ab-angle->ABCF D

Percentage Accurate: 81.2% → 94.2%

Time: 2.3s

Alternatives: 2

Speedup: 1.0×

• 26.9% 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: 81.2% 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: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

3. Taylor expanded in a around 0

   \[\leadsto \color{blue}{-1 \cdot \left({a}^{2} \cdot {b}^{2}\right)} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

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

   2. unpow2 N/A

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

   3. associate-*r* N/A

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

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

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. unpow2 N/A

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

   8. associate-*l* N/A

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

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

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

   10. lower-*.f64 N/A

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

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

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

   12. lower-*.f64 N/A

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

   13. lower-neg.f64 94.8

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

5. Simplified 94.8%

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

6. Final simplification 94.8%

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

Alternative 2: 81.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.8%

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

3. Final simplification 81.8%

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

Reproduce

herbie shell --seed 2024215 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))