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in t around 0 78.9%

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

      1. +-commutative 78.9%

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

      2. +-commutative 78.9%

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

      3. associate-*r* 89.2%

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

      4. distribute-rgt-in 96.3%

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

   7. Simplified 96.3%

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

   if -9.60000000000000097e130 < z < 2.49999999999999988e67

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+130} \lor \neg \left(z \leq 2.5 \cdot 10^{+67}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(\frac{t}{y} + z \cdot \frac{b}{y}\right) + \left(z + \frac{x}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 2e+304)
     t_1
     (* y (+ (* a (+ (/ t y) (* z (/ b y)))) (+ z (/ x y)))))))

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 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = y * ((a * ((t / y) + (z * (b / y)))) + (z + (x / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b)
    if (t_1 <= 2d+304) then
        tmp = t_1
    else
        tmp = y * ((a * ((t / y) + (z * (b / y)))) + (z + (x / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (y * z)) + (t * a)) + ((z * a) * b);
	double tmp;
	if (t_1 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = y * ((a * ((t / y) + (z * (b / y)))) + (z + (x / y)));
	}
	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 <= 2e+304:
		tmp = t_1
	else:
		tmp = y * ((a * ((t / y) + (z * (b / y)))) + (z + (x / y)))
	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 <= 2e+304)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(a * Float64(Float64(t / y) + Float64(z * Float64(b / y)))) + Float64(z + Float64(x / y))));
	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 <= 2e+304)
		tmp = t_1;
	else
		tmp = y * ((a * ((t / y) + (z * (b / y)))) + (z + (x / y)));
	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, 2e+304], t$95$1, N[(y * N[(N[(a * N[(N[(t / y), $MachinePrecision] + N[(z * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z + N[(x / y), $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)) < 1.9999999999999999e304

   1. Initial program 97.6%

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

   if 1.9999999999999999e304 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 63.3%

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

      1. associate-+l+ 63.3%

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

      2. associate-*l* 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in y around inf 76.1%

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

      1. associate-+r+ 76.1%

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

      2. +-commutative 76.1%

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

      3. associate-/l* 80.4%

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

      4. associate-/l* 82.6%

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

      5. distribute-lft-out 87.0%

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

      6. *-commutative 87.0%

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

      7. associate-/l* 91.3%

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

   7. Simplified 91.3%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(a \cdot \left(\frac{t}{y} + z \cdot \frac{b}{y}\right) + \left(z + \frac{x}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.7% 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 97.1%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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* 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in z around inf 80.0%

