Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 91.8% → 96.9%

Time: 8.5s

Alternatives: 14

Speedup: 0.8×

• 33.3% 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: 91.8% 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: 96.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (y * z)) + (t * a)) + (b * (z * a));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * (a + ((x + (z * (y + (a * b)))) / t));
	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[(b * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(a + N[(N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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 99.2%

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

   3. Taylor expanded in t around -inf 50.0%

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

      1. associate-*r* 50.0%

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

      2. mul-1-neg 50.0%

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

      3. distribute-lft-out 50.0%

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

      4. +-commutative 50.0%

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

      5. associate-*r* 50.0%

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

      6. distribute-rgt-in 81.3%

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

   5. Simplified 81.3%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(-1 \cdot \left(a + \frac{z \cdot \left(a \cdot b + y\right) + x}{t}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

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

Alternative 2: 96.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 44.3%

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

      1. +-commutative 44.3%

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

      2. associate-*r* 44.3%

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

      3. distribute-rgt-in 75.5%

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

   5. Simplified 75.5%

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

4. Final simplification 97.7%

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

Alternative 3: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+159} \lor \neg \left(z \leq 1.5 \cdot 10^{+256}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e+108)
   (* a (* z b))
   (if (<= z 1.7e-45)
     (+ x (* t a))
     (if (or (<= z 1.9e+159) (not (<= z 1.5e+256)))
       (+ x (* y z))
       (* z (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+108) {
		tmp = a * (z * b);
	} else if (z <= 1.7e-45) {
		tmp = x + (t * a);
	} else if ((z <= 1.9e+159) || !(z <= 1.5e+256)) {
		tmp = x + (y * z);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.2d+108)) then
        tmp = a * (z * b)
    else if (z <= 1.7d-45) then
        tmp = x + (t * a)
    else if ((z <= 1.9d+159) .or. (.not. (z <= 1.5d+256))) then
        tmp = x + (y * z)
    else
        tmp = z * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+108) {
		tmp = a * (z * b);
	} else if (z <= 1.7e-45) {
		tmp = x + (t * a);
	} else if ((z <= 1.9e+159) || !(z <= 1.5e+256)) {
		tmp = x + (y * z);
	} else {
		tmp = z * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.2e+108:
		tmp = a * (z * b)
	elif z <= 1.7e-45:
		tmp = x + (t * a)
	elif (z <= 1.9e+159) or not (z <= 1.5e+256):
		tmp = x + (y * z)
	else:
		tmp = z * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e+108)
		tmp = Float64(a * Float64(z * b));
	elseif (z <= 1.7e-45)
		tmp = Float64(x + Float64(t * a));
	elseif ((z <= 1.9e+159) || !(z <= 1.5e+256))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(z * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.2e+108)
		tmp = a * (z * b);
	elseif (z <= 1.7e-45)
		tmp = x + (t * a);
	elseif ((z <= 1.9e+159) || ~((z <= 1.5e+256)))
		tmp = x + (y * z);
	else
		tmp = z * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e+108], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-45], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.9e+159], N[Not[LessEqual[z, 1.5e+256]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.20000000000000019e108

   1. Initial program 84.9%

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

   3. Taylor expanded in z around inf 78.4%

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

      1. +-commutative 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in a around inf 59.1%

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

   if -4.20000000000000019e108 < z < 1.70000000000000002e-45

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 75.2%

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

      1. +-commutative 75.2%

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

   5. Simplified 75.2%

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

   if 1.70000000000000002e-45 < z < 1.89999999999999983e159 or 1.5e256 < z

   1. Initial program 88.6%

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

   3. Taylor expanded in a around 0 62.7%

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

   if 1.89999999999999983e159 < z < 1.5e256

   1. Initial program 67.0%

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

   3. Taylor expanded in z around inf 83.4%

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

      1. +-commutative 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in a around inf 56.8%

