Details

sample208.0ms

Algorithm

intervals

Results

61.0ms	306×	body	80	nan
60.0ms	131×	body	320	valid
37.0ms	122×	body	160	valid
0.0ms	3×	body	80	valid

simplify11.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (25.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize38.0ms

Local error

Found 4 expressions with local error:

6.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite161.0ms

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:

78.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
42.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

463.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
453.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
62.0ms	(sqrt (- (* g g) (* h h)))
86.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

72 → 72

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	177	1390
1	385	1217
2	1281	1121
done	5000	1072

prune642.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 34.6b

localize34.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
6.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite111.0ms

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:

8.0ms	(- (* g g) (* h h))
82.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
10.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
506.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
82.0ms	(sqrt (- (* g g) (* h h)))
85.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

71 → 71

Iterations

Useful iterations: done (1.9s)

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

prune800.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 34.0b

localize29.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite62.0ms

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))
17.0ms	(- (* g g) (* h h))
15.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* g g) (* h h))
38.0ms	(- (* g g) (* h h))
91.0ms	(sqrt (- (* g g) (* h h)))
97.0ms	(sqrt (- (* g g) (* h h)))

simplify3.6s

Counts

70 → 70

Iterations

Useful iterations: 2 (94.0ms)

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

prune510.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 34.0b

localize29.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite63.0ms

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:

13.0ms	(- (* g g) (* h h))
13.0ms	(- (* g g) (* h h))
14.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* g g) (* h h))
44.0ms	(- (* g g) (* h h))
64.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

70 → 70

Iterations

Useful iterations: 2 (58.0ms)

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

prune391.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 34.0b

regimes958.0ms

Accuracy

66.8% (1.2b remaining)

Error of 31.9b against oracle of 30.7b and baseline of 34.3b

bsearch358.0ms

Steps

Iters	Range		Point
12	-8.46579077171639e-185	-2.054593841555946e-229	-8.359356862874829e-185

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	83
1	41	83
done	41	83

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.4s	3717×	body	320	valid
1.3s	8068×	body	80	nan
1.2s	4133×	body	160	valid
345.0ms	150×	body	80	valid