Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	284×	pre	80	false
5.0ms	256×	pre	80	true

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	97	11
4	179	11
5	293	11
6	458	11
7	1418	11
done	5000	11

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 13.8b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
0.0b	(- (* a a) (* b b))
13.4b	(/ (- (* a a) (* b b)) (* a a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`sqrt-prod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 52

Calls

3 calls:

1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
4.0ms	(- (* a a) (* b b))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

series26.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
6.0ms	(- (* a a) (* b b))
9.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify857.0ms

Counts

61 → 61

Iterations

Useful iterations: done (855.0ms)

Iter	Nodes	Cost
0	90	893
1	224	771
2	791	676
done	5000	668

prune85.0ms

Filtered

43 candidates to 61 candidates (-41.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	2	63

Merged error: 0.0b

Counts

63 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ a b) a)
0.0b	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b	(/ (- a b) a)
0.0b	(* (/ (+ a b) a) (/ (- a b) a))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 143

Calls

4 calls:

6.0ms	(/ (+ a b) a)
2.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
9.0ms	(/ (- a b) a)
17.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series29.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (+ a b) a)
10.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
5.0ms	(/ (- a b) a)
10.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify1.1s

Counts

155 → 155

Iterations

Useful iterations: 2 (512.0ms)

Iter	Nodes	Cost
0	182	1937
1	485	1843
2	1784	1679
done	5001	1679

prune181.0ms

Filtered

110 candidates to 155 candidates (-40.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	154	3	157

Merged error: 0b

Counts

157 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a b))
0.0b	(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
0.1b	(/ (sqrt (- a b)) (sqrt a))
0.1b	(/ (sqrt (- a b)) (sqrt a))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

183×	`sqrt-prod`
144×	`times-frac`
141×	`add-sqr-sqrt`
140×	`*-un-lft-identity`
98×	`add-cube-cbrt`
52×	`associate-r`
49×	`add-exp-log` `add-cbrt-cube`
21×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`cbrt-undiv` `div-exp`
12×	`associate-/r*`
10×	`pow1`
6×	`sqrt-div`
5×	`frac-times` `associate-*l/`
4×	`associate-/l/` `add-log-exp`
3×	`flip3--` `associate-*r/` `pow-prod-down` `flip--` `div-inv`
2×	`sqrt-undiv` `frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 261

Calls

4 calls:

4.0ms	(sqrt (- a b))
31.0ms	(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
8.0ms	(/ (sqrt (- a b)) (sqrt a))
9.0ms	(/ (sqrt (- a b)) (sqrt a))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (- a b))
19.0ms	(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
11.0ms	(/ (sqrt (- a b)) (sqrt a))
12.0ms	(/ (sqrt (- a b)) (sqrt a))

simplify1.3s

Counts

273 → 273

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	258	5159
1	724	4583
2	3030	4045
done	5000	3839

prune217.0ms

Filtered

138 candidates to 273 candidates (-97.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	273	3	276

Merged error: 0b

Counts

276 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- a (/ (* b b) a))
0.0b	(sqrt (fabs (* (/ 1 a) (- a (/ (* b b) a)))))
0.2b	(* (/ 1 a) (- a (/ (* b b) a)))
13.0b	(/ (* b b) a)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-exp-log`
16×	`times-frac`
15×	`add-cube-cbrt`
14×	`add-cbrt-cube`
13×	`associate-l`
7×	`pow1`
6×	`associate-r` `add-log-exp`
5×	`prod-exp`
4×	`div-exp` `difference-of-squares`
3×	`cbrt-undiv` `sub-neg` `flip3--` `associate-/r*` `sqrt-prod` `flip--` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `div-inv` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l*`

Counts

4 → 95

Calls

4 calls:

5.0ms	(- a (/ (* b b) a))
2.0ms	(sqrt (fabs (* (/ 1 a) (- a (/ (* b b) a)))))
12.0ms	(* (/ 1 a) (- a (/ (* b b) a)))
5.0ms	(/ (* b b) a)

series28.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- a (/ (* b b) a))
8.0ms	(sqrt (fabs (* (/ 1 a) (- a (/ (* b b) a)))))
10.0ms	(* (/ 1 a) (- a (/ (* b b) a)))
4.0ms	(/ (* b b) a)

simplify1.4s

Counts

107 → 107

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	156	1415
1	371	1219
2	1137	1086
done	5000	1074

prune136.0ms

Filtered

74 candidates to 107 candidates (-44.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	107	3	110

Merged error: 0b

Counts

110 → 3

regimes106.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	11	13
done	11	13

end0.0ms

sample990.0ms

Algorithm

intervals

Results

285.0ms	8000×	body	80	valid
146.0ms	8000×	pre	80	true
142.0ms	7875×	pre	80	false

Details

sample37.0ms

simplify4.0s

prune9.0ms

localize12.0ms

rewrite15.0ms

series26.0ms

simplify857.0ms

prune85.0ms

localize9.0ms

rewrite39.0ms

series29.0ms

simplify1.1s

prune181.0ms

localize12.0ms

rewrite66.0ms

series52.0ms

simplify1.3s

prune217.0ms

localize12.0ms

rewrite27.0ms

series28.0ms

simplify1.4s

prune136.0ms

regimes106.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample990.0ms

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