ab-angle->ABCF D

Percentage Accurate: 82.4% → 99.7%

Time: 7.6s

Alternatives: 4

Speedup: 0.9×

• 28.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ -\left(\left(a \cdot a\right) \cdot b\right) \cdot b \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

C

double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

Initial Program: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ -\left(\left(a \cdot a\right) \cdot b\right) \cdot b \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))

C

double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -(((a * a) * b) * b)
end function

Java

public static double code(double a, double b) {
	return -(((a * a) * b) * b);
}

Python

def code(a, b):
	return -(((a * a) * b) * b)

Julia

function code(a, b)
	return Float64(-Float64(Float64(Float64(a * a) * b) * b))
end

MATLAB

function tmp = code(a, b)
	tmp = -(((a * a) * b) * b);
end

Wolfram

code[a_, b_] := (-N[(N[(N[(a * a), $MachinePrecision] * b), $MachinePrecision] * b), $MachinePrecision])

Alternative 1: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ [a, b_m] = \mathsf{sort}([a, b_m])\\ \\ \frac{b\_m}{\frac{-1}{a}} \cdot \left(b\_m \cdot a\right) \end{array} \]

FPCore

b_m = (fabs.f64 b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
(FPCore (a b_m) :precision binary64 (* (/ b_m (/ -1.0 a)) (* b_m a)))

C

b_m = fabs(b);
assert(a < b_m);
double code(double a, double b_m) {
	return (b_m / (-1.0 / a)) * (b_m * a);
}

Fortran

b_m = abs(b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
real(8) function code(a, b_m)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    code = (b_m / ((-1.0d0) / a)) * (b_m * a)
end function

Java

b_m = Math.abs(b);
assert a < b_m;
public static double code(double a, double b_m) {
	return (b_m / (-1.0 / a)) * (b_m * a);
}

Python

b_m = math.fabs(b)
[a, b_m] = sort([a, b_m])
def code(a, b_m):
	return (b_m / (-1.0 / a)) * (b_m * a)

Julia

b_m = abs(b)
a, b_m = sort([a, b_m])
function code(a, b_m)
	return Float64(Float64(b_m / Float64(-1.0 / a)) * Float64(b_m * a))
end

MATLAB

b_m = abs(b);
a, b_m = num2cell(sort([a, b_m])){:}
function tmp = code(a, b_m)
	tmp = (b_m / (-1.0 / a)) * (b_m * a);
end

Wolfram

b_m = N[Abs[b], $MachinePrecision]
NOTE: a and b_m should be sorted in increasing order before calling this function.
code[a_, b$95$m_] := N[(N[(b$95$m / N[(-1.0 / a), $MachinePrecision]), $MachinePrecision] * N[(b$95$m * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.0%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right) \]

   2. unswap-sqr N/A

      \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot b\right), \left(a \cdot b\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(a \cdot b\right)\right)\right) \]

   5. *-lowering-*.f64 99.6%

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

4. Applied egg-rr 99.6%

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

   1. unpow1 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left({\left(a \cdot b\right)}^{1}\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   2. sqr-pow N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left({\left(a \cdot b\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(a \cdot b\right)}^{\left(\frac{1}{2}\right)}\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\left({\left(a \cdot b\right)}^{\left(\frac{1}{2}\right)}\right), \left({\left(a \cdot b\right)}^{\left(\frac{1}{2}\right)}\right)\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   4. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(\left(a \cdot b\right), \left(\frac{1}{2}\right)\right), \left({\left(a \cdot b\right)}^{\left(\frac{1}{2}\right)}\right)\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\frac{1}{2}\right)\right), \left({\left(a \cdot b\right)}^{\left(\frac{1}{2}\right)}\right)\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{*.f64}\left(a, b\right), \frac{1}{2}\right), \left({\left(a \cdot b\right)}^{\left(\frac{1}{2}\right)}\right)\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. pow-lowering-pow.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{*.f64}\left(a, b\right), \frac{1}{2}\right), \mathsf{pow.f64}\left(\left(a \cdot b\right), \left(\frac{1}{2}\right)\right)\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{*.f64}\left(a, b\right), \frac{1}{2}\right), \mathsf{pow.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\frac{1}{2}\right)\right)\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

   9. metadata-eval 54.4%

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{pow.f64}\left(\mathsf{*.f64}\left(a, b\right), \frac{1}{2}\right), \mathsf{pow.f64}\left(\mathsf{*.f64}\left(a, b\right), \frac{1}{2}\right)\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

6. Applied egg-rr 54.4%

   \[\leadsto -\color{blue}{\left({\left(a \cdot b\right)}^{0.5} \cdot {\left(a \cdot b\right)}^{0.5}\right)} \cdot \left(a \cdot b\right) \]
7. Step-by-step derivation

   1. distribute-lft-neg-in N/A

      \[\leadsto \left(\mathsf{neg}\left({\left(a \cdot b\right)}^{\frac{1}{2}} \cdot {\left(a \cdot b\right)}^{\frac{1}{2}}\right)\right) \cdot \color{blue}{\left(a \cdot b\right)} \]

   2. pow-prod-up N/A

      \[\leadsto \left(\mathsf{neg}\left({\left(a \cdot b\right)}^{\left(\frac{1}{2} + \frac{1}{2}\right)}\right)\right) \cdot \left(a \cdot b\right) \]

   3. metadata-eval N/A

      \[\leadsto \left(\mathsf{neg}\left({\left(a \cdot b\right)}^{1}\right)\right) \cdot \left(a \cdot b\right) \]

   4. unpow1 N/A

      \[\leadsto \left(\mathsf{neg}\left(a \cdot b\right)\right) \cdot \left(a \cdot b\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(a \cdot b\right)\right), \color{blue}{\left(a \cdot b\right)}\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(b \cdot a\right)\right), \left(a \cdot b\right)\right) \]

   7. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(\mathsf{neg}\left(a\right)\right)\right), \left(\color{blue}{a} \cdot b\right)\right) \]

   8. /-rgt-identity N/A

      \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(\mathsf{neg}\left(\frac{a}{1}\right)\right)\right), \left(a \cdot b\right)\right) \]

   9. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \left(\mathsf{neg}\left(\frac{1}{\frac{1}{a}}\right)\right)\right), \left(a \cdot b\right)\right) \]

   10. distribute-frac-neg2 N/A

       \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \frac{1}{\mathsf{neg}\left(\frac{1}{a}\right)}\right), \left(a \cdot b\right)\right) \]

   11. un-div-inv N/A

       \[\leadsto \mathsf{*.f64}\left(\left(\frac{b}{\mathsf{neg}\left(\frac{1}{a}\right)}\right), \left(\color{blue}{a} \cdot b\right)\right) \]

   12. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, \left(\mathsf{neg}\left(\frac{1}{a}\right)\right)\right), \left(\color{blue}{a} \cdot b\right)\right) \]

   13. distribute-neg-frac N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, \left(\frac{\mathsf{neg}\left(1\right)}{a}\right)\right), \left(a \cdot b\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, \left(\frac{-1}{a}\right)\right), \left(a \cdot b\right)\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, \mathsf{/.f64}\left(-1, a\right)\right), \left(a \cdot b\right)\right) \]

   16. *-lowering-*.f64 99.7%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, \mathsf{/.f64}\left(-1, a\right)\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

8. Applied egg-rr 99.7%

   \[\leadsto \color{blue}{\frac{b}{\frac{-1}{a}} \cdot \left(a \cdot b\right)} \]

9. Final simplification 99.7%

   \[\leadsto \frac{b}{\frac{-1}{a}} \cdot \left(b \cdot a\right) \]
10. Add Preprocessing

Alternative 2: 99.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ [a, b_m] = \mathsf{sort}([a, b_m])\\ \\ \left(b\_m \cdot a\right) \cdot \left(0 - b\_m \cdot a\right) \end{array} \]

FPCore

b_m = (fabs.f64 b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
(FPCore (a b_m) :precision binary64 (* (* b_m a) (- 0.0 (* b_m a))))

C

b_m = fabs(b);
assert(a < b_m);
double code(double a, double b_m) {
	return (b_m * a) * (0.0 - (b_m * a));
}

Fortran

b_m = abs(b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
real(8) function code(a, b_m)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    code = (b_m * a) * (0.0d0 - (b_m * a))
end function

Java

b_m = Math.abs(b);
assert a < b_m;
public static double code(double a, double b_m) {
	return (b_m * a) * (0.0 - (b_m * a));
}

Python

b_m = math.fabs(b)
[a, b_m] = sort([a, b_m])
def code(a, b_m):
	return (b_m * a) * (0.0 - (b_m * a))

Julia

b_m = abs(b)
a, b_m = sort([a, b_m])
function code(a, b_m)
	return Float64(Float64(b_m * a) * Float64(0.0 - Float64(b_m * a)))
end

MATLAB

b_m = abs(b);
a, b_m = num2cell(sort([a, b_m])){:}
function tmp = code(a, b_m)
	tmp = (b_m * a) * (0.0 - (b_m * a));
end

Wolfram

b_m = N[Abs[b], $MachinePrecision]
NOTE: a and b_m should be sorted in increasing order before calling this function.
code[a_, b$95$m_] := N[(N[(b$95$m * a), $MachinePrecision] * N[(0.0 - N[(b$95$m * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.0%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right) \]

   2. unswap-sqr N/A

      \[\leadsto \mathsf{neg.f64}\left(\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\left(a \cdot b\right), \left(a \cdot b\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(a \cdot b\right)\right)\right) \]

   5. *-lowering-*.f64 99.6%

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(a, b\right)\right)\right) \]

4. Applied egg-rr 99.6%

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

5. Final simplification 99.6%

   \[\leadsto \left(b \cdot a\right) \cdot \left(0 - b \cdot a\right) \]
6. Add Preprocessing

