Difference of squares

Percentage Accurate: 94.1% → 100.0%

Time: 5.3s

Alternatives: 5

Speedup: 0.6×

• 43.6% 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: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot b \leq 5 \cdot 10^{+82}:\\ \;\;\;\;a \cdot a - b \cdot b\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} \cdot \mathsf{fma}\left(a, \frac{1}{b} \cdot \frac{a}{b}, -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= (* b b) 5e+82)
   (- (* a a) (* b b))
   (* (pow b 2.0) (fma a (* (/ 1.0 b) (/ a b)) -1.0))))

C

double code(double a, double b) {
	double tmp;
	if ((b * b) <= 5e+82) {
		tmp = (a * a) - (b * b);
	} else {
		tmp = pow(b, 2.0) * fma(a, ((1.0 / b) * (a / b)), -1.0);
	}
	return tmp;
}

Julia

function code(a, b)
	tmp = 0.0
	if (Float64(b * b) <= 5e+82)
		tmp = Float64(Float64(a * a) - Float64(b * b));
	else
		tmp = Float64((b ^ 2.0) * fma(a, Float64(Float64(1.0 / b) * Float64(a / b)), -1.0));
	end
	return tmp
end

Wolfram

code[a_, b_] := If[LessEqual[N[(b * b), $MachinePrecision], 5e+82], N[(N[(a * a), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision], N[(N[Power[b, 2.0], $MachinePrecision] * N[(a * N[(N[(1.0 / b), $MachinePrecision] * N[(a / b), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b b) < 5.00000000000000015e82

   1. Initial program 100.0%

      \[a \cdot a - b \cdot b \]
   2. Add Preprocessing

   if 5.00000000000000015e82 < (*.f64 b b)

   1. Initial program 83.5%

      \[a \cdot a - b \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 83.5%

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

      1. unpow2 83.5%

         \[\leadsto {b}^{2} \cdot \left(\frac{\color{blue}{a \cdot a}}{{b}^{2}} - 1\right) \]

      2. associate-/l* 90.4%

         \[\leadsto {b}^{2} \cdot \left(\color{blue}{a \cdot \frac{a}{{b}^{2}}} - 1\right) \]

      3. fmm-def 90.4%

         \[\leadsto {b}^{2} \cdot \color{blue}{\mathsf{fma}\left(a, \frac{a}{{b}^{2}}, -1\right)} \]

      4. metadata-eval 90.4%

         \[\leadsto {b}^{2} \cdot \mathsf{fma}\left(a, \frac{a}{{b}^{2}}, \color{blue}{-1}\right) \]

   5. Simplified 90.4%

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

      1. *-un-lft-identity 90.4%

         \[\leadsto {b}^{2} \cdot \mathsf{fma}\left(a, \frac{\color{blue}{1 \cdot a}}{{b}^{2}}, -1\right) \]

      2. unpow2 90.4%

         \[\leadsto {b}^{2} \cdot \mathsf{fma}\left(a, \frac{1 \cdot a}{\color{blue}{b \cdot b}}, -1\right) \]

      3. times-frac 100.0%

         \[\leadsto {b}^{2} \cdot \mathsf{fma}\left(a, \color{blue}{\frac{1}{b} \cdot \frac{a}{b}}, -1\right) \]

   7. Applied egg-rr 100.0%

      \[\leadsto {b}^{2} \cdot \mathsf{fma}\left(a, \color{blue}{\frac{1}{b} \cdot \frac{a}{b}}, -1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot b \leq 5 \cdot 10^{+82}:\\ \;\;\;\;a \cdot a - b \cdot b\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} \cdot \mathsf{fma}\left(a, \frac{1}{b} \cdot \frac{a}{b}, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot b \leq 10^{+88}:\\ \;\;\;\;a \cdot a - b \cdot b\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} \cdot \left(-1 + \frac{\frac{a}{b}}{\frac{b}{a}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= (* b b) 1e+88)
   (- (* a a) (* b b))
   (* (pow b 2.0) (+ -1.0 (/ (/ a b) (/ b a))))))

C

double code(double a, double b) {
	double tmp;
	if ((b * b) <= 1e+88) {
		tmp = (a * a) - (b * b);
	} else {
		tmp = pow(b, 2.0) * (-1.0 + ((a / b) / (b / a)));
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b * b) <= 1d+88) then
        tmp = (a * a) - (b * b)
    else
        tmp = (b ** 2.0d0) * ((-1.0d0) + ((a / b) / (b / a)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if ((b * b) <= 1e+88) {
		tmp = (a * a) - (b * b);
	} else {
		tmp = Math.pow(b, 2.0) * (-1.0 + ((a / b) / (b / a)));
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if (b * b) <= 1e+88:
		tmp = (a * a) - (b * b)
	else:
		tmp = math.pow(b, 2.0) * (-1.0 + ((a / b) / (b / a)))
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (Float64(b * b) <= 1e+88)
		tmp = Float64(Float64(a * a) - Float64(b * b));
	else
		tmp = Float64((b ^ 2.0) * Float64(-1.0 + Float64(Float64(a / b) / Float64(b / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if ((b * b) <= 1e+88)
		tmp = (a * a) - (b * b);
	else
		tmp = (b ^ 2.0) * (-1.0 + ((a / b) / (b / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[N[(b * b), $MachinePrecision], 1e+88], N[(N[(a * a), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision], N[(N[Power[b, 2.0], $MachinePrecision] * N[(-1.0 + N[(N[(a / b), $MachinePrecision] / N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b b) < 9.99999999999999959e87