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

4. Final simplification 96.1%

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

Alternative 4: 40.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4200000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= y -6.6e+25)
     (* y z)
     (if (<= y -2.2e-172)
       t_1
       (if (<= y -4.9e-259)
         x
         (if (<= y 1.6e-289)
           t_1
           (if (<= y 1.4e-218) x (if (<= y 4200000.0) (* t a) (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * a) * b;
	double tmp;
	if (y <= -6.6e+25) {
		tmp = y * z;
	} else if (y <= -2.2e-172) {
		tmp = t_1;
	} else if (y <= -4.9e-259) {
		tmp = x;
	} else if (y <= 1.6e-289) {
		tmp = t_1;
	} else if (y <= 1.4e-218) {
		tmp = x;
	} else if (y <= 4200000.0) {
		tmp = t * a;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (z * a) * b
    if (y <= (-6.6d+25)) then
        tmp = y * z
    else if (y <= (-2.2d-172)) then
        tmp = t_1
    else if (y <= (-4.9d-259)) then
        tmp = x
    else if (y <= 1.6d-289) then
        tmp = t_1
    else if (y <= 1.4d-218) then
        tmp = x
    else if (y <= 4200000.0d0) then
        tmp = t * a
    else
        tmp = 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 t_1 = (z * a) * b;
	double tmp;
	if (y <= -6.6e+25) {
		tmp = y * z;
	} else if (y <= -2.2e-172) {
		tmp = t_1;
	} else if (y <= -4.9e-259) {
		tmp = x;
	} else if (y <= 1.6e-289) {
		tmp = t_1;
	} else if (y <= 1.4e-218) {
		tmp = x;
	} else if (y <= 4200000.0) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if y <= -6.6e+25:
		tmp = y * z
	elif y <= -2.2e-172:
		tmp = t_1
	elif y <= -4.9e-259:
		tmp = x
	elif y <= 1.6e-289:
		tmp = t_1
	elif y <= 1.4e-218:
		tmp = x
	elif y <= 4200000.0:
		tmp = t * a
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (y <= -6.6e+25)
		tmp = Float64(y * z);
	elseif (y <= -2.2e-172)
		tmp = t_1;
	elseif (y <= -4.9e-259)
		tmp = x;
	elseif (y <= 1.6e-289)
		tmp = t_1;
	elseif (y <= 1.4e-218)
		tmp = x;
	elseif (y <= 4200000.0)
		tmp = Float64(t * a);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * a) * b;
	tmp = 0.0;
	if (y <= -6.6e+25)
		tmp = y * z;
	elseif (y <= -2.2e-172)
		tmp = t_1;
	elseif (y <= -4.9e-259)
		tmp = x;
	elseif (y <= 1.6e-289)
		tmp = t_1;
	elseif (y <= 1.4e-218)
		tmp = x;
	elseif (y <= 4200000.0)
		tmp = t * a;
	else
		tmp = y * z;
	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[y, -6.6e+25], N[(y * z), $MachinePrecision], If[LessEqual[y, -2.2e-172], t$95$1, If[LessEqual[y, -4.9e-259], x, If[LessEqual[y, 1.6e-289], t$95$1, If[LessEqual[y, 1.4e-218], x, If[LessEqual[y, 4200000.0], N[(t * a), $MachinePrecision], N[(y * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.6000000000000002e25 or 4.2e6 < y

   1. Initial program 90.4%

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

      1. associate-+l+ 90.4%

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

      2. associate-*l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around inf 53.0%

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

      1. *-commutative 53.0%

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

   7. Simplified 53.0%

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

   if -6.6000000000000002e25 < y < -2.20000000000000009e-172 or -4.90000000000000023e-259 < y < 1.6000000000000001e-289

   1. Initial program 95.7%

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

      1. associate-+l+ 95.7%

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

      2. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in y around inf 62.0%

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

      1. associate-+r+ 62.0%

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

      2. +-commutative 62.0%

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

      3. associate-/l* 60.0%

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

      4. associate-/l* 53.7%

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

      5. distribute-lft-out 53.7%

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

      6. *-commutative 53.7%

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

      7. associate-/l* 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in t around 0 50.0%

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

      1. associate-+r+ 50.0%

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

      2. associate-/l* 43.7%

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

      3. *-commutative 43.7%

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

      4. associate-*r/ 43.7%

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

   10. Simplified 43.7%

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

   11. Taylor expanded in a around inf 36.7%

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

       1. *-commutative 36.7%

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

       2. associate-*r* 44.6%

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

       3. *-commutative 44.6%

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

   13. Simplified 44.6%

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

   if -2.20000000000000009e-172 < y < -4.90000000000000023e-259 or 1.6000000000000001e-289 < y < 1.40000000000000004e-218

   1. Initial program 97.0%

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

      1. associate-+l+ 97.0%

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

      2. associate-*l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around inf 63.8%

