Average Error: 0.0 → 0.0
Time: 3.6s
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

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

Runtime

Time bar (total: 3.6s)Debug logProfile

start102.0ms

Algorithm
intervals

setup39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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))

series28.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

28.0ms
(- (* a a) (* b b))

simplify88.0ms

Counts
8 → 20
Calls

8 calls. Slowest were:

36.0ms
(/ (exp (* a a)) (exp (* b b)))
20.0ms
(fma a a (- (* b b)))
10.0ms
(- (pow a 2) (pow b 2))

prune157.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune6.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

herbie shell --seed 2018357 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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