Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	256×	pre	80	true
5.0ms	256×	body	80	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	18	7
2	38	7
3	57	7
4	58	7
done	58	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* a (+ (+ b c) d))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `associate-r`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube` `distribute-lft-out`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp` `unswap-sqr`

Counts

1 → 24

Calls

1 calls:

39.0ms

(* a (+ (+ b c) d))

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

(* a (+ (+ b c) d))

simplify770.0ms

Counts

27 → 27

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	52	255
1	146	240
2	485	212
3	2128	212
done	5000	212

prune52.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* a (+ b c))
0.1b	(+ (* a (+ b c)) (* a d))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-r` `add-cbrt-cube` `add-log-exp`
3×	`associate-l`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

10.0ms	(* a (+ b c))
5.0ms	(+ (* a (+ b c)) (* a d))

series58.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* a (+ b c))
34.0ms	(+ (* a (+ b c)) (* a d))

simplify1.1s

Counts

43 → 43

Iterations

Useful iterations: 3 (251.0ms)

Iter	Nodes	Cost
0	73	417
1	222	351
2	708	325
3	2645	323
done	5001	323

prune81.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ b c) d))
0.4b	(* (sqrt a) (sqrt (+ (+ b c) d)))
0.4b	(* (sqrt a) (sqrt (+ (+ b c) d)))
0.5b	(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

68×	`pow1`
41×	`pow-prod-down`
30×	`add-sqr-sqrt`
29×	`sqrt-prod`
28×	`*-un-lft-identity`
21×	`sqrt-pow1` `pow1/2`
20×	`add-exp-log` `add-cbrt-cube`
18×	`sqrt-div` `associate-*r/`
17×	`associate-r`
13×	`add-cube-cbrt` `associate-l`
10×	`prod-exp` `cbrt-unprod`
9×	`flip3-+` `flip-+` `distribute-lft-out`
8×	`pow-prod-up` `unswap-sqr`
7×	`sqrt-unprod`
6×	`pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `associate-*l/`
1×	`pow2` `rem-sqrt-square` `swap-sqr` `rem-square-sqrt`

Counts

4 → 137

Calls

4 calls:

17.0ms	(sqrt (+ (+ b c) d))
40.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
41.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
90.0ms	(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (+ b c) d))
171.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
175.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
51.0ms	(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))

simplify626.0ms

Counts

149 → 149

Iterations

Useful iterations: done (622.0ms)

Iter	Nodes	Cost
0	162	2281
1	421	1733
2	1517	1535
done	5000	1505

prune279.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt a) (sqrt (+ (+ b c) d)))
0.4b	(* (sqrt a) (sqrt (+ (+ b c) d)))
0.5b	(* (* (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))) (sqrt (* (sqrt a) (sqrt (+ (+ b c) d))))) (* (sqrt a) (sqrt (+ (+ b c) d))))
0.5b	(* (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))) (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))))

rewrite587.0ms

Algorithm

rewrite-expression-head

Rules

277×	`pow1`
200×	`sqrt-pow1`
151×	`pow-prod-down`
118×	`sqrt-div`
94×	`pow1/2`
89×	`pow-prod-up`
80×	`associate-*r/`
35×	`flip3-+` `flip-+`
34×	`add-sqr-sqrt`
32×	`frac-times`
28×	`sqrt-prod`
27×	`pow-sqr`
26×	`*-un-lft-identity`
22×	`add-exp-log` `add-cbrt-cube`
21×	`associate-r`
17×	`associate-l`
16×	`add-cube-cbrt` `associate-*l/`
15×	`pow-plus`
11×	`prod-exp` `cbrt-unprod`
9×	`unswap-sqr`
6×	`sqrt-unprod` `distribute-lft-out`
4×	`swap-sqr` `*-commutative` `add-log-exp`
1×	`pow2` `rem-square-sqrt`

Counts

4 → 241

Calls

4 calls:

41.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
41.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
392.0ms	(* (* (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))) (sqrt (* (sqrt a) (sqrt (+ (+ b c) d))))) (* (sqrt a) (sqrt (+ (+ b c) d))))
95.0ms	(* (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))) (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
171.0ms	(* (sqrt a) (sqrt (+ (+ b c) d)))
50.0ms	(* (* (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))) (sqrt (* (sqrt a) (sqrt (+ (+ b c) d))))) (* (sqrt a) (sqrt (+ (+ b c) d))))
173.0ms	(* (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))) (sqrt (* (sqrt a) (sqrt (+ (+ b c) d)))))

simplify70.0ms

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	249	5583