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

      1. associate-*r* 61.9%

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

      2. *-commutative 61.9%

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

   8. Simplified 61.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-45}:\\ \;\;\;\;x + t \cdot a\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+159} \lor \neg \left(z \leq 1.5 \cdot 10^{+256}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot z\\ \mathbf{if}\;t \leq -6.7 \cdot 10^{+173}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y z))))
   (if (<= t -6.7e+173)
     (* t a)
     (if (<= t -1.32e+94)
       t_1
       (if (<= t -3.8e+67) (* a (* z b)) (if (<= t 1.7e+134) t_1 (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (t <= -6.7e+173) {
		tmp = t * a;
	} else if (t <= -1.32e+94) {
		tmp = t_1;
	} else if (t <= -3.8e+67) {
		tmp = a * (z * b);
	} else if (t <= 1.7e+134) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * z)
    if (t <= (-6.7d+173)) then
        tmp = t * a
    else if (t <= (-1.32d+94)) then
        tmp = t_1
    else if (t <= (-3.8d+67)) then
        tmp = a * (z * b)
    else if (t <= 1.7d+134) then
        tmp = t_1
    else
        tmp = t * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * z);
	double tmp;
	if (t <= -6.7e+173) {
		tmp = t * a;
	} else if (t <= -1.32e+94) {
		tmp = t_1;
	} else if (t <= -3.8e+67) {
		tmp = a * (z * b);
	} else if (t <= 1.7e+134) {
		tmp = t_1;
	} else {
		tmp = t * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * z)
	tmp = 0
	if t <= -6.7e+173:
		tmp = t * a
	elif t <= -1.32e+94:
		tmp = t_1
	elif t <= -3.8e+67:
		tmp = a * (z * b)
	elif t <= 1.7e+134:
		tmp = t_1
	else:
		tmp = t * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * z))
	tmp = 0.0
	if (t <= -6.7e+173)
		tmp = Float64(t * a);
	elseif (t <= -1.32e+94)
		tmp = t_1;
	elseif (t <= -3.8e+67)
		tmp = Float64(a * Float64(z * b));
	elseif (t <= 1.7e+134)
		tmp = t_1;
	else
		tmp = Float64(t * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * z);
	tmp = 0.0;
	if (t <= -6.7e+173)
		tmp = t * a;
	elseif (t <= -1.32e+94)
		tmp = t_1;
	elseif (t <= -3.8e+67)
		tmp = a * (z * b);
	elseif (t <= 1.7e+134)
		tmp = t_1;
	else
		tmp = t * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.7e+173], N[(t * a), $MachinePrecision], If[LessEqual[t, -1.32e+94], t$95$1, If[LessEqual[t, -3.8e+67], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+134], t$95$1, N[(t * a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7000000000000002e173 or 1.70000000000000009e134 < t

   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 t around -inf 93.0%

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

      1. associate-*r* 93.0%

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

      2. mul-1-neg 93.0%

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

      3. distribute-lft-out 93.0%

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

      4. +-commutative 93.0%

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

      5. associate-*r* 88.8%

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

      6. distribute-rgt-in 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in t around inf 68.2%

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

   if -6.7000000000000002e173 < t < -1.32000000000000003e94 or -3.8000000000000002e67 < t < 1.70000000000000009e134

