ab-angle->ABCF D

Percentage Accurate: 82.8% → 99.7%

Time: 10.0s

Alternatives: 6

Speedup: 0.9×

• 27.7% 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: 82.8% 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

\[\begin{array}{l} \\ \left(a \cdot b\right) \cdot \left(0 - a \cdot b\right) \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (* (* a b) (- 0.0 (* a b))))

C

double code(double a, double b) {
	return (a * b) * (0.0 - (a * b));
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (a * b) * (0.0d0 - (a * b))
end function

Java

public static double code(double a, double b) {
	return (a * b) * (0.0 - (a * b));
}

Python

def code(a, b):
	return (a * b) * (0.0 - (a * b))

Julia

function code(a, b)
	return Float64(Float64(a * b) * Float64(0.0 - Float64(a * b)))
end

MATLAB

function tmp = code(a, b)
	tmp = (a * b) * (0.0 - (a * b));
end

Wolfram

code[a_, b_] := N[(N[(a * b), $MachinePrecision] * N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.0%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
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 99.7%

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

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 2: 37.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := b \cdot \left(b \cdot \left(a \cdot a\right)\right)\\ \mathbf{if}\;t\_0 \leq 10^{-258}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;0 - a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (let* ((t_0 (* b (* b (* a a))))) (if (<= t_0 1e-258) t_0 (- 0.0 (* a b)))))

C

double code(double a, double b) {
	double t_0 = b * (b * (a * a));
	double tmp;
	if (t_0 <= 1e-258) {
		tmp = t_0;
	} else {
		tmp = 0.0 - (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_0
    real(8) :: tmp
    t_0 = b * (b * (a * a))
    if (t_0 <= 1d-258) then
        tmp = t_0
    else
        tmp = 0.0d0 - (a * b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double t_0 = b * (b * (a * a));
	double tmp;
	if (t_0 <= 1e-258) {
		tmp = t_0;
	} else {
		tmp = 0.0 - (a * b);
	}
	return tmp;
}

Python

def code(a, b):
	t_0 = b * (b * (a * a))
	tmp = 0
	if t_0 <= 1e-258:
		tmp = t_0
	else:
		tmp = 0.0 - (a * b)
	return tmp

Julia

function code(a, b)
	t_0 = Float64(b * Float64(b * Float64(a * a)))
	tmp = 0.0
	if (t_0 <= 1e-258)
		tmp = t_0;
	else
		tmp = Float64(0.0 - Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	t_0 = b * (b * (a * a));
	tmp = 0.0;
	if (t_0 <= 1e-258)
		tmp = t_0;
	else
		tmp = 0.0 - (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := Block[{t$95$0 = N[(b * N[(b * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e-258], t$95$0, N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (*.f64 a a) b) b) < 9.99999999999999954e-259

   1. Initial program 81.2%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
   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 71.3%

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

   if 9.99999999999999954e-259 < (*.f64 (*.f64 (*.f64 a a) b) b)

   1. Initial program 87.3%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
   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. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 81.4%

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

   4. Applied egg-rr 81.4%

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

   6. Applied egg-rr 14.7%

      \[\leadsto -\color{blue}{\left(b \cdot 1\right)} \cdot a \]
   7. Step-by-step derivation

      1. *-rgt-identity 14.7%

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

   8. Applied egg-rr 14.7%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(b \cdot \left(a \cdot a\right)\right) \leq 10^{-258}:\\ \;\;\;\;b \cdot \left(b \cdot \left(a \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0 - a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 32.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{+105}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;0 - a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= b 2.4e+105) (* (* a b) (* a b)) (- 0.0 (* a b))))

C

double code(double a, double b) {
	double tmp;
	if (b <= 2.4e+105) {
		tmp = (a * b) * (a * b);
	} else {
		tmp = 0.0 - (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.4d+105) then
        tmp = (a * b) * (a * b)
    else
        tmp = 0.0d0 - (a * b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 2.4e+105) {
		tmp = (a * b) * (a * b);
	} else {
		tmp = 0.0 - (a * b);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 2.4e+105:
		tmp = (a * b) * (a * b)
	else:
		tmp = 0.0 - (a * b)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 2.4e+105)
		tmp = Float64(Float64(a * b) * Float64(a * b));
	else
		tmp = Float64(0.0 - Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 2.4e+105)
		tmp = (a * b) * (a * b);
	else
		tmp = 0.0 - (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 2.4e+105], N[(N[(a * b), $MachinePrecision] * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.39999999999999975e105

