ab-angle->ABCF D

Percentage Accurate: 82.1% → 99.7%

Time: 4.2s

Alternatives: 5

Speedup: 1.0×

• 27.6% 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: 82.1% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ -{\left(b \cdot a\right)}^{2} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (- (pow (* b a) 2.0)))

C

double code(double a, double b) {
	return -pow((b * a), 2.0);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = -((b * a) ** 2.0d0)
end function

Java

public static double code(double a, double b) {
	return -Math.pow((b * a), 2.0);
}

Python

def code(a, b):
	return -math.pow((b * a), 2.0)

Julia

function code(a, b)
	return Float64(-(Float64(b * a) ^ 2.0))
end

MATLAB

function tmp = code(a, b)
	tmp = -((b * a) ^ 2.0);
end

Wolfram

code[a_, b_] := (-N[Power[N[(b * a), $MachinePrecision], 2.0], $MachinePrecision])

Derivation

1. Initial program 77.2%

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

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. lift-*.f64 N/A

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

   5. unswap-sqr N/A

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

   6. pow2 N/A

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

   7. lower-pow.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 99.7

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

4. Applied rewrites 99.7%

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

Alternative 2: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.2%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
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-lft-neg-in N/A

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

   10. lower-*.f64 N/A

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

   11. lower-neg.f64 N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 99.7

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

4. Applied rewrites 99.7%

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

5. Final simplification 99.7%

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

Alternative 3: 82.1% accurate, 1.0× speedup

Math

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

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(a * a) * b) * Float64(-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]

Derivation

1. Initial program 77.2%

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

3. Final simplification 77.2%

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

Alternative 4: 29.0% accurate, 1.1× speedup

Math

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

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(Float64(b * Float64(a * a)) * b)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.2%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
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. +-lft-identity N/A

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

   3. flip3-+ N/A

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

   4. distribute-neg-frac N/A

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

4. Applied rewrites 25.7%

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

Alternative 5: 28.9% accurate, 1.1× speedup

Math

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

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 * a) * Float64(b * a))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.2%

   \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
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. +-lft-identity N/A

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

   3. flip3-+ N/A

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

   4. distribute-neg-frac N/A

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

4. Applied rewrites 25.7%

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

Reproduce

herbie shell --seed 2024327 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))