ab-angle->ABCF D

Percentage Accurate: 82.1% → 99.7%

Time: 5.6s

Alternatives: 5

Speedup: 1.0×

• 28.1% 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: 82.1% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around 0 74.4%

   \[\leadsto -\color{blue}{{a}^{2} \cdot {b}^{2}} \]
4. Step-by-step derivation

   1. unpow2 74.4%

      \[\leadsto -\color{blue}{\left(a \cdot a\right)} \cdot {b}^{2} \]

   2. unpow2 74.4%

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

   3. swap-sqr 99.7%

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

   4. unpow2 99.7%

      \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{2}} \]

5. Simplified 99.7%

   \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{2}} \]
6. Step-by-step derivation

   1. unpow2 99.7%

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

7. Applied egg-rr 99.7%

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

   1. pow1 99.7%

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

   2. metadata-eval 99.7%

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

   3. pow-div 79.9%

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

   4. add-sqr-sqrt 79.9%

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

   5. sqrt-unprod 67.9%

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

   6. sqr-neg 67.9%

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

   7. sub0-neg 67.9%

      \[\leadsto -\left(\frac{\sqrt{\color{blue}{\left(0 - {a}^{2}\right)} \cdot \left(-{a}^{2}\right)}}{{a}^{1}} \cdot b\right) \cdot \left(a \cdot b\right) \]

   8. sub0-neg 67.9%

      \[\leadsto -\left(\frac{\sqrt{\left(0 - {a}^{2}\right) \cdot \color{blue}{\left(0 - {a}^{2}\right)}}}{{a}^{1}} \cdot b\right) \cdot \left(a \cdot b\right) \]

   9. sqrt-unprod 12.6%

      \[\leadsto -\left(\frac{\color{blue}{\sqrt{0 - {a}^{2}} \cdot \sqrt{0 - {a}^{2}}}}{{a}^{1}} \cdot b\right) \cdot \left(a \cdot b\right) \]

   10. add-sqr-sqrt 27.5%

       \[\leadsto -\left(\frac{\color{blue}{0 - {a}^{2}}}{{a}^{1}} \cdot b\right) \cdot \left(a \cdot b\right) \]

   11. pow1 27.5%

       \[\leadsto -\left(\frac{0 - {a}^{2}}{\color{blue}{a}} \cdot b\right) \cdot \left(a \cdot b\right) \]

   12. clear-num 27.5%

       \[\leadsto -\left(\color{blue}{\frac{1}{\frac{a}{0 - {a}^{2}}}} \cdot b\right) \cdot \left(a \cdot b\right) \]

   13. associate-*l/ 27.5%

       \[\leadsto -\color{blue}{\frac{1 \cdot b}{\frac{a}{0 - {a}^{2}}}} \cdot \left(a \cdot b\right) \]

   14. *-un-lft-identity 27.5%

       \[\leadsto -\frac{\color{blue}{b}}{\frac{a}{0 - {a}^{2}}} \cdot \left(a \cdot b\right) \]

   15. clear-num 27.5%

       \[\leadsto -\frac{b}{\color{blue}{\frac{1}{\frac{0 - {a}^{2}}{a}}}} \cdot \left(a \cdot b\right) \]

   16. add-sqr-sqrt 12.6%

       \[\leadsto -\frac{b}{\frac{1}{\frac{\color{blue}{\sqrt{0 - {a}^{2}} \cdot \sqrt{0 - {a}^{2}}}}{a}}} \cdot \left(a \cdot b\right) \]

9. Applied egg-rr 99.7%

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

10. Final simplification 99.7%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around 0 74.4%

   \[\leadsto -\color{blue}{{a}^{2} \cdot {b}^{2}} \]
4. Step-by-step derivation

   1. unpow2 74.4%

      \[\leadsto -\color{blue}{\left(a \cdot a\right)} \cdot {b}^{2} \]

   2. unpow2 74.4%

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

   3. swap-sqr 99.7%

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

   4. unpow2 99.7%

      \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{2}} \]

