Average Error: 0.0 → 0.0
Time: 1.8s
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 2019022 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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

Details

Time bar (total: 1.5s)Debug log

sample30.0ms

Algorithm
intervals
Results
21.0ms454×body80valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(- (* a a) (* b b))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×difference-of-squares
1×flip--
1×log1p-expm1-u
1×add-cube-cbrt
1×add-exp-log
1×prod-diff
1×diff-log
1×fma-neg
1×add-cbrt-cube
1×flip3--
1×*-un-lft-identity
1×sub-neg
1×pow1
1×expm1-log1p-u
1×add-sqr-sqrt
Counts
1 → 17
Calls
1 calls:
Slowest
2.0ms
(- (* a a) (* b b))

series22.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
22.0ms
(- (* a a) (* b b))

simplify66.0ms

Counts
8 → 20
Calls
8 calls:
Slowest
29.0ms
(/ (exp (* a a)) (exp (* b b)))
13.0ms
(fma a a (- (* b b)))
5.0ms
(fma (- b) b (* b b))
5.0ms
(- (pow a 2) (pow b 2))
5.0ms
(- (pow a 2) (pow b 2))

prune108.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune5.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s14356×body80valid