   1. Initial program 93.3%

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

   3. Taylor expanded in a around 0 61.9%

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

   if -1.32000000000000003e94 < t < -3.8000000000000002e67

   1. Initial program 86.5%

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

   3. Taylor expanded in z around inf 71.6%

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

      1. +-commutative 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in a around inf 71.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.7 \cdot 10^{+173}:\\ \;\;\;\;t \cdot a\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+134}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.4e+44)
   (* b (* z a))
   (if (<= b -1.76e-43)
     (* y z)
     (if (<= b 1.42e-188) x (if (<= b 5e-8) (* t a) (* a (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e+44) {
		tmp = b * (z * a);
	} else if (b <= -1.76e-43) {
		tmp = y * z;
	} else if (b <= 1.42e-188) {
		tmp = x;
	} else if (b <= 5e-8) {
		tmp = t * a;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.4d+44)) then
        tmp = b * (z * a)
    else if (b <= (-1.76d-43)) then
        tmp = y * z
    else if (b <= 1.42d-188) then
        tmp = x
    else if (b <= 5d-8) then
        tmp = t * a
    else
        tmp = a * (z * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e+44) {
		tmp = b * (z * a);
	} else if (b <= -1.76e-43) {
		tmp = y * z;
	} else if (b <= 1.42e-188) {
		tmp = x;
	} else if (b <= 5e-8) {
		tmp = t * a;
	} else {
		tmp = a * (z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.4e+44:
		tmp = b * (z * a)
	elif b <= -1.76e-43:
		tmp = y * z
	elif b <= 1.42e-188:
		tmp = x
	elif b <= 5e-8:
		tmp = t * a
	else:
		tmp = a * (z * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.4e+44)
		tmp = Float64(b * Float64(z * a));
	elseif (b <= -1.76e-43)
		tmp = Float64(y * z);
	elseif (b <= 1.42e-188)
		tmp = x;
	elseif (b <= 5e-8)
		tmp = Float64(t * a);
	else
		tmp = Float64(a * Float64(z * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.4e+44)
		tmp = b * (z * a);
	elseif (b <= -1.76e-43)
		tmp = y * z;
	elseif (b <= 1.42e-188)
		tmp = x;
	elseif (b <= 5e-8)
		tmp = t * a;
	else
		tmp = a * (z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.4e+44], N[(b * N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.76e-43], N[(y * z), $MachinePrecision], If[LessEqual[b, 1.42e-188], x, If[LessEqual[b, 5e-8], N[(t * a), $MachinePrecision], N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.4e44

   1. Initial program 88.4%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. +-commutative 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in a around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. associate-*r* 54.0%

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

   8. Simplified 54.0%

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

   if -3.4e44 < b < -1.7600000000000001e-43

   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 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -1.7600000000000001e-43 < b < 1.4200000000000001e-188

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 46.3%

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

   if 1.4200000000000001e-188 < b < 4.9999999999999998e-8

   1. Initial program 91.1%

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

   3. Taylor expanded in t around -inf 84.9%

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

      1. associate-*r* 84.9%

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

      2. mul-1-neg 84.9%

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

      3. distribute-lft-out 84.9%

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

      4. +-commutative 84.9%

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

      5. associate-*r* 84.9%

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

      6. distribute-rgt-in 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in t around inf 49.2%

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

   if 4.9999999999999998e-8 < b

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 50.3%

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

      1. +-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in a around inf 45.4%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(z \cdot a\right)\\ \mathbf{elif}\;b \leq -1.76 \cdot 10^{-43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(z \cdot b\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-40}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-8}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* z b))))
   (if (<= b -9.2e+44)
     t_1
     (if (<= b -1.15e-40)
       (* y z)
       (if (<= b 2.65e-188) x (if (<= b 1.35e-8) (* t a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (b <= -9.2e+44) {
		tmp = t_1;
	} else if (b <= -1.15e-40) {
		tmp = y * z;
	} else if (b <= 2.65e-188) {
		tmp = x;
	} else if (b <= 1.35e-8) {
		tmp = t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (z * b)
    if (b <= (-9.2d+44)) then
        tmp = t_1
    else if (b <= (-1.15d-40)) then
        tmp = y * z
    else if (b <= 2.65d-188) then
        tmp = x
    else if (b <= 1.35d-8) then
        tmp = t * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (z * b);
	double tmp;
	if (b <= -9.2e+44) {
		tmp = t_1;
	} else if (b <= -1.15e-40) {
		tmp = y * z;
	} else if (b <= 2.65e-188) {
		tmp = x;
	} else if (b <= 1.35e-8) {
		tmp = t * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (z * b)
	tmp = 0
	if b <= -9.2e+44:
		tmp = t_1
	elif b <= -1.15e-40:
		tmp = y * z
	elif b <= 2.65e-188:
		tmp = x
	elif b <= 1.35e-8:
		tmp = t * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(z * b))
	tmp = 0.0
	if (b <= -9.2e+44)
		tmp = t_1;
	elseif (b <= -1.15e-40)
		tmp = Float64(y * z);
	elseif (b <= 2.65e-188)
		tmp = x;
	elseif (b <= 1.35e-8)
		tmp = Float64(t * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (z * b);
	tmp = 0.0;
	if (b <= -9.2e+44)
		tmp = t_1;
	elseif (b <= -1.15e-40)
		tmp = y * z;
	elseif (b <= 2.65e-188)
		tmp = x;
	elseif (b <= 1.35e-8)
		tmp = t * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+44], t$95$1, If[LessEqual[b, -1.15e-40], N[(y * z), $MachinePrecision], If[LessEqual[b, 2.65e-188], x, If[LessEqual[b, 1.35e-8], N[(t * a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.20000000000000018e44 or 1.35000000000000001e-8 < b