5. Simplified 99.7%

   \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{2}} \]
6. Step-by-step derivation

   1. unpow2 99.7%

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

7. Applied egg-rr 99.7%

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

8. Final simplification 99.7%

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

Alternative 3: 29.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

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

   1. distribute-rgt-neg-in 79.9%

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

   2. associate-*l* 93.1%

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

3. Simplified 93.1%

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

   1. neg-sub0 93.1%

      \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{\left(0 - b\right)} \]

   2. sub-neg 93.1%

      \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{\left(0 + \left(-b\right)\right)} \]

   3. add-sqr-sqrt 48.5%

      \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \left(0 + \color{blue}{\sqrt{-b} \cdot \sqrt{-b}}\right) \]

   4. sqrt-unprod 53.9%

      \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \left(0 + \color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}\right) \]

   5. sqr-neg 53.9%

      \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \left(0 + \sqrt{\color{blue}{b \cdot b}}\right) \]

   6. sqrt-unprod 11.8%

      \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \left(0 + \color{blue}{\sqrt{b} \cdot \sqrt{b}}\right) \]

   7. add-sqr-sqrt 27.5%

      \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \left(0 + \color{blue}{b}\right) \]

6. Applied egg-rr 27.5%

   \[\leadsto \left(a \cdot \left(a \cdot b\right)\right) \cdot \color{blue}{\left(0 + b\right)} \]
7. Step-by-step derivation

   1. +-lft-identity 27.5%

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

8. Simplified 27.5%

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

9. Final simplification 27.5%

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

Alternative 4: 29.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

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

   1. add-sqr-sqrt 26.6%

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

   2. sqrt-unprod 27.6%

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

   3. sqr-neg 27.6%

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

   4. sqrt-unprod 27.5%

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

   5. add-sqr-sqrt 27.5%

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

   6. associate-*l* 27.3%

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

   7. swap-sqr 27.4%

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

4. Applied egg-rr 27.4%

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

5. Final simplification 27.4%

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

Alternative 5: 29.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

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

   1. associate-*l* 74.4%

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

   2. associate-*r* 83.2%

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

   3. *-commutative 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. distribute-rgt-neg-in 83.2%

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

   6. associate-*r* 95.3%

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

3. Simplified 95.3%

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

   1. neg-sub0 95.3%

      \[\leadsto a \cdot \left(b \cdot \left(b \cdot \color{blue}{\left(0 - a\right)}\right)\right) \]

   2. sub-neg 95.3%

      \[\leadsto a \cdot \left(b \cdot \left(b \cdot \color{blue}{\left(0 + \left(-a\right)\right)}\right)\right) \]

   3. add-sqr-sqrt 48.0%

      \[\leadsto a \cdot \left(b \cdot \left(b \cdot \left(0 + \color{blue}{\sqrt{-a} \cdot \sqrt{-a}}\right)\right)\right) \]

   4. sqrt-unprod 54.0%

      \[\leadsto a \cdot \left(b \cdot \left(b \cdot \left(0 + \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}}\right)\right)\right) \]

   5. sqr-neg 54.0%

      \[\leadsto a \cdot \left(b \cdot \left(b \cdot \left(0 + \sqrt{\color{blue}{a \cdot a}}\right)\right)\right) \]

   6. sqrt-prod 15.3%

      \[\leadsto a \cdot \left(b \cdot \left(b \cdot \left(0 + \color{blue}{\sqrt{a} \cdot \sqrt{a}}\right)\right)\right) \]

   7. add-sqr-sqrt 27.5%

      \[\leadsto a \cdot \left(b \cdot \left(b \cdot \left(0 + \color{blue}{a}\right)\right)\right) \]

6. Applied egg-rr 27.5%

   \[\leadsto a \cdot \left(b \cdot \left(b \cdot \color{blue}{\left(0 + a\right)}\right)\right) \]
7. Step-by-step derivation

   1. +-lft-identity 27.5%

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

8. Simplified 27.5%

   \[\leadsto a \cdot \left(b \cdot \left(b \cdot \color{blue}{a}\right)\right) \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024113 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))