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

   if 1.40000000000000004e-218 < y < 4.2e6

   1. Initial program 85.8%

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

      1. associate-+l+ 85.8%

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

      2. associate-*l* 93.2%

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

   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 t around inf 45.1%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+25}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-172}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-289}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4200000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+180}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+117}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= a -1.85e+209)
     t_1
     (if (<= a -1.55e+180)
       (* t a)
       (if (<= a -4.5e+44)
         (* (* z a) b)
         (if (<= a 3.8e+117) (+ x (* y z)) 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 <= -1.85e+209) {
		tmp = t_1;
	} else if (a <= -1.55e+180) {
		tmp = t * a;
	} else if (a <= -4.5e+44) {
		tmp = (z * a) * b;
	} else if (a <= 3.8e+117) {
		tmp = x + (y * z);
	} 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 <= (-1.85d+209)) then
        tmp = t_1
    else if (a <= (-1.55d+180)) then
        tmp = t * a
    else if (a <= (-4.5d+44)) then
        tmp = (z * a) * b
    else if (a <= 3.8d+117) then
        tmp = x + (y * z)
    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 <= -1.85e+209) {
		tmp = t_1;
	} else if (a <= -1.55e+180) {
		tmp = t * a;
	} else if (a <= -4.5e+44) {
		tmp = (z * a) * b;
	} else if (a <= 3.8e+117) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if a <= -1.85e+209:
		tmp = t_1
	elif a <= -1.55e+180:
		tmp = t * a
	elif a <= -4.5e+44:
		tmp = (z * a) * b
	elif a <= 3.8e+117:
		tmp = x + (y * z)
	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 <= -1.85e+209)
		tmp = t_1;
	elseif (a <= -1.55e+180)
		tmp = Float64(t * a);
	elseif (a <= -4.5e+44)
		tmp = Float64(Float64(z * a) * b);
	elseif (a <= 3.8e+117)
		tmp = Float64(x + Float64(y * z));
	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 <= -1.85e+209)
		tmp = t_1;
	elseif (a <= -1.55e+180)
		tmp = t * a;
	elseif (a <= -4.5e+44)
		tmp = (z * a) * b;
	elseif (a <= 3.8e+117)
		tmp = x + (y * z);
	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, -1.85e+209], t$95$1, If[LessEqual[a, -1.55e+180], N[(t * a), $MachinePrecision], If[LessEqual[a, -4.5e+44], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[a, 3.8e+117], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.85e209 or 3.8000000000000002e117 < a

   1. Initial program 80.8%

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

      1. associate-+l+ 80.8%

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

      2. associate-*l* 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in y around inf 73.3%

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

      1. associate-+r+ 73.3%

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

      2. +-commutative 73.3%

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

      3. associate-/l* 76.5%

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

      4. associate-/l* 78.1%

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

      5. distribute-lft-out 80.0%

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

      6. *-commutative 80.0%

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

      7. associate-/l* 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in t around 0 61.4%

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

      1. associate-+r+ 61.4%

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

      2. associate-/l* 63.1%

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

      3. *-commutative 63.1%

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

      4. associate-*r/ 61.5%

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

   10. Simplified 61.5%

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

   11. Taylor expanded in a around inf 58.2%

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

   if -1.85e209 < a < -1.54999999999999999e180

   1. Initial program 63.6%

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

      1. associate-+l+ 63.6%

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

      2. associate-*l* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in t around inf 65.8%

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

   if -1.54999999999999999e180 < a < -4.5e44

   1. Initial program 84.9%

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

      1. associate-+l+ 84.9%

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

      2. associate-*l* 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in y around inf 75.9%

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

      1. associate-+r+ 75.9%

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

      2. +-commutative 75.9%

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

      3. associate-/l* 75.8%

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

      4. associate-/l* 75.8%

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

      5. distribute-lft-out 75.8%

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

      6. *-commutative 75.8%

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

      7. associate-/l* 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in t around 0 56.9%

