Details

sample66.0ms

Algorithm

intervals

Results

22.0ms	117×	body	320	valid
15.0ms	136×	body	160	valid
12.0ms	246×	body	80	nan
0.0ms	3×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	119	36
3	284	36
4	529	36
5	772	36
6	944	36
7	1144	36
8	2472	36
done	5001	36

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize21.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite44.0ms

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:

16.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
314.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
43.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify480.0ms

Counts

72 → 72

Iterations

Useful iterations: done (478.0ms)

Iter	Nodes	Cost
0	177	1390
1	392	1217
2	1364	1121
done	5000	1088

prune399.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 32.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite30.0ms

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:

3.0ms	(- (* g g) (* h h))
19.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
48.0ms	(sqrt (- (* g g) (* h h)))
44.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

71 → 71

Iterations

Useful iterations: 3 (364.0ms)

Iter	Nodes	Cost
0	135	1086
1	290	956
2	987	870
3	3894	859
done	5000	859

prune408.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.9b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
1.4b	(- (* g g) (* h h))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite14.0ms

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:

2.0ms	(- (* g g) (* h h))
2.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(- (* g g) (* h h))
30.0ms	(- (* g g) (* h h))
44.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify942.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	55	808
1	122	744
2	423	640
3	1665	640
done	5001	640

prune396.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
1.4b	(- (* g g) (* h h))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite14.0ms

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:

2.0ms	(- (* g g) (* h h))
3.0ms	(- (* g g) (* h h))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (* g g) (* h h))
34.0ms	(- (* g g) (* h h))
43.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify939.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	55	808
1	122	744
2	423	640
3	1665	640
done	5001	640

prune336.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 31.9b

regimes591.0ms

Accuracy

65.6% (1.2b remaining)

Error of 31.6b against oracle of 30.3b and baseline of 33.9b

bsearch137.0ms

Steps

Iters	Range		Point
9	-1.4950050582891928e-169	-1.4248292396361266e-175	-1.2934885954313043e-169

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	66
1	39	66
done	39	66

end0.0ms

sample1.8s

Algorithm

intervals

Results

594.0ms	3698×	body	320	valid
453.0ms	4149×	body	160	valid
400.0ms	7929×	body	80	nan
12.0ms	153×	body	80	valid