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 57.1%

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

      1. +-commutative 57.1%

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

   5. Simplified 57.1%

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

   6. Taylor expanded in a around inf 49.2%

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

   if -9.20000000000000018e44 < b < -1.15e-40

   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 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -1.15e-40 < b < 2.65000000000000007e-188

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 46.3%

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

   if 2.65000000000000007e-188 < b < 1.35000000000000001e-8

   1. Initial program 91.1%

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

   3. Taylor expanded in t around -inf 84.9%

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

      1. associate-*r* 84.9%

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

      2. mul-1-neg 84.9%

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

      3. distribute-lft-out 84.9%

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

      4. +-commutative 84.9%

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

      5. associate-*r* 84.9%

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

      6. distribute-rgt-in 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in t around inf 49.2%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-40}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-188}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-8}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+171}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+46} \lor \neg \left(b \leq 0.0035\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+171)
   (+ x (* z (+ y (* a b))))
   (if (or (<= b -1.25e+46) (not (<= b 0.0035)))
     (+ 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 (b <= -1.1e+171) {
		tmp = x + (z * (y + (a * b)));
	} else if ((b <= -1.25e+46) || !(b <= 0.0035)) {
		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 (b <= (-1.1d+171)) then
        tmp = x + (z * (y + (a * b)))
    else if ((b <= (-1.25d+46)) .or. (.not. (b <= 0.0035d0))) 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 (b <= -1.1e+171) {
		tmp = x + (z * (y + (a * b)));
	} else if ((b <= -1.25e+46) || !(b <= 0.0035)) {
		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 b <= -1.1e+171:
		tmp = x + (z * (y + (a * b)))
	elif (b <= -1.25e+46) or not (b <= 0.0035):
		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 (b <= -1.1e+171)
		tmp = Float64(x + Float64(z * Float64(y + Float64(a * b))));
	elseif ((b <= -1.25e+46) || !(b <= 0.0035))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + 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 (b <= -1.1e+171)
		tmp = x + (z * (y + (a * b)));
	elseif ((b <= -1.25e+46) || ~((b <= 0.0035)))
		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[LessEqual[b, -1.1e+171], N[(x + N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.25e+46], N[Not[LessEqual[b, 0.0035]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e171

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0 61.7%

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

      1. +-commutative 61.7%

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

      2. associate-*r* 80.4%

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

      3. distribute-rgt-in 86.1%

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

   5. Simplified 86.1%

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

   if -1.1e171 < b < -1.2500000000000001e46 or 0.00350000000000000007 < b

   1. Initial program 91.2%

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

   3. Taylor expanded in a around 0 93.8%

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

   4. Taylor expanded in a around inf 92.7%

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

   if -1.2500000000000001e46 < b < 0.00350000000000000007

   1. Initial program 93.7%

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

   3. Taylor expanded in b around 0 93.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+171}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+46} \lor \neg \left(b \leq 0.0035\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+45} \lor \neg \left(b \leq 0.003\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.5e+45) (not (<= b 0.003)))
   (+ 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 ((b <= -8.5e+45) || !(b <= 0.003)) {
		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 ((b <= (-8.5d+45)) .or. (.not. (b <= 0.003d0))) 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 ((b <= -8.5e+45) || !(b <= 0.003)) {
		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 (b <= -8.5e+45) or not (b <= 0.003):
		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 ((b <= -8.5e+45) || !(b <= 0.003))
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	else
		tmp = Float64(x + 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 ((b <= -8.5e+45) || ~((b <= 0.003)))
		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[b, -8.5e+45], N[Not[LessEqual[b, 0.003]], $MachinePrecision]], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.4999999999999996e45 or 0.0030000000000000001 < b

