Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
Internal Precision: 128
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]

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

Derivation

  1. Initial program 0.0

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

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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

Details

Time bar (total: 4.7s)Debug log

sample33.0ms

Algorithm
intervals

simplify12.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

12.0ms
(- (* a a) (* b b))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* a a) (* b b))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

4.0ms
(- (* a a) (* b b))

series23.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

23.0ms
(- (* a a) (* b b))

simplify70.0ms

Counts
8 → 20
Calls

8 calls. Slowest were:

20.0ms
(/ (exp (* a a)) (exp (* b b)))
15.0ms
(- (pow a 2) (pow b 2))
11.0ms
(- (pow a 2) (pow b 2))

prune165.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (+ a b) (- a b))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
1 → 31
Calls

1 calls. Slowest were:

8.0ms
(* (+ a b) (- a b))

series37.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

37.0ms
(* (+ a b) (- a b))

simplify2.4s

Counts
27 → 34
Calls

27 calls. Slowest were:

560.0ms
(* (+ (* a a) (- (* b b) (* a b))) (+ (* a a) (+ (* b b) (* a b))))
394.0ms
(* (+ (pow a 3) (pow b 3)) (- (pow a 3) (pow b 3)))
232.0ms
(* (- a b) (+ (* a a) (+ (* b b) (* a b))))

prune199.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals