Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.8% → 97.1%

Time: 8.9s

Alternatives: 10

Speedup: 0.5×

• 32.3% 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: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))))
   (if (<= t_1 1e+304) t_1 (fma z y (* a (fma b z t))))))

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 <= 1e+304) {
		tmp = t_1;
	} else {
		tmp = fma(z, y, (a * fma(b, z, 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(Float64(z * a) * b))
	tmp = 0.0
	if (t_1 <= 1e+304)
		tmp = t_1;
	else
		tmp = fma(z, y, Float64(a * fma(b, z, t)));
	end
	return 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, 1e+304], t$95$1, N[(z * y + N[(a * N[(b * z + 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)) < 9.9999999999999994e303

   1. Initial program 98.1%

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

   if 9.9999999999999994e303 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 81.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 98.0

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

   5. Applied rewrites 98.0%

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

4. Final simplification 98.1%

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

Alternative 2: 85.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{a}{y}, \mathsf{fma}\left(b, z, t\right), z\right), x\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-231}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y (fma (/ a y) (fma b z t) z) x)))
   (if (<= y -9.8e-151) t_1 (if (<= y 3.2e-231) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, fma((a / y), fma(b, z, t), z), x);
	double tmp;
	if (y <= -9.8e-151) {
		tmp = t_1;
	} else if (y <= 3.2e-231) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, fma(Float64(a / y), fma(b, z, t), z), x)
	tmp = 0.0
	if (y <= -9.8e-151)
		tmp = t_1;
	elseif (y <= 3.2e-231)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(a / y), $MachinePrecision] * N[(b * z + t), $MachinePrecision] + z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -9.8e-151], t$95$1, If[LessEqual[y, 3.2e-231], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999933e-151 or 3.20000000000000008e-231 < y

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-lft-in N/A

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

      4. +-commutative N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. *-inverses N/A

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

      9. *-rgt-identity N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 93.0%

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

   if -9.79999999999999933e-151 < y < 3.20000000000000008e-231

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 81.1%

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

Alternative 3: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, y, a \cdot \mathsf{fma}\left(b, z, t\right)\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z y (* a (fma b z t)))))
   (if (<= b -1.05e+144) t_1 (if (<= b 2.15e+120) (fma a t (fma z y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, y, (a * fma(b, z, t)));
	double tmp;
	if (b <= -1.05e+144) {
		tmp = t_1;
	} else if (b <= 2.15e+120) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, y, Float64(a * fma(b, z, t)))
	tmp = 0.0
	if (b <= -1.05e+144)
		tmp = t_1;
	elseif (b <= 2.15e+120)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * y + N[(a * N[(b * z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+144], t$95$1, If[LessEqual[b, 2.15e+120], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.04999999999999998e144 or 2.1500000000000001e120 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1.04999999999999998e144 < b < 2.1500000000000001e120

   1. Initial program 95.5%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 94.1%

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

Alternative 4: 80.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+170}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(b, z, t\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(a, b, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e+170)
   (* a (fma b z t))
   (if (<= b 1.1e+124) (fma a t (fma z y x)) (* z (fma a b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+170) {
		tmp = a * fma(b, z, t);
	} else if (b <= 1.1e+124) {
		tmp = fma(a, t, fma(z, y, x));
	} else {
		tmp = z * fma(a, b, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e+170)
		tmp = Float64(a * fma(b, z, t));
	elseif (b <= 1.1e+124)
		tmp = fma(a, t, fma(z, y, x));
	else
		tmp = Float64(z * fma(a, b, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e+170], N[(a * N[(b * z + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+124], N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision], N[(z * N[(a * b + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.59999999999999989e170

   1. Initial program 97.1%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 71.7

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

   5. Applied rewrites 71.7%

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

   if -1.59999999999999989e170 < b < 1.1e124

   1. Initial program 95.6%

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

   3. Taylor expanded in b around 0

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

   5. Applied rewrites 93.3%

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

   if 1.1e124 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 70.4

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

   5. Applied rewrites 70.4%

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

Alternative 5: 74.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \mathsf{fma}\left(a, b, y\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.24:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (fma a b y))))
   (if (<= z -5e-57) t_1 (if (<= z 0.24) (fma a t x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * fma(a, b, y);
	double tmp;
	if (z <= -5e-57) {
		tmp = t_1;
	} else if (z <= 0.24) {
		tmp = fma(a, t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * fma(a, b, y))
	tmp = 0.0
	if (z <= -5e-57)
		tmp = t_1;
	elseif (z <= 0.24)
		tmp = fma(a, t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a * b + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-57], t$95$1, If[LessEqual[z, 0.24], N[(a * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-57 or 0.23999999999999999 < z

