Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.2% → 99.4%

Time: 14.9s

Alternatives: 14

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: 92.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+19} \lor \neg \left(z \leq 7 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5e+19) (not (<= z 7e-12)))
   (* z (+ y (+ (* a (+ b (/ t z))) (/ x z))))
   (+ (+ 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 <= -5e+19) || !(z <= 7e-12)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} 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 <= (-5d+19)) .or. (.not. (z <= 7d-12))) then
        tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
    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 <= -5e+19) || !(z <= 7e-12)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} 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 <= -5e+19) or not (z <= 7e-12):
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
	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 <= -5e+19) || !(z <= 7e-12))
		tmp = Float64(z * Float64(y + Float64(Float64(a * Float64(b + Float64(t / z))) + Float64(x / z))));
	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 <= -5e+19) || ~((z <= 7e-12)))
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	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, -5e+19], N[Not[LessEqual[z, 7e-12]], $MachinePrecision]], N[(z * N[(y + N[(N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / z), $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 < -5e19 or 7.0000000000000001e-12 < z

   1. Initial program 81.3%

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

      1. associate-+l+ 81.3%

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

      2. associate-*l* 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in z around inf 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-+r+ 92.5%

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

      3. associate-/l* 95.8%

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

      4. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   if -5e19 < z < 7.0000000000000001e-12

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+19} \lor \neg \left(z \leq 7 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + \left(t \cdot a + a \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.8% accurate, 0.4× speedup

Math

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

FPCore

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

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 + (t / z))));
	}
	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 + (t / z))));
	}
	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 + (t / z))))
	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 * Float64(b + Float64(t / z)))));
	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 + (t / z))));
	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 * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.3%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   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* 5.3%

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

   3. Simplified 5.3%

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

   5. Taylor expanded in z around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. associate-+r+ 57.9%

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

      3. associate-/l* 78.9%

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

      4. distribute-lft-out 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 98.5%

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

Alternative 3: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot a\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+110}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-31} \lor \neg \left(a \leq 2.5 \cdot 10^{+15}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t a))))
   (if (<= a -2.6e+142)
     t_1
     (if (<= a -3.8e+110)
       (* (* z a) b)
       (if (or (<= a -6.5e-31) (not (<= a 2.5e+15))) t_1 (+ x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * a);
	double tmp;
	if (a <= -2.6e+142) {
		tmp = t_1;
	} else if (a <= -3.8e+110) {
		tmp = (z * a) * b;
	} else if ((a <= -6.5e-31) || !(a <= 2.5e+15)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x + (t * a)
    if (a <= (-2.6d+142)) then
        tmp = t_1
    else if (a <= (-3.8d+110)) then
        tmp = (z * a) * b
    else if ((a <= (-6.5d-31)) .or. (.not. (a <= 2.5d+15))) then
        tmp = t_1
    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 t_1 = x + (t * a);
	double tmp;
	if (a <= -2.6e+142) {
		tmp = t_1;
	} else if (a <= -3.8e+110) {
		tmp = (z * a) * b;
	} else if ((a <= -6.5e-31) || !(a <= 2.5e+15)) {
		tmp = t_1;
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * a)
	tmp = 0
	if a <= -2.6e+142:
		tmp = t_1
	elif a <= -3.8e+110:
		tmp = (z * a) * b
	elif (a <= -6.5e-31) or not (a <= 2.5e+15):
		tmp = t_1
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * a))
	tmp = 0.0
	if (a <= -2.6e+142)
		tmp = t_1;
	elseif (a <= -3.8e+110)
		tmp = Float64(Float64(z * a) * b);
	elseif ((a <= -6.5e-31) || !(a <= 2.5e+15))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * a);
	tmp = 0.0;
	if (a <= -2.6e+142)
		tmp = t_1;
	elseif (a <= -3.8e+110)
		tmp = (z * a) * b;
	elseif ((a <= -6.5e-31) || ~((a <= 2.5e+15)))
		tmp = t_1;
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+142], t$95$1, If[LessEqual[a, -3.8e+110], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[Or[LessEqual[a, -6.5e-31], N[Not[LessEqual[a, 2.5e+15]], $MachinePrecision]], t$95$1, N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.60000000000000021e142 or -3.79999999999999989e110 < a < -6.49999999999999967e-31 or 2.5e15 < a

