Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
Cost: 448
\[a \cdot a - b \cdot b\]
↓
\[\left(a + b\right) \cdot \left(a - b\right)\]
a \cdot a - b \cdot b
↓
\left(a + b\right) \cdot \left(a - b\right)
(FPCore (a b) :precision binary64 (- (* a a) (* b b)))
↓
(FPCore (a b) :precision binary64 (* (+ a b) (- a b)))
double code(double a, double b) {
	return (a * a) - (b * b);
}
↓
double code(double a, double b) {
	return (a + b) * (a - b);
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(a + b\right) \cdot \left(a - b\right)\]

Alternatives

Alternative 1
Error12.8
Cost849
\[\begin{array}{l} \mathbf{if}\;a \leq -3.224450515213971 \cdot 10^{-37} \lor \neg \left(a \leq -5.926855860335571 \cdot 10^{-51} \lor \neg \left(a \leq -5.2058524450127765 \cdot 10^{-65}\right) \land a \leq 7.150922772501069 \cdot 10^{-13}\right):\\ \;\;\;\;a \cdot a\\ \mathbf{else}:\\ \;\;\;\;-b \cdot b\\ \end{array}\]
Alternative 2
Error28.5
Cost192
\[a \cdot a\]
Alternative 3
Error55.3
Cost64
\[0\]
Alternative 4
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[a \cdot a - b \cdot b\]
  2. Using strategy rm

  3. Applied difference-of-squares_binary64_34570.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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