Details

sample92.0ms

Algorithm

intervals

Results

29.0ms	133×	body	320	valid
20.0ms	294×	body	80	nan
17.0ms	118×	body	160	valid
0.0ms	5×	body	80	valid

simplify10.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	122	36
3	297	36
4	583	36
5	891	36
6	1079	36
7	1300	36
8	2491	36
done	5000	36

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize32.0ms

Local error

Found 4 expressions with local error:

6.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `flip--`
4×	`add-exp-log` `frac-times` `sqrt-div` `associate-*r/` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*l/` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

72.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
99.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
10.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

405.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
448.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
93.0ms	(sqrt (- (* g g) (* h h)))
63.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

72 → 72

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	177	1390
1	385	1217
2	1281	1121
done	5001	1072

prune655.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.4b

localize41.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
51.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
17.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
371.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
66.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

71 → 71

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	135	1086
1	286	956
2	846	870
3	3101	859
done	5000	836

prune670.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.9b

localize31.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

11.0ms	(- (* g g) (* h h))
81.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
10.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* g g) (* h h))
441.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
83.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))

simplify2.1s

Counts

71 → 71

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	135	1086
1	286	956
2	846	870
3	3101	859
done	5000	836

prune665.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 27.9b

localize56.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* g g) (* h h))
1.6b	(- (* g g) (* h h))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

17.0ms	(- (* g g) (* h h))
11.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* g g) (* h h))
62.0ms	(- (* g g) (* h h))
66.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))

simplify3.6s

Counts

70 → 70

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	55	808
1	120	744
2	301	640
3	975	640
4	4860	640
done	5000	640

prune460.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 27.9b

regimes1.4s

Accuracy

48% (1.9b remaining)

Error of 32.0b against oracle of 30.1b and baseline of 33.8b

bsearch257.0ms

Steps

Iters	Range		Point
9	1.6490879497201852e-148	1.926606898512398e-141	1.684852146070775e-148

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	90
1	40	90
done	40	90

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.8s	8064×	body	80	nan
1.6s	3719×	body	320	valid
1.5s	4126×	body	160	valid
16.0ms	155×	body	80	valid