ab-angle->ABCF D

Percentage Accurate: 81.7% → 99.6%

Time: 5.3s

Alternatives: 5

Speedup: 1.0×

• 28.5% 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: 81.7% 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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.4%

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

   1. lift-neg.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. associate-*l* N/A

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

   5. lift-*.f64 N/A

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

   6. unswap-sqr N/A

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

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

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

   8. lower-*.f64 N/A

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

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

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

   10. lower-*.f64 N/A

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

   11. lower-neg.f64 N/A

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

   12. lower-*.f64 99.7

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

4. Applied rewrites 99.7%

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

Alternative 2: 94.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.7%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-*.f64 94.4

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

4. Applied rewrites 94.4%

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

5. Final simplification 94.4%

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

Reproduce

herbie shell --seed 2024226 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))