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

      1. associate-+r+ 56.9%

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

      2. associate-/l* 56.9%

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

      3. *-commutative 56.9%

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

      4. associate-*r/ 56.9%

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

   10. Simplified 56.9%

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

   11. Taylor expanded in a around inf 46.3%

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

       1. *-commutative 46.3%

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

       2. associate-*r* 46.4%

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

       3. *-commutative 46.4%

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

   13. Simplified 46.4%

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

   if -4.5e44 < a < 3.8000000000000002e117

   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* 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 a around 0 73.4%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{+180}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+117}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+157} \lor \neg \left(z \leq 1.4 \cdot 10^{+108}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.8e+157) (not (<= z 1.4e+108)))
   (+ x (* z (+ y (* a b))))
   (+ (+ x (* y z)) (* b (* a (+ z (/ t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.8e+157) || !(z <= 1.4e+108)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + (b * (a * (z + (t / b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.8d+157)) .or. (.not. (z <= 1.4d+108))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = (x + (y * z)) + (b * (a * (z + (t / b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.8e+157) || !(z <= 1.4e+108)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = (x + (y * z)) + (b * (a * (z + (t / b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.8e+157) or not (z <= 1.4e+108):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = (x + (y * z)) + (b * (a * (z + (t / b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.8e+157) || !(z <= 1.4e+108))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(b * Float64(a * Float64(z + Float64(t / b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.8e+157) || ~((z <= 1.4e+108)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = (x + (y * z)) + (b * (a * (z + (t / b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.8e+157], N[Not[LessEqual[z, 1.4e+108]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * N[(z + N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8000000000000003e157 or 1.3999999999999999e108 < z

   1. Initial program 78.0%

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

      1. associate-+l+ 78.0%

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

      2. associate-*l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in t around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. +-commutative 81.4%

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

      3. associate-*r* 92.0%

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

      4. distribute-rgt-in 100.0%

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

   7. Simplified 100.0%

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

   if -9.8000000000000003e157 < z < 1.3999999999999999e108

   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* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in b around inf 89.5%

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

      1. associate-/l* 87.9%

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

      2. distribute-lft-out 88.9%

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

   7. Simplified 88.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+157} \lor \neg \left(z \leq 1.4 \cdot 10^{+108}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + b \cdot \left(a \cdot \left(z + \frac{t}{b}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+69} \lor \neg \left(x \leq 7 \cdot 10^{-84}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.9e+69) (not (<= x 7e-84)))
   (+ x (* z (+ y (* a b))))
   (+ (* (* z a) b) (+ (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.9e+69) || !(x <= 7e-84)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = ((z * a) * b) + ((y * z) + (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 ((x <= (-1.9d+69)) .or. (.not. (x <= 7d-84))) then
        tmp = x + (z * (y + (a * b)))
    else
        tmp = ((z * a) * b) + ((y * z) + (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 ((x <= -1.9e+69) || !(x <= 7e-84)) {
		tmp = x + (z * (y + (a * b)));
	} else {
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.9e+69) or not (x <= 7e-84):
		tmp = x + (z * (y + (a * b)))
	else:
		tmp = ((z * a) * b) + ((y * z) + (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.9e+69) || !(x <= 7e-84))
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	else
		tmp = Float64(Float64(Float64(z * a) * b) + Float64(Float64(y * z) + Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.9e+69) || ~((x <= 7e-84)))
		tmp = x + (z * (y + (a * b)));
	else
		tmp = ((z * a) * b) + ((y * z) + (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.9e+69], N[Not[LessEqual[x, 7e-84]], $MachinePrecision]], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000014e69 or 7.0000000000000002e-84 < x

