Details

sample85.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify785.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2244
3	434
2	100
1	33
0	15

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
3.8b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite929.0ms

Algorithm

rewrite-expression-head

Rules

4332×	`*-un-lft-identity`
2696×	`times-frac`
2173×	`distribute-lft-out`
778×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1221

Calls

4 calls:

114.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
206.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
340.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
161.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
193.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
198.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
129.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.2s

Counts

1233 → 1233

Iterations

Iter	Nodes
2	4172
1	1424
0	605

prune13.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
0.5b	(/ 1 (sqrt (+ 2 (+ beta alpha))))
0.6b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
3.8b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite7.4s

Algorithm

rewrite-expression-head

Rules

199267×	`*-un-lft-identity`
178314×	`times-frac`
91485×	`distribute-lft-out`
50929×	`add-sqr-sqrt` `add-cube-cbrt`
43685×	`sqrt-prod`
5984×	`associate-/r/`
3008×	`div-inv`
2977×	`flip3-+` `flip-+`
2956×	`sqrt-div`
1310×	`associate-/r*`
75×	`add-exp-log`
63×	`associate-/l*`
54×	`div-exp`
45×	`add-cbrt-cube`
29×	`cbrt-undiv`
6×	`pow1`
5×	`rec-exp` `1-exp`
4×	`clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`
3×	`pow-flip`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 40388

Calls

4 calls:

465.0ms	(/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
29.0ms	(/ 1 (sqrt (+ 2 (+ beta alpha))))
181.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
164.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
107.0ms	(/ 1 (sqrt (+ 2 (+ beta alpha))))
222.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))
144.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify9.6m

Iterations

Iter	Nodes
0	9043