   1. Initial program 82.9%

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

      1. associate-+l+ 82.9%

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

      2. associate-*l* 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in z around 0 61.4%

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

      1. +-commutative 61.4%

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

   7. Simplified 61.4%

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

   if -2.60000000000000021e142 < a < -3.79999999999999989e110

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf 61.3%

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

   4. Taylor expanded in x around inf 80.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + \left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right) + 1\right)} \]

      2. associate-+r+ 80.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \frac{y \cdot z}{x}\right)} + 1\right) \]

      3. associate-+l+ 80.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right)} \]

      4. associate-/l* 80.2%

         \[\leadsto x \cdot \left(\left(\color{blue}{a \cdot \frac{t}{x}} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      5. associate-/l* 80.3%

         \[\leadsto x \cdot \left(\left(a \cdot \frac{t}{x} + \color{blue}{a \cdot \frac{b \cdot z}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      6. distribute-lft-out 80.3%

         \[\leadsto x \cdot \left(\color{blue}{a \cdot \left(\frac{t}{x} + \frac{b \cdot z}{x}\right)} + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      7. *-commutative 80.3%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \frac{\color{blue}{z \cdot b}}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      8. associate-/l* 80.4%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \color{blue}{z \cdot \frac{b}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      9. associate-/l* 90.4%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + z \cdot \frac{b}{x}\right) + \left(\color{blue}{y \cdot \frac{z}{x}} + 1\right)\right) \]

      10. fma-define 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in b around inf 80.0%

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

      1. associate-*r* 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-*r* 80.3%

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

   9. Simplified 80.3%

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

   if -6.49999999999999967e-31 < a < 2.5e15

   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* 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 a around 0 83.2%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+142}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+110}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-31} \lor \neg \left(a \leq 2.5 \cdot 10^{+15}\right):\\ \;\;\;\;x + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.5e-32)
   (* (* z a) b)
   (if (<= z 9e-291)
     x
     (if (<= z 3.7e-122) (* t a) (if (<= z 2.4e+122) x (* a (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e-32) {
		tmp = (z * a) * b;
	} else if (z <= 9e-291) {
		tmp = x;
	} else if (z <= 3.7e-122) {
		tmp = t * a;
	} else if (z <= 2.4e+122) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-6.5d-32)) then
        tmp = (z * a) * b
    else if (z <= 9d-291) then
        tmp = x
    else if (z <= 3.7d-122) then
        tmp = t * a
    else if (z <= 2.4d+122) then
        tmp = x
    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 tmp;
	if (z <= -6.5e-32) {
		tmp = (z * a) * b;
	} else if (z <= 9e-291) {
		tmp = x;
	} else if (z <= 3.7e-122) {
		tmp = t * a;
	} else if (z <= 2.4e+122) {
		tmp = x;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.5e-32:
		tmp = (z * a) * b
	elif z <= 9e-291:
		tmp = x
	elif z <= 3.7e-122:
		tmp = t * a
	elif z <= 2.4e+122:
		tmp = x
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.5e-32)
		tmp = Float64(Float64(z * a) * b);
	elseif (z <= 9e-291)
		tmp = x;
	elseif (z <= 3.7e-122)
		tmp = Float64(t * a);
	elseif (z <= 2.4e+122)
		tmp = x;
	else
		tmp = 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 <= -6.5e-32)
		tmp = (z * a) * b;
	elseif (z <= 9e-291)
		tmp = x;
	elseif (z <= 3.7e-122)
		tmp = t * a;
	elseif (z <= 2.4e+122)
		tmp = x;
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.5e-32], N[(N[(z * a), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[z, 9e-291], x, If[LessEqual[z, 3.7e-122], N[(t * a), $MachinePrecision], If[LessEqual[z, 2.4e+122], x, N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.49999999999999988e-32

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 77.7%

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

   4. Taylor expanded in x around inf 64.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + \left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 64.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right) + 1\right)} \]

      2. associate-+r+ 64.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \frac{y \cdot z}{x}\right)} + 1\right) \]

      3. associate-+l+ 64.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right)} \]