Alternative 3: 28.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ [a, b_m] = \mathsf{sort}([a, b_m])\\ \\ b\_m \cdot \left(b\_m \cdot \left(a \cdot a\right)\right) \end{array} \]

FPCore

b_m = (fabs.f64 b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
(FPCore (a b_m) :precision binary64 (* b_m (* b_m (* a a))))

C

b_m = fabs(b);
assert(a < b_m);
double code(double a, double b_m) {
	return b_m * (b_m * (a * a));
}

Fortran

b_m = abs(b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
real(8) function code(a, b_m)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    code = b_m * (b_m * (a * a))
end function

Java

b_m = Math.abs(b);
assert a < b_m;
public static double code(double a, double b_m) {
	return b_m * (b_m * (a * a));
}

Python

b_m = math.fabs(b)
[a, b_m] = sort([a, b_m])
def code(a, b_m):
	return b_m * (b_m * (a * a))

Julia

b_m = abs(b)
a, b_m = sort([a, b_m])
function code(a, b_m)
	return Float64(b_m * Float64(b_m * Float64(a * a)))
end

MATLAB

b_m = abs(b);
a, b_m = num2cell(sort([a, b_m])){:}
function tmp = code(a, b_m)
	tmp = b_m * (b_m * (a * a));
end

Wolfram

b_m = N[Abs[b], $MachinePrecision]
NOTE: a and b_m should be sorted in increasing order before calling this function.
code[a_, b$95$m_] := N[(b$95$m * N[(b$95$m * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.0%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto \mathsf{neg}\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{neg}\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) \]

   3. +-lft-identity N/A

      \[\leadsto \mathsf{neg}\left(\left(0 + a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right) \]

   4. flip3-+ N/A

      \[\leadsto \mathsf{neg}\left(\frac{{0}^{3} + {\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}^{3}}{0 \cdot 0 + \left(\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) - 0 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)}\right) \]

   5. distribute-neg-frac N/A

      \[\leadsto \frac{\mathsf{neg}\left(\left({0}^{3} + {\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}^{3}\right)\right)}{\color{blue}{0 \cdot 0 + \left(\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) - 0 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)}} \]

4. Applied egg-rr 28.0%

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

5. Final simplification 28.0%

   \[\leadsto b \cdot \left(b \cdot \left(a \cdot a\right)\right) \]
6. Add Preprocessing

Alternative 4: 28.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ [a, b_m] = \mathsf{sort}([a, b_m])\\ \\ \left(b\_m \cdot a\right) \cdot \left(b\_m \cdot a\right) \end{array} \]

FPCore

b_m = (fabs.f64 b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
(FPCore (a b_m) :precision binary64 (* (* b_m a) (* b_m a)))

C

b_m = fabs(b);
assert(a < b_m);
double code(double a, double b_m) {
	return (b_m * a) * (b_m * a);
}

Fortran

b_m = abs(b)
NOTE: a and b_m should be sorted in increasing order before calling this function.
real(8) function code(a, b_m)
    real(8), intent (in) :: a
    real(8), intent (in) :: b_m
    code = (b_m * a) * (b_m * a)
end function

Java

b_m = Math.abs(b);
assert a < b_m;
public static double code(double a, double b_m) {
	return (b_m * a) * (b_m * a);
}

Python

b_m = math.fabs(b)
[a, b_m] = sort([a, b_m])
def code(a, b_m):
	return (b_m * a) * (b_m * a)

Julia

b_m = abs(b)
a, b_m = sort([a, b_m])
function code(a, b_m)
	return Float64(Float64(b_m * a) * Float64(b_m * a))
end

MATLAB

b_m = abs(b);
a, b_m = num2cell(sort([a, b_m])){:}
function tmp = code(a, b_m)
	tmp = (b_m * a) * (b_m * a);
end

Wolfram

b_m = N[Abs[b], $MachinePrecision]
NOTE: a and b_m should be sorted in increasing order before calling this function.
code[a_, b$95$m_] := N[(N[(b$95$m * a), $MachinePrecision] * N[(b$95$m * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.0%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Add Preprocessing
3. Step-by-step derivation

   1. associate-*l* N/A

      \[\leadsto \mathsf{neg}\left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{neg}\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) \]

   3. +-lft-identity N/A

      \[\leadsto \mathsf{neg}\left(\left(0 + a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right) \]

   4. flip3-+ N/A

      \[\leadsto \mathsf{neg}\left(\frac{{0}^{3} + {\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}^{3}}{0 \cdot 0 + \left(\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) - 0 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)}\right) \]

   5. distribute-neg-frac N/A

      \[\leadsto \frac{\mathsf{neg}\left(\left({0}^{3} + {\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}^{3}\right)\right)}{\color{blue}{0 \cdot 0 + \left(\left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right) - 0 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right)}} \]

4. Applied egg-rr 27.9%

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

5. Final simplification 27.9%

   \[\leadsto \left(b \cdot a\right) \cdot \left(b \cdot a\right) \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024155 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))