   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 z around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 74.6

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

   5. Applied rewrites 74.6%

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

   if -5.0000000000000002e-57 < z < 0.23999999999999999

   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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 79.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 72.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \mathsf{fma}\left(b, z, t\right)\\ \mathbf{if}\;a \leq -1.32 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (fma b z t))))
   (if (<= a -1.32e+19) t_1 (if (<= a 2.6e-60) (fma z y x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * fma(b, z, t);
	double tmp;
	if (a <= -1.32e+19) {
		tmp = t_1;
	} else if (a <= 2.6e-60) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * fma(b, z, t))
	tmp = 0.0
	if (a <= -1.32e+19)
		tmp = t_1;
	elseif (a <= 2.6e-60)
		tmp = fma(z, y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(b * z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.32e+19], t$95$1, If[LessEqual[a, 2.6e-60], N[(z * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.32e19 or 2.5999999999999998e-60 < a

   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 a around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 74.1

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

   5. Applied rewrites 74.1%

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

   if -1.32e19 < a < 2.5999999999999998e-60

   1. Initial program 97.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 74.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   5. Applied rewrites 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 63.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.4e+38) (fma z y x) (if (<= y 4.5e+102) (fma a t x) (fma z y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.4e+38) {
		tmp = fma(z, y, x);
	} else if (y <= 4.5e+102) {
		tmp = fma(a, t, x);
	} else {
		tmp = fma(z, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.4e+38)
		tmp = fma(z, y, x);
	elseif (y <= 4.5e+102)
		tmp = fma(a, t, x);
	else
		tmp = fma(z, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.4e+38], N[(z * y + x), $MachinePrecision], If[LessEqual[y, 4.5e+102], N[(a * t + x), $MachinePrecision], N[(z * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3999999999999997e38 or 4.50000000000000021e102 < y

   1. Initial program 94.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 74.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   5. Applied rewrites 74.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, y, x\right)} \]

   if -6.3999999999999997e38 < y < 4.50000000000000021e102

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 65.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 58.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+150}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.3e+150) (* y z) (if (<= y 5.3e+172) (fma a t x) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.3e+150) {
		tmp = y * z;
	} else if (y <= 5.3e+172) {
		tmp = fma(a, t, x);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.3e+150)
		tmp = Float64(y * z);
	elseif (y <= 5.3e+172)
		tmp = fma(a, t, x);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.3e+150], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.3e+172], N[(a * t + x), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.30000000000000013e150 or 5.3e172 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.9

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

   5. Applied rewrites 74.9%

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

   if -5.30000000000000013e150 < y < 5.3e172

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 62.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]

   5. Applied rewrites 62.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, t, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+150}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(a, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.2e+38) (* y z) (if (<= y 1.15e+91) (* t a) (* y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e+38) {
		tmp = y * z;
	} else if (y <= 1.15e+91) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-6.2d+38)) then
        tmp = y * z
    else if (y <= 1.15d+91) then
        tmp = t * a
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e+38) {
		tmp = y * z;
	} else if (y <= 1.15e+91) {
		tmp = t * a;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.2e+38:
		tmp = y * z
	elif y <= 1.15e+91:
		tmp = t * a
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.2e+38)
		tmp = Float64(y * z);
	elseif (y <= 1.15e+91)
		tmp = Float64(t * a);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.2e+38)
		tmp = y * z;
	elseif (y <= 1.15e+91)
		tmp = t * a;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.2e+38], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.15e+91], N[(t * a), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000035e38 or 1.14999999999999996e91 < y

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 58.3

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

   5. Applied rewrites 58.3%

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

   if -6.20000000000000035e38 < y < 1.14999999999999996e91

   1. Initial program 94.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 33.4

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

   5. Applied rewrites 33.4%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+91}:\\ \;\;\;\;t \cdot a\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 27.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ t \cdot a \end{array} \]

FPCore

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

C

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

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 = t * a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

3. Taylor expanded in t around inf

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

   1. lower-*.f64 28.1

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

5. Applied rewrites 28.1%

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

6. Final simplification 28.1%

   \[\leadsto t \cdot a \]
7. Add Preprocessing

Developer Target 1: 97.9% accurate, 0.8× 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 2024226 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))