Details

sample618.0ms

Algorithm

intervals

Results

471.0ms	257×	body	80	nan
68.0ms	106×	body	320	valid
51.0ms	141×	body	160	valid
2.0ms	9×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
5	2018
4	871
3	351
2	114
1	44
0	19

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.5b

localize36.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
8.7b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

21.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
18.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
6.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series797.0ms

Counts

4 → 12

Calls

4 calls:

351.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
308.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
78.0ms	(sqrt (- (* g g) (* h h)))
59.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

77 → 77

Iterations

Iter	Nodes
3	3345
2	1065
1	423
0	205

prune1.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.2b

localize56.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.4b	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
16.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
10.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* g g) (* h h))
333.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
66.0ms	(sqrt (- (* g g) (* h h)))
62.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
3	3207
2	932
1	328
0	154

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.7b

localize55.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
3.4b	(- (* g g) (* h h))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
9.0ms	(- (* g g) (* h h))
12.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* g g) (* h h))
47.0ms	(- (* g g) (* h h))
74.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))

simplify4.1s

Counts

70 → 70

Iterations

Iter	Nodes
4	8597
3	1562
2	358
1	124
0	55

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.7b

localize71.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
3.4b	(- (* g g) (* h h))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
6.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
49.0ms	(- (* g g) (* h h))
76.0ms	(sqrt (- (* g g) (* h h)))
87.0ms	(sqrt (- (* g g) (* h h)))

simplify4.3s

Counts

70 → 70

Iterations

Iter	Nodes
4	8597
3	1562
2	358
1	124
0	55

prune1.3s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 30.7b

regimes879.0ms

Accuracy

25.3% (1.4b remaining)

Error of 30.5b against oracle of 29.1b and baseline of 31.0b

bsearch556.0ms

Steps

Iters	Range		Point
8	1.101565841888519e-09	7.101228369635622e-07	4.929200091909158e-08
9	4.357350291335334e-183	4.09161270623166e-175	4.0263109172966606e-175

simplify24.0ms

Iterations

Iter	Nodes
2	55
1	55
0	45

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.9s	3697×	body	320	valid
2.3s	4150×	body	160	valid
2.0s	7982×	body	80	nan
393.0ms	153×	body	80	valid