   1. Initial program 89.8%

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

      1. associate-+l+ 89.8%

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

      2. associate-*l* 93.3%

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

   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 t around 0 83.1%

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

      1. +-commutative 83.1%

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

      2. +-commutative 83.1%

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

      3. associate-*r* 82.4%

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

      4. distribute-rgt-in 84.9%

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

   7. Simplified 84.9%

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

   if -1.90000000000000014e69 < x < 7.0000000000000002e-84

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 85.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+69} \lor \neg \left(x \leq 7 \cdot 10^{-84}\right):\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(y \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+245}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-9} \lor \neg \left(z \leq 10^{+66}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+245)
   (* (* z a) b)
   (if (or (<= z -7.6e-9) (not (<= z 1e+66))) (+ x (* y z)) (+ x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+245) {
		tmp = (z * a) * b;
	} else if ((z <= -7.6e-9) || !(z <= 1e+66)) {
		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 (z <= (-1.05d+245)) then
        tmp = (z * a) * b
    else if ((z <= (-7.6d-9)) .or. (.not. (z <= 1d+66))) 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 (z <= -1.05e+245) {
		tmp = (z * a) * b;
	} else if ((z <= -7.6e-9) || !(z <= 1e+66)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.05e+245:
		tmp = (z * a) * b
	elif (z <= -7.6e-9) or not (z <= 1e+66):
		tmp = x + (y * z)
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+245)
		tmp = Float64(Float64(z * a) * b);
	elseif ((z <= -7.6e-9) || !(z <= 1e+66))
		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 (z <= -1.05e+245)
		tmp = (z * a) * b;
	elseif ((z <= -7.6e-9) || ~((z <= 1e+66)))
		tmp = x + (y * z);
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+245], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[Or[LessEqual[z, -7.6e-9], N[Not[LessEqual[z, 1e+66]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999998e245

   1. Initial program 67.1%

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

      1. associate-+l+ 67.1%

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

      2. associate-*l* 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in y around inf 60.8%

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

      1. associate-+r+ 60.8%

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

      2. +-commutative 60.8%

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

      3. associate-/l* 69.2%

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

      4. associate-/l* 69.2%

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

      5. distribute-lft-out 69.2%

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

      6. *-commutative 69.2%

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

      7. associate-/l* 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in t around 0 69.2%

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

      1. associate-+r+ 69.2%

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

      2. associate-/l* 69.2%

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

      3. *-commutative 69.2%

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

      4. associate-*r/ 69.2%

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

   10. Simplified 69.2%

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

   11. Taylor expanded in a around inf 75.4%

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

       1. *-commutative 75.4%

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

       2. associate-*r* 75.5%

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

       3. *-commutative 75.5%

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

   13. Simplified 75.5%

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

   if -1.04999999999999998e245 < z < -7.60000000000000023e-9 or 9.99999999999999945e65 < z

   1. Initial program 85.5%

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

      1. associate-+l+ 85.5%

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

      2. associate-*l* 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in a around 0 67.7%

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

   if -7.60000000000000023e-9 < z < 9.99999999999999945e65

   1. Initial program 97.8%

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

      1. associate-+l+ 97.8%

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

      2. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around 0 70.7%

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

      1. +-commutative 70.7%

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

   7. Simplified 70.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+245}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-9} \lor \neg \left(z \leq 10^{+66}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+82} \lor \neg \left(a \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.3e+82) (not (<= a 8.5e+19)))
   (* 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 <= -2.3e+82) || !(a <= 8.5e+19)) {
		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 <= (-2.3d+82)) .or. (.not. (a <= 8.5d+19))) 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 <= -2.3e+82) || !(a <= 8.5e+19)) {
		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 <= -2.3e+82) or not (a <= 8.5e+19):
		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 <= -2.3e+82) || !(a <= 8.5e+19))
		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 <= -2.3e+82) || ~((a <= 8.5e+19)))
		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, -2.3e+82], N[Not[LessEqual[a, 8.5e+19]], $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 < -2.29999999999999988e82 or 8.5e19 < a

   1. Initial program 82.8%

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

      1. associate-+l+ 82.8%

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

      2. associate-*l* 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 a around inf 82.2%

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

   if -2.29999999999999988e82 < a < 8.5e19

   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* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in t around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. +-commutative 78.5%

