Details

sample60.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
9.0ms	176×	body	80	valid
7.0ms	29×	body	1280	valid
4.0ms	76×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	87	16
5	95	16
done	95	16

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 35.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

11.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
12.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts

84 → 84

Iterations

Useful iterations: 3 (956.0ms)

Iter	Nodes	Cost
0	151	1588
1	375	1487
2	1252	1337
3	4904	1327
done	5000	1327

prune202.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	71	13	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	14	85

Merged error: 5.7b

Counts

85 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
9.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	120	1002
1	273	905
2	978	831
3	3810	825
done	5001	825

prune142.0ms

Filtered

50 candidates to 72 candidates (-44.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	72	14	86

Merged error: 5.7b

Counts

86 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`add-exp-log`
22×	`add-cube-cbrt` `associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 107

Calls

4 calls:

18.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
10.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.0s

Counts

119 → 119

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	217	2444
1	585	2232
2	1854	1962
done	5000	1962

prune201.0ms

Filtered

80 candidates to 119 candidates (-48.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	5	7	12
Picked	0	1	1
Done	0	1	1
Total	121	12	133

Merged error: 5.7b

Counts

133 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) (/ 1 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.5b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`add-exp-log`
22×	`add-cube-cbrt` `associate-l`
16×	`add-cbrt-cube`
13×	`associate-r`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 108

Calls

4 calls:

18.0ms	(* (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) (/ 1 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) (/ 1 a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.2s

Counts

120 → 120

Iterations

Useful iterations: 2 (368.0ms)

Iter	Nodes	Cost
0	219	2457
1	610	2248
2	1722	1972
done	5000	1972

prune171.0ms

Filtered

81 candidates to 120 candidates (-48.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	120	12	132

Merged error: 5.7b

Counts

132 → 12

regimes557.0ms

Accuracy

84.5% (4.4b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 34.6b

bsearch57.0ms

Steps

Iters	Range		Point
7	2.951159271200378e-80	1.7529870675191086e-78	4.6400941224451665e-79
9	-1.5966504054646543e+104	-1.4637683111029664e+99	-4.4199075788330844e+101

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	40
1	31	40
done	31	40

end0.0ms

sample1.7s

Algorithm

intervals

Results

345.0ms	1070×	body	2560	valid
327.0ms	5828×	body	80	valid
239.0ms	906×	body	1280	valid
166.0ms	2970×	body	80	nan
100.0ms	484×	body	640	valid
52.0ms	129×	body	5120	valid
30.0ms	200×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample60.0ms

simplify50.0ms

prune8.0ms

localize10.0ms

rewrite28.0ms

series68.0ms

simplify1.8s

prune202.0ms

localize11.0ms

rewrite25.0ms

series43.0ms

simplify2.4s

prune142.0ms

localize12.0ms

rewrite40.0ms

series69.0ms

simplify1.0s

prune201.0ms

localize12.0ms

rewrite39.0ms

series69.0ms

simplify1.2s

prune171.0ms

regimes557.0ms

bsearch57.0ms

simplify3.0ms

end0.0ms

sample1.7s

Profiling