   1. Initial program 92.1%

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

   3. Taylor expanded in a around 0 87.5%

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

   4. Taylor expanded in a around inf 85.9%

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

   if -8.4999999999999996e45 < b < 0.0030000000000000001

   1. Initial program 93.7%

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

   3. Taylor expanded in b around 0 93.6%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+45} \lor \neg \left(b \leq 0.003\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-201} \lor \neg \left(a \leq 5 \cdot 10^{-201}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4.3e-201) (not (<= a 5e-201)))
   (+ 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 <= -4.3e-201) || !(a <= 5e-201)) {
		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 <= (-4.3d-201)) .or. (.not. (a <= 5d-201))) 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 <= -4.3e-201) || !(a <= 5e-201)) {
		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 <= -4.3e-201) or not (a <= 5e-201):
		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 <= -4.3e-201) || !(a <= 5e-201))
		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 <= -4.3e-201) || ~((a <= 5e-201)))
		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, -4.3e-201], N[Not[LessEqual[a, 5e-201]], $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 < -4.2999999999999997e-201 or 4.9999999999999999e-201 < a

   1. Initial program 91.3%

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

   3. Taylor expanded in a around 0 96.1%

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

   4. Taylor expanded in a around inf 86.0%

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

   if -4.2999999999999997e-201 < a < 4.9999999999999999e-201

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 90.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-201} \lor \neg \left(a \leq 5 \cdot 10^{-201}\right):\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;x + b \cdot \left(z \cdot \left(a + \frac{y}{b}\right)\right)\\ \mathbf{elif}\;b \leq 0.0032:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+92)
   (+ x (* b (* z (+ a (/ y b)))))
   (if (<= b 0.0032) (+ x (+ (* y z) (* t a))) (+ x (* a (+ t (* z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+92) {
		tmp = x + (b * (z * (a + (y / b))));
	} else if (b <= 0.0032) {
		tmp = x + ((y * z) + (t * a));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.5d+92)) then
        tmp = x + (b * (z * (a + (y / b))))
    else if (b <= 0.0032d0) then
        tmp = x + ((y * z) + (t * a))
    else
        tmp = x + (a * (t + (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+92) {
		tmp = x + (b * (z * (a + (y / b))));
	} else if (b <= 0.0032) {
		tmp = x + ((y * z) + (t * a));
	} else {
		tmp = x + (a * (t + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+92:
		tmp = x + (b * (z * (a + (y / b))))
	elif b <= 0.0032:
		tmp = x + ((y * z) + (t * a))
	else:
		tmp = x + (a * (t + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+92)
		tmp = Float64(x + Float64(b * Float64(z * Float64(a + Float64(y / b)))));
	elseif (b <= 0.0032)
		tmp = Float64(x + Float64(Float64(y * z) + Float64(t * a)));
	else
		tmp = Float64(x + Float64(a * Float64(t + Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+92)
		tmp = x + (b * (z * (a + (y / b))));
	elseif (b <= 0.0032)
		tmp = x + ((y * z) + (t * a));
	else
		tmp = x + (a * (t + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+92], N[(x + N[(b * N[(z * N[(a + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0032], N[(x + N[(N[(y * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.49999999999999986e92

   1. Initial program 90.1%

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

   3. Taylor expanded in a around 0 79.4%

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

   4. Taylor expanded in b around inf 92.1%

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

      1. associate-+r+ 92.1%

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

      2. +-commutative 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-/l* 96.0%

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

      5. associate-/l* 99.8%

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

      6. distribute-lft-out 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around inf 90.4%