      4. associate-/l* 62.7%

         \[\leadsto x \cdot \left(\left(\color{blue}{a \cdot \frac{t}{x}} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      5. associate-/l* 65.7%

         \[\leadsto x \cdot \left(\left(a \cdot \frac{t}{x} + \color{blue}{a \cdot \frac{b \cdot z}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      6. distribute-lft-out 70.2%

         \[\leadsto x \cdot \left(\color{blue}{a \cdot \left(\frac{t}{x} + \frac{b \cdot z}{x}\right)} + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      7. *-commutative 70.2%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \frac{\color{blue}{z \cdot b}}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      8. associate-/l* 74.5%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \color{blue}{z \cdot \frac{b}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      9. associate-/l* 71.6%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + z \cdot \frac{b}{x}\right) + \left(\color{blue}{y \cdot \frac{z}{x}} + 1\right)\right) \]

      10. fma-define 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in b around inf 45.6%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

      3. associate-*r* 45.6%

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

   9. Simplified 45.6%

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

   if -6.49999999999999988e-32 < z < 8.99999999999999948e-291 or 3.6999999999999997e-122 < z < 2.4000000000000002e122

   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* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 49.1%

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

   if 8.99999999999999948e-291 < z < 3.6999999999999997e-122

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 89.8%

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

   4. Taylor expanded in t around inf 57.0%

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

   if 2.4000000000000002e122 < z

   1. Initial program 62.3%

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

   3. Taylor expanded in y around inf 56.7%

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

   4. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + \left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right) + 1\right)} \]

      2. associate-+r+ 62.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \frac{y \cdot z}{x}\right)} + 1\right) \]

      3. associate-+l+ 62.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right)} \]

      4. associate-/l* 65.0%

         \[\leadsto x \cdot \left(\left(\color{blue}{a \cdot \frac{t}{x}} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      5. associate-/l* 62.1%

         \[\leadsto x \cdot \left(\left(a \cdot \frac{t}{x} + \color{blue}{a \cdot \frac{b \cdot z}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      6. distribute-lft-out 68.0%

         \[\leadsto x \cdot \left(\color{blue}{a \cdot \left(\frac{t}{x} + \frac{b \cdot z}{x}\right)} + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      7. *-commutative 68.0%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \frac{\color{blue}{z \cdot b}}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      8. associate-/l* 68.1%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \color{blue}{z \cdot \frac{b}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      9. associate-/l* 79.8%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + z \cdot \frac{b}{x}\right) + \left(\color{blue}{y \cdot \frac{z}{x}} + 1\right)\right) \]

      10. fma-define 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in b around inf 57.1%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-122}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= z -8e-31)
     t_1
     (if (<= z 1.45e-289)
       x
       (if (<= z 3.9e-122) (* t a) (if (<= z 2.4e+122) x 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 (z <= -8e-31) {
		tmp = t_1;
	} else if (z <= 1.45e-289) {
		tmp = x;
	} else if (z <= 3.9e-122) {
		tmp = t * a;
	} else if (z <= 2.4e+122) {
		tmp = 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 = a * (z * b)
    if (z <= (-8d-31)) then
        tmp = t_1
    else if (z <= 1.45d-289) then
        tmp = x
    else if (z <= 3.9d-122) then
        tmp = t * a
    else if (z <= 2.4d+122) then
        tmp = 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 = a * (z * b);
	double tmp;
	if (z <= -8e-31) {
		tmp = t_1;
	} else if (z <= 1.45e-289) {
		tmp = x;
	} else if (z <= 3.9e-122) {
		tmp = t * a;
	} else if (z <= 2.4e+122) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if z <= -8e-31:
		tmp = t_1
	elif z <= 1.45e-289:
		tmp = x
	elif z <= 3.9e-122:
		tmp = t * a
	elif z <= 2.4e+122:
		tmp = x
	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 (z <= -8e-31)
		tmp = t_1;
	elseif (z <= 1.45e-289)
		tmp = x;
	elseif (z <= 3.9e-122)
		tmp = Float64(t * a);
	elseif (z <= 2.4e+122)
		tmp = x;
	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 (z <= -8e-31)
		tmp = t_1;
	elseif (z <= 1.45e-289)
		tmp = x;
	elseif (z <= 3.9e-122)
		tmp = t * a;
	elseif (z <= 2.4e+122)
		tmp = x;
	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[z, -8e-31], t$95$1, If[LessEqual[z, 1.45e-289], x, If[LessEqual[z, 3.9e-122], N[(t * a), $MachinePrecision], If[LessEqual[z, 2.4e+122], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.000000000000001e-31 or 2.4000000000000002e122 < z

