Details

sample72.0ms

Algorithm

intervals

Results

48.0ms

689×

body

valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	29
1	51	29
2	134	29
3	317	29
4	694	29
5	1469	29
6	3214	29
done	5001	29

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
1.1b	(* (* b b) (+ 3.0 a))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`associate-r`
10×	`add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `flip-+` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

16.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
9.0ms	(* (* a a) (- 1.0 a))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
9.0ms	(* (* b b) (+ 3.0 a))

series49.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
6.0ms	(* (* a a) (- 1.0 a))
24.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(* (* b b) (+ 3.0 a))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: 2 (548.0ms)

Iter	Nodes	Cost
0	228	1603
1	663	1501
2	2752	1345
done	5001	1345

prune174.0ms

Filtered

71 candidates to 106 candidates (-49.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	4	107

Merged error: 0.2b

Counts

107 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
1.1b	(* (* b b) (+ 3.0 a))
7.8b	(sqrt (+ (* a a) (* b b)))
7.8b	(sqrt (+ (* a a) (* b b)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`sqrt-prod`
21×	`add-exp-log` `*-un-lft-identity`
19×	`add-cube-cbrt`
17×	`unswap-sqr`
14×	`associate-r`
12×	`swap-sqr` `prod-exp` `sqr-pow`
11×	`pow1` `associate-l` `add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
4×	`sqrt-div` `pow-prod-down` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 124

Calls

4 calls:

15.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
9.0ms	(* (* b b) (+ 3.0 a))
4.0ms	(sqrt (+ (* a a) (* b b)))
4.0ms	(sqrt (+ (* a a) (* b b)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0))
6.0ms	(* (* b b) (+ 3.0 a))
6.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

simplify940.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (263.0ms)

Iter	Nodes	Cost
0	172	3031
1	417	2282
2	1561	2102
done	5000	2102

prune194.0ms

Filtered

80 candidates to 136 candidates (-70.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	138	2	140

Merged error: 0b

Counts

140 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
1.1b	(* (* b b) (+ 3.0 a))
7.8b	(sqrt (+ (* a a) (* b b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1`
16×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
13×	`*-un-lft-identity`
12×	`associate-r`
9×	`add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`flip3-+` `associate-l` `flip-+`
4×	`distribute-rgt-in` `distribute-lft-in` `frac-add` `add-log-exp`
3×	`flip3--` `sqrt-prod` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

13.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
9.0ms	(* (* a a) (- 1.0 a))
11.0ms	(* (* b b) (+ 3.0 a))
4.0ms	(sqrt (+ (* a a) (* b b)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
6.0ms	(* (* a a) (- 1.0 a))
6.0ms	(* (* b b) (+ 3.0 a))
6.0ms	(sqrt (+ (* a a) (* b b)))

simplify1.2s

Counts

104 → 104

Iterations

Useful iterations: 2 (485.0ms)

Iter	Nodes	Cost
0	205	1529
1	605	1399
2	2735	1259
done	5001	1259

prune152.0ms

Filtered

69 candidates to 104 candidates (-50.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	104	2	106

Merged error: 0b

Counts

106 → 2

regimes103.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	32
1	27	32
done	27	32

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s

20932×

body

valid

Details

sample72.0ms

simplify3.0s

prune3.0ms

localize16.0ms

rewrite42.0ms

series49.0ms

simplify1.2s

prune174.0ms

localize19.0ms

rewrite37.0ms

series57.0ms

simplify940.0ms

prune194.0ms

localize18.0ms

rewrite40.0ms

series31.0ms

simplify1.2s

prune152.0ms

regimes103.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling