Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	234×	body	80	valid
3.0ms	26×	body	640	valid
2.0ms	16×	body	1280	valid
1.0ms	17×	body	320	valid
0.0ms	5×	body	160	valid

simplify26.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	27	9
3	78	9
4	242	9
5	523	9
6	926	9
7	1617	9
8	2126	9
9	2743	9
10	2890	9
11	3210	9
12	3282	9
13	3512	9
14	3640	9
15	3875	9
16	3899	9
done	3899	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- 1.0 x) (- 1.0 y))
1.6b	(+ x (* (- 1.0 x) (- 1.0 y)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`flip3--` `flip--`
5×	`associate-r` `associate-l`
4×	`pow1` `add-exp-log` `distribute-rgt-in` `frac-times` `add-cube-cbrt` `sub-neg` `associate-+r+` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 49

Calls

2 calls:

73.0ms	(* (- 1.0 x) (- 1.0 y))
14.0ms	(+ x (* (- 1.0 x) (- 1.0 y)))

series78.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* (- 1.0 x) (- 1.0 y))
43.0ms	(+ x (* (- 1.0 x) (- 1.0 y)))

simplify3.8s

Counts

55 → 55

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	101	691
1	277	649
2	1061	617
3	4798	611
done	5001	607

prune160.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (* y (- x 1.0)))
0.0b	(* y (- x 1.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

14.0ms	(+ 1.0 (* y (- x 1.0)))
43.0ms	(* y (- x 1.0))

series71.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ 1.0 (* y (- x 1.0)))
44.0ms	(* y (- x 1.0))

simplify1.7s

Counts

47 → 47

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	73	409
1	173	381
2	506	351
3	2212	351
done	5000	351

prune108.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (- x 1.0))
0.0b	(sqrt (+ 1.0 (* y (- x 1.0))))
0.0b	(sqrt (+ 1.0 (* y (- x 1.0))))
0.2b	(* (sqrt (+ 1.0 (* y (- x 1.0)))) (sqrt (+ 1.0 (* y (- x 1.0)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`sqrt-prod`
23×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt` `sqrt-div`
11×	`associate-r`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-l`
8×	`add-exp-log` `flip3-+` `swap-sqr` `add-cbrt-cube` `flip-+`
5×	`pow-prod-up` `unswap-sqr`
4×	`frac-times` `associate-*r/` `pow-prod-down` `add-log-exp`
3×	`pow-sqr`
2×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `distribute-lft-in` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod`
1×	`pow2` `flip3--` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

26.0ms	(* y (- x 1.0))
5.0ms	(sqrt (+ 1.0 (* y (- x 1.0))))
9.0ms	(sqrt (+ 1.0 (* y (- x 1.0))))
52.0ms	(* (sqrt (+ 1.0 (* y (- x 1.0)))) (sqrt (+ 1.0 (* y (- x 1.0)))))

series58.0ms

Calls

1 calls:

38.0ms

(* (sqrt (+ 1.0 (* y (- x 1.0)))) (sqrt (+ 1.0 (* y (- x 1.0)))))