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 70.6%

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

   4. Taylor expanded in x around inf 63.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + \left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 63.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right) + 1\right)} \]

      2. associate-+r+ 63.4%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \frac{y \cdot z}{x}\right)} + 1\right) \]

      3. associate-+l+ 63.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right)} \]

      4. associate-/l* 63.4%

         \[\leadsto x \cdot \left(\left(\color{blue}{a \cdot \frac{t}{x}} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      5. associate-/l* 64.5%

         \[\leadsto x \cdot \left(\left(a \cdot \frac{t}{x} + \color{blue}{a \cdot \frac{b \cdot z}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      6. distribute-lft-out 69.5%

         \[\leadsto x \cdot \left(\color{blue}{a \cdot \left(\frac{t}{x} + \frac{b \cdot z}{x}\right)} + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      7. *-commutative 69.5%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \frac{\color{blue}{z \cdot b}}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      8. associate-/l* 72.3%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \color{blue}{z \cdot \frac{b}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      9. associate-/l* 74.4%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + z \cdot \frac{b}{x}\right) + \left(\color{blue}{y \cdot \frac{z}{x}} + 1\right)\right) \]

      10. fma-define 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in b around inf 49.5%

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

   if -8.000000000000001e-31 < z < 1.45000000000000003e-289 or 3.8999999999999999e-122 < z < 2.4000000000000002e122

   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* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 49.1%

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

   if 1.45000000000000003e-289 < z < 3.8999999999999999e-122

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 89.8%

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

   4. Taylor expanded in t around inf 57.0%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-122}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-59} \lor \neg \left(z \leq 5.5 \cdot 10^{-82}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e-59) (not (<= z 5.5e-82)))
   (* z (+ y (+ (* a (+ b (/ t z))) (/ x z))))
   (+ (+ x (* y z)) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.5e-59) || !(z <= 5.5e-82)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (x + (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 ((z <= (-5.5d-59)) .or. (.not. (z <= 5.5d-82))) then
        tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
    else
        tmp = (x + (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 ((z <= -5.5e-59) || !(z <= 5.5e-82)) {
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	} else {
		tmp = (x + (y * z)) + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.5e-59) or not (z <= 5.5e-82):
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)))
	else:
		tmp = (x + (y * z)) + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.5e-59) || !(z <= 5.5e-82))
		tmp = Float64(z * Float64(y + Float64(Float64(a * Float64(b + Float64(t / z))) + Float64(x / z))));
	else
		tmp = Float64(Float64(x + 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 ((z <= -5.5e-59) || ~((z <= 5.5e-82)))
		tmp = z * (y + ((a * (b + (t / z))) + (x / z)));
	else
		tmp = (x + (y * z)) + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.5e-59], N[Not[LessEqual[z, 5.5e-82]], $MachinePrecision]], N[(z * N[(y + N[(N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000014e-59 or 5.4999999999999998e-82 < z

   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* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around inf 91.4%

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

      1. +-commutative 91.4%

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

      2. associate-+r+ 91.4%

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

      3. associate-/l* 94.0%

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

      4. distribute-lft-out 97.3%

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

   7. Simplified 97.3%

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

   if -5.50000000000000014e-59 < z < 5.4999999999999998e-82

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 94.0%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-59} \lor \neg \left(z \leq 5.5 \cdot 10^{-82}\right):\\ \;\;\;\;z \cdot \left(y + \left(a \cdot \left(b + \frac{t}{z}\right) + \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{elif}\;z \leq 1350000000:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.45e-12)
   (* z (+ y (* a (+ b (/ t z)))))
   (if (<= z 1350000000.0)
     (+ (+ x (* y z)) (* t a))
     (* z (+ y (+ (/ x z) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.45e-12) {
		tmp = z * (y + (a * (b + (t / z))));
	} else if (z <= 1350000000.0) {
		tmp = (x + (y * z)) + (t * a);
	} else {
		tmp = z * (y + ((x / z) + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.45d-12)) then
        tmp = z * (y + (a * (b + (t / z))))
    else if (z <= 1350000000.0d0) then
        tmp = (x + (y * z)) + (t * a)
    else
        tmp = z * (y + ((x / z) + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.45e-12) {
		tmp = z * (y + (a * (b + (t / z))));
	} else if (z <= 1350000000.0) {
		tmp = (x + (y * z)) + (t * a);
	} else {
		tmp = z * (y + ((x / z) + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.45e-12:
		tmp = z * (y + (a * (b + (t / z))))
	elif z <= 1350000000.0:
		tmp = (x + (y * z)) + (t * a)
	else:
		tmp = z * (y + ((x / z) + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.45e-12)
		tmp = Float64(z * Float64(y + Float64(a * Float64(b + Float64(t / z)))));
	elseif (z <= 1350000000.0)
		tmp = Float64(Float64(x + Float64(y * z)) + Float64(t * a));
	else
		tmp = Float64(z * Float64(y + Float64(Float64(x / z) + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.45e-12)
		tmp = z * (y + (a * (b + (t / z))));
	elseif (z <= 1350000000.0)
		tmp = (x + (y * z)) + (t * a);
	else
		tmp = z * (y + ((x / z) + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.45e-12], N[(z * N[(y + N[(a * N[(b + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1350000000.0], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision], N[(z * N[(y + N[(N[(x / z), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.45e-12

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. associate-*l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around inf 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-+r+ 95.1%

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

      3. associate-/l* 96.7%

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

      4. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 90.8%

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

   if -3.45e-12 < z < 1.35e9

   1. Initial program 99.2%

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

      1. associate-+l+ 99.2%

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

      2. associate-*l* 99.2%

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

   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 t around inf 90.0%

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

   if 1.35e9 < z

   1. Initial program 77.9%

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

      1. associate-+l+ 77.9%

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

      2. associate-*l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in z around inf 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-+r+ 93.0%

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

      3. associate-/l* 98.2%

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

      4. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 94.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(y + a \cdot \left(b + \frac{t}{z}\right)\right)\\ \mathbf{elif}\;z \leq 1350000000:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y + \left(\frac{x}{z} + a \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot a\right) \cdot b\\ \mathbf{if}\;a \leq -5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+36}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+129}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z a) b)))
   (if (<= a -5e+108)
     t_1
     (if (<= a -9.2e+36) (* t a) (if (<= a 4.6e+129) (+ x (* y z)) t_1)))))

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 <= -5e+108) {
		tmp = t_1;
	} else if (a <= -9.2e+36) {
		tmp = t * a;
	} else if (a <= 4.6e+129) {
		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 = (z * a) * b
    if (a <= (-5d+108)) then
        tmp = t_1
    else if (a <= (-9.2d+36)) then
        tmp = t * a
    else if (a <= 4.6d+129) 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 = (z * a) * b;
	double tmp;
	if (a <= -5e+108) {
		tmp = t_1;
	} else if (a <= -9.2e+36) {
		tmp = t * a;
	} else if (a <= 4.6e+129) {
		tmp = x + (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * a) * b
	tmp = 0
	if a <= -5e+108:
		tmp = t_1
	elif a <= -9.2e+36:
		tmp = t * a
	elif a <= 4.6e+129:
		tmp = x + (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * a) * b)
	tmp = 0.0
	if (a <= -5e+108)
		tmp = t_1;
	elseif (a <= -9.2e+36)
		tmp = Float64(t * a);
	elseif (a <= 4.6e+129)
		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 = (z * a) * b;
	tmp = 0.0;
	if (a <= -5e+108)
		tmp = t_1;
	elseif (a <= -9.2e+36)
		tmp = t * a;
	elseif (a <= 4.6e+129)
		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[(N[(z * a), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[a, -5e+108], t$95$1, If[LessEqual[a, -9.2e+36], N[(t * a), $MachinePrecision], If[LessEqual[a, 4.6e+129], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.99999999999999991e108 or 4.59999999999999981e129 < a

   1. Initial program 78.5%

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

   3. Taylor expanded in y around inf 65.1%

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

   4. Taylor expanded in x around inf 67.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + \left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \left(\frac{a \cdot \left(b \cdot z\right)}{x} + \frac{y \cdot z}{x}\right)\right) + 1\right)} \]

      2. associate-+r+ 67.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \frac{y \cdot z}{x}\right)} + 1\right) \]

      3. associate-+l+ 67.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(\frac{a \cdot t}{x} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right)} \]

      4. associate-/l* 67.1%

         \[\leadsto x \cdot \left(\left(\color{blue}{a \cdot \frac{t}{x}} + \frac{a \cdot \left(b \cdot z\right)}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      5. associate-/l* 69.7%

         \[\leadsto x \cdot \left(\left(a \cdot \frac{t}{x} + \color{blue}{a \cdot \frac{b \cdot z}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      6. distribute-lft-out 77.4%

         \[\leadsto x \cdot \left(\color{blue}{a \cdot \left(\frac{t}{x} + \frac{b \cdot z}{x}\right)} + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      7. *-commutative 77.4%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \frac{\color{blue}{z \cdot b}}{x}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      8. associate-/l* 76.1%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + \color{blue}{z \cdot \frac{b}{x}}\right) + \left(\frac{y \cdot z}{x} + 1\right)\right) \]

      9. associate-/l* 82.5%

         \[\leadsto x \cdot \left(a \cdot \left(\frac{t}{x} + z \cdot \frac{b}{x}\right) + \left(\color{blue}{y \cdot \frac{z}{x}} + 1\right)\right) \]

      10. fma-define 82.5%

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

   6. Simplified 82.5%

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

   7. Taylor expanded in b around inf 53.8%

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

      1. associate-*r* 53.2%

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

      2. *-commutative 53.2%

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

      3. associate-*r* 55.1%

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

   9. Simplified 55.1%

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

   if -4.99999999999999991e108 < a < -9.19999999999999986e36

   1. Initial program 83.7%

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

   3. Taylor expanded in y around inf 73.0%

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

   4. Taylor expanded in t around inf 65.3%

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

   if -9.19999999999999986e36 < a < 4.59999999999999981e129

   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* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in a around 0 74.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+108}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{+36}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+129}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+59} \lor \neg \left(a \leq 9.8 \cdot 10^{+14}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -9.5e+59) (not (<= a 9.8e+14)))
   (+ x (* a (+ t (* z b))))
   (+ (+ x (* y z)) (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -9.5e+59) || !(a <= 9.8e+14)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (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 ((a <= (-9.5d+59)) .or. (.not. (a <= 9.8d+14))) then
        tmp = x + (a * (t + (z * b)))
    else
        tmp = (x + (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 ((a <= -9.5e+59) || !(a <= 9.8e+14)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = (x + (y * z)) + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -9.5e+59) or not (a <= 9.8e+14):
		tmp = x + (a * (t + (z * b)))
	else:
		tmp = (x + (y * z)) + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -9.5e+59) || !(a <= 9.8e+14))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(Float64(x + 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 ((a <= -9.5e+59) || ~((a <= 9.8e+14)))
		tmp = x + (a * (t + (z * b)));
	else
		tmp = (x + (y * z)) + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -9.5e+59], N[Not[LessEqual[a, 9.8e+14]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -9.50000000000000023e59 or 9.8e14 < a

   1. Initial program 80.0%

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

      1. associate-+l+ 80.0%

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

      2. +-commutative 80.0%

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

      3. fma-define 80.1%

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

      4. associate-*l* 83.7%

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

      5. *-commutative 83.7%

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

      6. *-commutative 83.7%

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

      7. distribute-rgt-out 92.3%

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

      8. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around 0 95.3%

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

   if -9.50000000000000023e59 < a < 9.8e14

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. associate-*l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 89.8%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+59} \lor \neg \left(a \leq 9.8 \cdot 10^{+14}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-86} \lor \neg \left(a \leq 3.2 \cdot 10^{-51}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.7e-86) (not (<= a 3.2e-51)))
   (+ x (* 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 <= -2.7e-86) || !(a <= 3.2e-51)) {
		tmp = x + (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 <= (-2.7d-86)) .or. (.not. (a <= 3.2d-51))) then
        tmp = x + (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 <= -2.7e-86) || !(a <= 3.2e-51)) {
		tmp = x + (a * (t + (z * b)));
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.7e-86) or not (a <= 3.2e-51):
		tmp = x + (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 <= -2.7e-86) || !(a <= 3.2e-51))
		tmp = Float64(x + 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 <= -2.7e-86) || ~((a <= 3.2e-51)))
		tmp = x + (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, -2.7e-86], N[Not[LessEqual[a, 3.2e-51]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.69999999999999992e-86 or 3.2e-51 < a

