Difference of squares

Percentage Accurate: 94.1% → 96.9%

Time: 3.9s

Alternatives: 3

Speedup: 0.1×

• 42.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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

MATLAB

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

Wolfram

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

Initial Program: 94.1% accurate, 1.0× speedup

Math

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

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 92.2%

   \[a \cdot a - b \cdot b \]
2. Step-by-step derivation

   1. sqr-neg 92.2%

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

   2. cancel-sign-sub 92.2%

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

   3. fma-def 95.3%

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

3. Simplified 95.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, a, b \cdot \left(-b\right)\right)} \]
4. Add Preprocessing

5. Final simplification 95.3%

   \[\leadsto \mathsf{fma}\left(a, a, b \cdot \left(-b\right)\right) \]
6. Add Preprocessing

Alternative 2: 56.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(a, b):
	return a * (a + (b * -2.0))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. difference-of-squares 100.0%

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

   2. add-sqr-sqrt 48.7%

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

   3. sqrt-prod 74.6%

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

   4. sqr-neg 74.6%

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

   5. sqrt-unprod 27.7%

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

   6. add-sqr-sqrt 52.8%

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

   7. sub-neg 52.8%

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

   8. pow1 52.8%

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

   9. pow1 52.8%

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

   10. pow-prod-up 52.8%

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

   11. add-sqr-sqrt 30.5%

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

   12. add-sqr-sqrt 13.3%

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

   13. difference-of-squares 13.3%

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

   14. metadata-eval 13.3%

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

   15. unpow-prod-down 13.3%

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

4. Applied egg-rr 13.3%

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

   1. unpow2 13.3%

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

   2. unpow2 13.3%

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

   3. unswap-sqr 13.3%

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

   4. difference-of-squares 13.3%

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

   5. unpow1/2 13.3%

      \[\leadsto \left(\color{blue}{{a}^{0.5}} \cdot \sqrt{a} - \sqrt{b} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   6. unpow1/2 13.3%

      \[\leadsto \left({a}^{0.5} \cdot \color{blue}{{a}^{0.5}} - \sqrt{b} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   7. pow-sqr 13.4%

      \[\leadsto \left(\color{blue}{{a}^{\left(2 \cdot 0.5\right)}} - \sqrt{b} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   8. metadata-eval 13.4%

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

   9. unpow1 13.4%

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

   10. unpow1/2 13.4%

       \[\leadsto \left(a - \color{blue}{{b}^{0.5}} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   11. unpow1/2 13.4%

       \[\leadsto \left(a - {b}^{0.5} \cdot \color{blue}{{b}^{0.5}}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   12. pow-sqr 13.4%

       \[\leadsto \left(a - \color{blue}{{b}^{\left(2 \cdot 0.5\right)}}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   13. metadata-eval 13.4%

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

   14. unpow1 13.4%

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

   15. difference-of-squares 13.4%

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

   16. unpow1/2 13.4%

       \[\leadsto \left(a - b\right) \cdot \left(\color{blue}{{a}^{0.5}} \cdot \sqrt{a} - \sqrt{b} \cdot \sqrt{b}\right) \]

   17. unpow1/2 13.4%

       \[\leadsto \left(a - b\right) \cdot \left({a}^{0.5} \cdot \color{blue}{{a}^{0.5}} - \sqrt{b} \cdot \sqrt{b}\right) \]

   18. pow-sqr 25.1%

       \[\leadsto \left(a - b\right) \cdot \left(\color{blue}{{a}^{\left(2 \cdot 0.5\right)}} - \sqrt{b} \cdot \sqrt{b}\right) \]

   19. metadata-eval 25.1%

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

   20. unpow1 25.1%

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

6. Simplified 52.8%

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

7. Taylor expanded in a around inf 51.5%

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

   1. *-commutative 51.5%

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

   2. associate-*l* 51.5%

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

   3. unpow2 51.5%

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

   4. distribute-lft-out 57.0%

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

9. Simplified 57.0%

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

10. Final simplification 57.0%

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

Alternative 3: 14.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. difference-of-squares 100.0%

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

   2. add-sqr-sqrt 48.7%

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

   3. sqrt-prod 74.6%

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

   4. sqr-neg 74.6%

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

   5. sqrt-unprod 27.7%

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

   6. add-sqr-sqrt 52.8%

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

   7. sub-neg 52.8%

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

   8. pow1 52.8%

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

   9. pow1 52.8%

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

   10. pow-prod-up 52.8%

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

   11. add-sqr-sqrt 30.5%

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

   12. add-sqr-sqrt 13.3%

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

   13. difference-of-squares 13.3%

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

   14. metadata-eval 13.3%

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

   15. unpow-prod-down 13.3%

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

4. Applied egg-rr 13.3%

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

   1. unpow2 13.3%

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

   2. unpow2 13.3%

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

   3. unswap-sqr 13.3%

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

   4. difference-of-squares 13.3%

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

   5. unpow1/2 13.3%

      \[\leadsto \left(\color{blue}{{a}^{0.5}} \cdot \sqrt{a} - \sqrt{b} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   6. unpow1/2 13.3%

      \[\leadsto \left({a}^{0.5} \cdot \color{blue}{{a}^{0.5}} - \sqrt{b} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   7. pow-sqr 13.4%

      \[\leadsto \left(\color{blue}{{a}^{\left(2 \cdot 0.5\right)}} - \sqrt{b} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   8. metadata-eval 13.4%

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

   9. unpow1 13.4%

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

   10. unpow1/2 13.4%

       \[\leadsto \left(a - \color{blue}{{b}^{0.5}} \cdot \sqrt{b}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   11. unpow1/2 13.4%

       \[\leadsto \left(a - {b}^{0.5} \cdot \color{blue}{{b}^{0.5}}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   12. pow-sqr 13.4%

       \[\leadsto \left(a - \color{blue}{{b}^{\left(2 \cdot 0.5\right)}}\right) \cdot \left(\left(\sqrt{a} + \sqrt{b}\right) \cdot \left(\sqrt{a} - \sqrt{b}\right)\right) \]

   13. metadata-eval 13.4%

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

   14. unpow1 13.4%

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

   15. difference-of-squares 13.4%

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

   16. unpow1/2 13.4%

       \[\leadsto \left(a - b\right) \cdot \left(\color{blue}{{a}^{0.5}} \cdot \sqrt{a} - \sqrt{b} \cdot \sqrt{b}\right) \]

   17. unpow1/2 13.4%

       \[\leadsto \left(a - b\right) \cdot \left({a}^{0.5} \cdot \color{blue}{{a}^{0.5}} - \sqrt{b} \cdot \sqrt{b}\right) \]

   18. pow-sqr 25.1%

       \[\leadsto \left(a - b\right) \cdot \left(\color{blue}{{a}^{\left(2 \cdot 0.5\right)}} - \sqrt{b} \cdot \sqrt{b}\right) \]

   19. metadata-eval 25.1%

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

   20. unpow1 25.1%

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

6. Simplified 52.8%

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

7. Taylor expanded in a around inf 51.5%

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

   1. *-commutative 51.5%

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

   2. associate-*l* 51.5%

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

   3. unpow2 51.5%

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

   4. distribute-lft-out 57.0%

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

9. Simplified 57.0%

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

10. Taylor expanded in a around 0 17.8%

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

11. Final simplification 17.8%

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

Developer target: 100.0% accurate, 1.0× speedup

Math

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

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 + 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]

Reproduce

herbie shell --seed 2024033 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

  :herbie-target
  (* (+ a b) (- a b))

  (- (* a a) (* b b)))