   1. Initial program 100.0%

      \[a \cdot a - b \cdot b \]
   2. Add Preprocessing

   if 9.99999999999999959e87 < (*.f64 b b)

   1. Initial program 83.3%

      \[a \cdot a - b \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 83.3%

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

      1. unpow2 83.3%

         \[\leadsto {b}^{2} \cdot \left(\frac{\color{blue}{a \cdot a}}{{b}^{2}} - 1\right) \]

      2. associate-/l* 90.4%

         \[\leadsto {b}^{2} \cdot \left(\color{blue}{a \cdot \frac{a}{{b}^{2}}} - 1\right) \]

      3. fmm-def 90.4%

         \[\leadsto {b}^{2} \cdot \color{blue}{\mathsf{fma}\left(a, \frac{a}{{b}^{2}}, -1\right)} \]

      4. metadata-eval 90.4%

         \[\leadsto {b}^{2} \cdot \mathsf{fma}\left(a, \frac{a}{{b}^{2}}, \color{blue}{-1}\right) \]

   5. Simplified 90.4%

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

      1. fma-undefine 90.4%

         \[\leadsto {b}^{2} \cdot \color{blue}{\left(a \cdot \frac{a}{{b}^{2}} + -1\right)} \]

      2. div-inv 90.4%

         \[\leadsto {b}^{2} \cdot \left(a \cdot \color{blue}{\left(a \cdot \frac{1}{{b}^{2}}\right)} + -1\right) \]

      3. associate-*r* 83.3%

         \[\leadsto {b}^{2} \cdot \left(\color{blue}{\left(a \cdot a\right) \cdot \frac{1}{{b}^{2}}} + -1\right) \]

      4. pow2 83.3%

         \[\leadsto {b}^{2} \cdot \left(\color{blue}{{a}^{2}} \cdot \frac{1}{{b}^{2}} + -1\right) \]

      5. pow-flip 83.3%

         \[\leadsto {b}^{2} \cdot \left({a}^{2} \cdot \color{blue}{{b}^{\left(-2\right)}} + -1\right) \]

      6. metadata-eval 83.3%

         \[\leadsto {b}^{2} \cdot \left({a}^{2} \cdot {b}^{\color{blue}{-2}} + -1\right) \]

   7. Applied egg-rr 83.3%

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

      1. metadata-eval 83.3%

         \[\leadsto {b}^{2} \cdot \left({a}^{2} \cdot {b}^{\color{blue}{\left(2 \cdot -1\right)}} + -1\right) \]

      2. pow-sqr 83.3%

         \[\leadsto {b}^{2} \cdot \left({a}^{2} \cdot \color{blue}{\left({b}^{-1} \cdot {b}^{-1}\right)} + -1\right) \]

      3. inv-pow 83.3%

         \[\leadsto {b}^{2} \cdot \left({a}^{2} \cdot \left(\color{blue}{\frac{1}{b}} \cdot {b}^{-1}\right) + -1\right) \]

      4. inv-pow 83.3%

         \[\leadsto {b}^{2} \cdot \left({a}^{2} \cdot \left(\frac{1}{b} \cdot \color{blue}{\frac{1}{b}}\right) + -1\right) \]

      5. unpow2 83.3%

         \[\leadsto {b}^{2} \cdot \left(\color{blue}{\left(a \cdot a\right)} \cdot \left(\frac{1}{b} \cdot \frac{1}{b}\right) + -1\right) \]

      6. swap-sqr 100.0%

         \[\leadsto {b}^{2} \cdot \left(\color{blue}{\left(a \cdot \frac{1}{b}\right) \cdot \left(a \cdot \frac{1}{b}\right)} + -1\right) \]

      7. div-inv 100.0%

         \[\leadsto {b}^{2} \cdot \left(\color{blue}{\frac{a}{b}} \cdot \left(a \cdot \frac{1}{b}\right) + -1\right) \]

      8. div-inv 100.0%

         \[\leadsto {b}^{2} \cdot \left(\frac{a}{b} \cdot \color{blue}{\frac{a}{b}} + -1\right) \]

      9. clear-num 100.0%

         \[\leadsto {b}^{2} \cdot \left(\frac{a}{b} \cdot \color{blue}{\frac{1}{\frac{b}{a}}} + -1\right) \]

