Details

sample63.0ms

Algorithm

intervals

Results

11.0ms	33×	body	2560	valid
10.0ms	176×	body	80	valid
8.0ms	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

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	76	16
4	90	16
5	98	16
done	98	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

localize14.0ms

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)))

rewrite30.0ms

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))
8.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 3 (436.0ms)

Iter	Nodes	Cost
0	151	1588
1	377	1487
2	1275	1337
3	4944	1327
done	5000	1327

prune199.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	72	12	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	12	85

Merged error: 5.7b

Counts

85 → 12

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)))

rewrite24.0ms

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))
8.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
10.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
18.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: 3 (378.0ms)

Iter	Nodes	Cost
0	120	1002
1	277	905
2	998	831
3	4085	825
done	5000	825

prune141.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	71	13	84

Merged error: 5.7b

Counts

84 → 13

localize16.0ms

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)))

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-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:

19.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
10.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify511.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (179.0ms)

Iter	Nodes	Cost
0	217	2444
1	596	2244
2	2175	1962
done	5001	1962

prune210.0ms

Filtered

80 candidates to 119 candidates (-48.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	120	12	132

Merged error: 5.7b

Counts

132 → 12

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)))

rewrite24.0ms

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)
5.0ms	(- (* 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)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
10.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: 3 (380.0ms)

Iter	Nodes	Cost
0	120	1002
1	277	905
2	998	831
3	4099	825
done	5000	825

prune91.0ms

Filtered

50 candidates to 72 candidates (-44.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	71	13	84

Merged error: 5.7b

Counts

84 → 13

regimes579.0ms

Accuracy

84.4% (4.5b remaining)

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

bsearch60.0ms

Steps

Iters	Range		Point
7	2.951159271200378e-80	1.7529870675191086e-78	4.6400941224451665e-79
9	-1.5966504054646543e+104	-1.4637683111029664e+99	-1.5731675121056404e+104

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	40
1	32	40
done	32	40

end0.0ms

sample1.8s

Algorithm

intervals

Results

349.0ms	1070×	body	2560	valid
342.0ms	5828×	body	80	valid
248.0ms	906×	body	1280	valid
166.0ms	2970×	body	80	nan
109.0ms	484×	body	640	valid
50.0ms	129×	body	5120	valid
32.0ms	200×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample63.0ms

simplify40.0ms

prune8.0ms

localize14.0ms

rewrite30.0ms

series73.0ms

simplify1.2s

prune199.0ms

localize11.0ms

rewrite24.0ms

series48.0ms

simplify1.1s

prune141.0ms

localize16.0ms

rewrite39.0ms

series73.0ms

simplify511.0ms

prune210.0ms

localize11.0ms

rewrite24.0ms

series46.0ms

simplify1.1s

prune91.0ms

regimes579.0ms

bsearch60.0ms

simplify3.0ms

end0.0ms

sample1.8s

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