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

   if -3.49999999999999986e92 < b < 0.00320000000000000015

   1. Initial program 92.7%

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

   3. Taylor expanded in b around 0 92.1%

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

   if 0.00320000000000000015 < b

   1. Initial program 96.2%

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

   3. Taylor expanded in a around 0 94.6%

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

   4. Taylor expanded in a around inf 89.4%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+92}:\\ \;\;\;\;x + b \cdot \left(z \cdot \left(a + \frac{y}{b}\right)\right)\\ \mathbf{elif}\;b \leq 0.0032:\\ \;\;\;\;x + \left(y \cdot z + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(t + z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 95.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.76 \cdot 10^{+129}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 1.76e+129)
   (+ x (+ (* y z) (* 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 (z <= 1.76e+129) {
		tmp = x + ((y * z) + (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 (z <= 1.76d+129) then
        tmp = x + ((y * z) + (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 (z <= 1.76e+129) {
		tmp = x + ((y * z) + (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 z <= 1.76e+129:
		tmp = x + ((y * z) + (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 (z <= 1.76e+129)
		tmp = Float64(x + Float64(Float64(y * z) + 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 (z <= 1.76e+129)
		tmp = x + ((y * z) + (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[LessEqual[z, 1.76e+129], N[(x + N[(N[(y * z), $MachinePrecision] + N[(a * N[(t + N[(z * b), $MachinePrecision]), $MachinePrecision]), $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 z < 1.76000000000000013e129

   1. Initial program 96.4%

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

   3. Taylor expanded in a around 0 97.3%

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

   if 1.76000000000000013e129 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in t around 0 70.0%

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

      1. +-commutative 70.0%

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

      2. associate-*r* 85.9%

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

      3. distribute-rgt-in 94.5%

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

   5. Simplified 94.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.76 \cdot 10^{+129}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+29} \lor \neg \left(z \leq 2.4 \cdot 10^{-42}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.8e+29) (not (<= z 2.4e-42)))
   (* z (+ y (* a b)))
   (+ x (* t a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.8e+29) || !(z <= 2.4e-42)) {
		tmp = z * (y + (a * b));
	} 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 <= (-8.8d+29)) .or. (.not. (z <= 2.4d-42))) then
        tmp = z * (y + (a * b))
    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 <= -8.8e+29) || !(z <= 2.4e-42)) {
		tmp = z * (y + (a * b));
	} else {
		tmp = x + (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.8e+29) or not (z <= 2.4e-42):
		tmp = z * (y + (a * b))
	else:
		tmp = x + (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.8e+29) || !(z <= 2.4e-42))
		tmp = Float64(z * Float64(y + Float64(a * b)));
	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 <= -8.8e+29) || ~((z <= 2.4e-42)))
		tmp = z * (y + (a * b));
	else
		tmp = x + (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.8e+29], N[Not[LessEqual[z, 2.4e-42]], $MachinePrecision]], N[(z * N[(y + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000005e29 or 2.40000000000000003e-42 < z

   1. Initial program 84.5%

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

   3. Taylor expanded in z around inf 77.6%

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

      1. +-commutative 77.6%

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

   5. Simplified 77.6%

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

   if -8.8000000000000005e29 < z < 2.40000000000000003e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.6%

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

      1. +-commutative 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+29} \lor \neg \left(z \leq 2.4 \cdot 10^{-42}\right):\\ \;\;\;\;z \cdot \left(y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+37} \lor \neg \left(t \leq 1900000000000\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e+37) (not (<= t 1900000000000.0))) (* t a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e+37) || !(t <= 1900000000000.0)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.6d+37)) .or. (.not. (t <= 1900000000000.0d0))) then
        tmp = t * a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e+37) || !(t <= 1900000000000.0)) {
		tmp = t * a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.6e+37) or not (t <= 1900000000000.0):
		tmp = t * a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.6e+37) || !(t <= 1900000000000.0))
		tmp = Float64(t * a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.6e+37) || ~((t <= 1900000000000.0)))
		tmp = t * a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.6e+37], N[Not[LessEqual[t, 1900000000000.0]], $MachinePrecision]], N[(t * a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.5999999999999999e37 or 1.9e12 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around -inf 92.1%

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

      1. associate-*r* 92.1%

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

      2. mul-1-neg 92.1%

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

      3. distribute-lft-out 92.1%

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

      4. +-commutative 92.1%

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

      5. associate-*r* 91.8%

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

      6. distribute-rgt-in 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in t around inf 51.3%

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

   if -2.5999999999999999e37 < t < 1.9e12

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 41.0%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+37} \lor \neg \left(t \leq 1900000000000\right):\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 26.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.0%

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

3. Taylor expanded in x around inf 28.4%

   \[\leadsto \color{blue}{x} \]
4. 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 2024111 
(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)))