      10. un-div-inv 100.0%

          \[\leadsto {b}^{2} \cdot \left(\color{blue}{\frac{\frac{a}{b}}{\frac{b}{a}}} + -1\right) \]

   9. Applied egg-rr 100.0%

      \[\leadsto {b}^{2} \cdot \left(\color{blue}{\frac{\frac{a}{b}}{\frac{b}{a}}} + -1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot b \leq 10^{+88}:\\ \;\;\;\;a \cdot a - b \cdot b\\ \mathbf{else}:\\ \;\;\;\;{b}^{2} \cdot \left(-1 + \frac{\frac{a}{b}}{\frac{b}{a}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{+199}:\\ \;\;\;\;\mathsf{fma}\left(a, a, b \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b + a\right) \cdot \left(b + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a 1e+199) (fma a a (* b (- b))) (* (+ b a) (+ b a))))

C

double code(double a, double b) {
	double tmp;
	if (a <= 1e+199) {
		tmp = fma(a, a, (b * -b));
	} else {
		tmp = (b + a) * (b + a);
	}
	return tmp;
}

Julia

function code(a, b)
	tmp = 0.0
	if (a <= 1e+199)
		tmp = fma(a, a, Float64(b * Float64(-b)));
	else
		tmp = Float64(Float64(b + a) * Float64(b + a));
	end
	return tmp
end

Wolfram

code[a_, b_] := If[LessEqual[a, 1e+199], N[(a * a + N[(b * (-b)), $MachinePrecision]), $MachinePrecision], N[(N[(b + a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.0000000000000001e199

   1. Initial program 93.9%

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

      1. sqr-neg 93.9%

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

      2. cancel-sign-sub 93.9%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

   if 1.0000000000000001e199 < a

   1. Initial program 81.5%

      \[a \cdot a - b \cdot b \]
   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. sub-neg 100.0%

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

      3. add-sqr-sqrt 59.3%

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

      4. sqrt-unprod 100.0%

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

      5. sqr-neg 100.0%

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

      6. sqrt-prod 40.7%

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

      7. add-sqr-sqrt 96.3%

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

   4. Applied egg-rr 96.3%

      \[\leadsto \color{blue}{\left(a + b\right) \cdot \left(a + b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{+199}:\\ \;\;\;\;\mathsf{fma}\left(a, a, b \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b + a\right) \cdot \left(b + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{+149}:\\ \;\;\;\;a \cdot a - b \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(b + a\right) \cdot \left(b + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= a 1e+149) (- (* a a) (* b b)) (* (+ b a) (+ b a))))

C

double code(double a, double b) {
	double tmp;
	if (a <= 1e+149) {
		tmp = (a * a) - (b * b);
	} else {
		tmp = (b + a) * (b + a);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1d+149) then
        tmp = (a * a) - (b * b)
    else
        tmp = (b + a) * (b + a)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (a <= 1e+149) {
		tmp = (a * a) - (b * b);
	} else {
		tmp = (b + a) * (b + a);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if a <= 1e+149:
		tmp = (a * a) - (b * b)
	else:
		tmp = (b + a) * (b + a)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (a <= 1e+149)
		tmp = Float64(Float64(a * a) - Float64(b * b));
	else
		tmp = Float64(Float64(b + a) * Float64(b + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (a <= 1e+149)
		tmp = (a * a) - (b * b);
	else
		tmp = (b + a) * (b + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[a, 1e+149], N[(N[(a * a), $MachinePrecision] - N[(b * b), $MachinePrecision]), $MachinePrecision], N[(N[(b + a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.00000000000000005e149

   1. Initial program 95.4%

      \[a \cdot a - b \cdot b \]
   2. Add Preprocessing

   if 1.00000000000000005e149 < a

   1. Initial program 75.7%

      \[a \cdot a - b \cdot b \]
   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. sub-neg 100.0%

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

      3. add-sqr-sqrt 64.9%

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

      4. sqrt-unprod 97.3%

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

      5. sqr-neg 97.3%

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

      6. sqrt-prod 32.4%

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

      7. add-sqr-sqrt 89.2%

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

   4. Applied egg-rr 89.2%

      \[\leadsto \color{blue}{\left(a + b\right) \cdot \left(a + b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{+149}:\\ \;\;\;\;a \cdot a - b \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(b + a\right) \cdot \left(b + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.3% accurate, 1.0× speedup

Math

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

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 92.6%

   \[a \cdot a - b \cdot b \]
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. sub-neg 100.0%

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

   3. add-sqr-sqrt 49.9%

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

   4. sqrt-unprod 73.1%

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

   5. sqr-neg 73.1%

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

   6. sqrt-prod 25.5%

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

   7. add-sqr-sqrt 54.1%

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

4. Applied egg-rr 54.1%

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

5. Final simplification 54.1%

   \[\leadsto \left(b + a\right) \cdot \left(b + a\right) \]
6. 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 2024115 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

  :alt
  (* (+ a b) (- a b))

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