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

      3. associate-*r* 86.0%

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

      4. distribute-rgt-in 87.3%

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

   7. Simplified 87.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+82} \lor \neg \left(a \leq 8.5 \cdot 10^{+19}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4200000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.5e+36)
   (* y z)
   (if (<= y 4.3e-218) x (if (<= y 4200000.0) (* t a) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.5e+36) {
		tmp = y * z;
	} else if (y <= 4.3e-218) {
		tmp = x;
	} else if (y <= 4200000.0) {
		tmp = t * a;
	} else {
		tmp = 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 (y <= (-5.5d+36)) then
        tmp = y * z
    else if (y <= 4.3d-218) then
        tmp = x
    else if (y <= 4200000.0d0) then
        tmp = t * a
    else
        tmp = 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 (y <= -5.5e+36) {
		tmp = y * z;
	} else if (y <= 4.3e-218) {
		tmp = x;
	} else if (y <= 4200000.0) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.5e+36:
		tmp = y * z
	elif y <= 4.3e-218:
		tmp = x
	elif y <= 4200000.0:
		tmp = t * a
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.5e+36)
		tmp = Float64(y * z);
	elseif (y <= 4.3e-218)
		tmp = x;
	elseif (y <= 4200000.0)
		tmp = Float64(t * a);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.5e+36)
		tmp = y * z;
	elseif (y <= 4.3e-218)
		tmp = x;
	elseif (y <= 4200000.0)
		tmp = t * a;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.5e+36], N[(y * z), $MachinePrecision], If[LessEqual[y, 4.3e-218], x, If[LessEqual[y, 4200000.0], N[(t * a), $MachinePrecision], N[(y * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000002e36 or 4.2e6 < y

   1. Initial program 90.0%

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

      1. associate-+l+ 90.0%

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

      2. associate-*l* 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 y around inf 54.2%

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

      1. *-commutative 54.2%

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

   7. Simplified 54.2%

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

   if -5.5000000000000002e36 < y < 4.3e-218

   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* 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 39.6%

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

   if 4.3e-218 < y < 4.2e6

   1. Initial program 85.8%

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

      1. associate-+l+ 85.8%

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

      2. associate-*l* 93.2%

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

   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 t around inf 45.1%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-218}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4200000:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-7} \lor \neg \left(a \leq 2.55 \cdot 10^{+19}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.85e-7) (not (<= a 2.55e+19)))
   (* 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 <= -1.85e-7) || !(a <= 2.55e+19)) {
		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 <= (-1.85d-7)) .or. (.not. (a <= 2.55d+19))) 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 <= -1.85e-7) || !(a <= 2.55e+19)) {
		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 <= -1.85e-7) or not (a <= 2.55e+19):
		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 <= -1.85e-7) || !(a <= 2.55e+19))
		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 <= -1.85e-7) || ~((a <= 2.55e+19)))
		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, -1.85e-7], N[Not[LessEqual[a, 2.55e+19]], $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 < -1.85000000000000002e-7 or 2.55e19 < a

   1. Initial program 83.0%

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

      1. associate-+l+ 83.0%

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

      2. associate-*l* 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 a around inf 79.5%

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

   if -1.85000000000000002e-7 < a < 2.55e19

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-*l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in a around 0 79.3%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{-7} \lor \neg \left(a \leq 2.55 \cdot 10^{+19}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-15} \lor \neg \left(a \leq 6.6 \cdot 10^{-94}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.6e-15) (not (<= a 6.6e-94))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.6e-15) || !(a <= 6.6e-94)) {
		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 ((a <= (-1.6d-15)) .or. (.not. (a <= 6.6d-94))) 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 ((a <= -1.6e-15) || !(a <= 6.6e-94)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.6e-15) or not (a <= 6.6e-94):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.6e-15) || !(a <= 6.6e-94))
		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 ((a <= -1.6e-15) || ~((a <= 6.6e-94)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.6e-15], N[Not[LessEqual[a, 6.6e-94]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e-15 or 6.6000000000000003e-94 < a

   1. Initial program 84.9%

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

      1. associate-+l+ 84.9%

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

      2. associate-*l* 92.0%

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

   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 t around inf 36.7%

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

   if -1.6e-15 < a < 6.6000000000000003e-94

   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* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf 41.5%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-15} \lor \neg \left(a \leq 6.6 \cdot 10^{-94}\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.6% 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 91.4%

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

   1. associate-+l+ 91.4%

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

   2. associate-*l* 91.5%

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

3. Simplified 91.5%

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

5. Taylor expanded in x around inf 25.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 97.4% 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 2024092 
(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)))