   1. Initial program 86.3%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
   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 31.0%

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

   if 2.39999999999999975e105 < b

   1. Initial program 76.0%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
   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. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 70.0%

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

   4. Applied egg-rr 70.0%

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

   6. Applied egg-rr 22.1%

      \[\leadsto -\color{blue}{\left(b \cdot 1\right)} \cdot a \]
   7. Step-by-step derivation

      1. *-rgt-identity 22.1%

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

   8. Applied egg-rr 22.1%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{+105}:\\ \;\;\;\;\left(a \cdot b\right) \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;0 - a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 19.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (if (<= b 8.2e-19) (* a b) -1.0))

C

double code(double a, double b) {
	double tmp;
	if (b <= 8.2e-19) {
		tmp = a * b;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8.2d-19) then
        tmp = a * b
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 8.2e-19) {
		tmp = a * b;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 8.2e-19:
		tmp = a * b
	else:
		tmp = -1.0
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 8.2e-19)
		tmp = Float64(a * b);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 8.2e-19)
		tmp = a * b;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 8.2e-19], N[(a * b), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if b < 8.1999999999999997e-19

   1. Initial program 85.2%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
   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 31.7%

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

   6. Applied egg-rr 22.3%

      \[\leadsto \color{blue}{\left(b \cdot 1\right)} \cdot a \]
   7. Step-by-step derivation

      1. *-rgt-identity 22.3%

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

   8. Applied egg-rr 22.3%

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

   if 8.1999999999999997e-19 < b

   1. Initial program 84.3%

      \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
   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. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 82.5%

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

   4. Applied egg-rr 82.5%

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

   6. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 18.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 22.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ 0 - a \cdot b \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- 0.0 (* a b)))

C

double code(double a, double b) {
	return 0.0 - (a * b);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = 0.0d0 - (a * b)
end function

Java

public static double code(double a, double b) {
	return 0.0 - (a * b);
}

Python

def code(a, b):
	return 0.0 - (a * b)

Julia

function code(a, b)
	return Float64(0.0 - Float64(a * b))
end

MATLAB

function tmp = code(a, b)
	tmp = 0.0 - (a * b);
end

Wolfram

code[a_, b_] := N[(0.0 - N[(a * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.0%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
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. associate-*r* N/A

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

   3. *-commutative N/A

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

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

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

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

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

   6. *-lowering-*.f64 83.0%

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

4. Applied egg-rr 83.0%

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

6. Applied egg-rr 23.5%

   \[\leadsto -\color{blue}{\left(b \cdot 1\right)} \cdot a \]
7. Step-by-step derivation

   1. *-rgt-identity 23.5%

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

8. Applied egg-rr 23.5%

   \[\leadsto -\color{blue}{b} \cdot a \]

9. Final simplification 23.5%

   \[\leadsto 0 - a \cdot b \]
10. Add Preprocessing

Alternative 6: 4.2% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (a b) :precision binary64 -1.0)

C

double code(double a, double b) {
	return -1.0;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -1.0d0
end function

Java

public static double code(double a, double b) {
	return -1.0;
}

Python

def code(a, b):
	return -1.0

Julia

function code(a, b)
	return -1.0
end

MATLAB

function tmp = code(a, b)
	tmp = -1.0;
end

Wolfram

code[a_, b_] := -1.0

Derivation

1. Initial program 85.0%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
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. associate-*r* N/A

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

   3. *-commutative N/A

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

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

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

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

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

   6. *-lowering-*.f64 83.0%

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

4. Applied egg-rr 83.0%

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

6. Applied egg-rr 4.1%

   \[\leadsto \color{blue}{-1} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024161 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))