   1. Initial program 85.9%

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

      1. associate-+l+ 85.9%

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

      2. +-commutative 85.9%

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

      3. fma-define 85.9%

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

      4. associate-*l* 88.4%

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

      5. *-commutative 88.4%

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

      6. *-commutative 88.4%

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

      7. distribute-rgt-out 94.2%

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

      8. *-commutative 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 88.6%

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

   if -2.69999999999999992e-86 < a < 3.2e-51

   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* 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 a around 0 90.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-86} \lor \neg \left(a \leq 3.2 \cdot 10^{-51}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-257}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 880000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.2e+34)
   x
   (if (<= x -1.62e-257) (* t a) (if (<= x 880000000000.0) (* y z) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.2e+34) {
		tmp = x;
	} else if (x <= -1.62e-257) {
		tmp = t * a;
	} else if (x <= 880000000000.0) {
		tmp = y * z;
	} 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 <= (-5.2d+34)) then
        tmp = x
    else if (x <= (-1.62d-257)) then
        tmp = t * a
    else if (x <= 880000000000.0d0) then
        tmp = y * z
    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 <= -5.2e+34) {
		tmp = x;
	} else if (x <= -1.62e-257) {
		tmp = t * a;
	} else if (x <= 880000000000.0) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.2e+34:
		tmp = x
	elif x <= -1.62e-257:
		tmp = t * a
	elif x <= 880000000000.0:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.2e+34)
		tmp = x;
	elseif (x <= -1.62e-257)
		tmp = Float64(t * a);
	elseif (x <= 880000000000.0)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.2e+34)
		tmp = x;
	elseif (x <= -1.62e-257)
		tmp = t * a;
	elseif (x <= 880000000000.0)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.2e+34], x, If[LessEqual[x, -1.62e-257], N[(t * a), $MachinePrecision], If[LessEqual[x, 880000000000.0], N[(y * z), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.19999999999999995e34 or 8.8e11 < x

   1. Initial program 89.6%

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

      1. associate-+l+ 89.6%

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

      2. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 51.6%

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

   if -5.19999999999999995e34 < x < -1.6200000000000001e-257

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 94.5%

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

   4. Taylor expanded in t around inf 43.6%

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

   if -1.6200000000000001e-257 < x < 8.8e11

   1. Initial program 90.8%

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

      1. associate-+l+ 90.8%

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

      2. associate-*l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 41.6%

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

      1. *-commutative 41.6%

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

   7. Simplified 41.6%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-257}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;x \leq 880000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-40} \lor \neg \left(a \leq 1.2 \cdot 10^{-38}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -5.6e-40) (not (<= a 1.2e-38)))
   (* 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 <= -5.6e-40) || !(a <= 1.2e-38)) {
		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 <= (-5.6d-40)) .or. (.not. (a <= 1.2d-38))) 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 <= -5.6e-40) || !(a <= 1.2e-38)) {
		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 <= -5.6e-40) or not (a <= 1.2e-38):
		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 <= -5.6e-40) || !(a <= 1.2e-38))
		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 <= -5.6e-40) || ~((a <= 1.2e-38)))
		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, -5.6e-40], N[Not[LessEqual[a, 1.2e-38]], $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 < -5.5999999999999999e-40 or 1.20000000000000011e-38 < a

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 75.5%

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

   4. Taylor expanded in a around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. *-commutative 75.8%

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

   6. Simplified 75.8%

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

   if -5.5999999999999999e-40 < a < 1.20000000000000011e-38

   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* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around 0 88.2%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-40} \lor \neg \left(a \leq 1.2 \cdot 10^{-38}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+73} \lor \neg \left(t \leq 13.6\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7e+73) (not (<= t 13.6))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7e+73) || !(t <= 13.6)) {
		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 ((t <= (-7d+73)) .or. (.not. (t <= 13.6d0))) 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 ((t <= -7e+73) || !(t <= 13.6)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7e+73) or not (t <= 13.6):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7e+73) || !(t <= 13.6))
		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 ((t <= -7e+73) || ~((t <= 13.6)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7e+73], N[Not[LessEqual[t, 13.6]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000004e73 or 13.5999999999999996 < t

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 77.8%

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

   4. Taylor expanded in t around inf 53.4%

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

   if -7.00000000000000004e73 < t < 13.5999999999999996

   1. Initial program 94.7%

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

      1. associate-+l+ 94.7%

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

      2. associate-*l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around inf 40.7%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+73} \lor \neg \left(t \leq 13.6\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.1% 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 91.0%

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

   1. associate-+l+ 91.0%

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

   2. associate-*l* 89.2%

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

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 x around inf 31.8%

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

Developer target: 97.1% 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 2024110 
(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)))