Difference of squares

Average Error: 0.01% → 0%

Time: 1.5s

Precision: binary64

Cost: 448

Math

\[a \cdot a - b \cdot b \]

↓

\[\left(a - b\right) \cdot \left(a + b\right) \]

FPCore

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

↓

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

C

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

↓

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 * a) - (b * b)
end function

↓

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 * a) - (b * b);
}

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.01%
Target	0%
Herbie	0%

\[\left(a + b\right) \cdot \left(a - b\right) \]

Derivation

1. Initial program 0.01

   \[a \cdot a - b \cdot b \]

2. Applied egg-rr 0

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

3. Final simplification 0

   \[\leadsto \left(a - b\right) \cdot \left(a + b\right) \]

Alternatives

Alternative 1
Error	21.08%
Cost	786

\[\begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-13} \lor \neg \left(b \leq -3.4 \cdot 10^{-72} \lor \neg \left(b \leq -1.34 \cdot 10^{-107}\right) \land b \leq 5.5 \cdot 10^{-81}\right):\\ \;\;\;\;b \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot a\\ \end{array} \]

Alternative 2
Error	43.56%
Cost	192

\[a \cdot a \]

Reproduce

herbie shell --seed 2023102 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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