Details

sample196.0ms

Algorithm

intervals

Results

68.0ms	104×	body	320	valid
51.0ms	146×	body	160	valid
47.0ms	285×	body	80	nan
1.0ms	6×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.3b

localize74.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
9.1b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite83.0ms

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` `insert-posit16` `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 → 69

Calls

4 calls:

13.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
30.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
23.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series786.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
307.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
76.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
3	3357
2	1069
1	426
0	208

prune1.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.8b

localize64.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
9.1b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`cbrt-prod` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `times-frac` `add-log-exp`
5×	`difference-of-squares`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `pow1/3` `diff-log` `div-inv` `distribute-lft-out--`

Counts

4 → 68

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
24.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
15.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
314.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
60.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify786.0ms

Counts

80 → 80

Iterations

Iter	Nodes
3	2664
2	767
1	322
0	158

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.3b

localize57.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite33.0ms

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` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 62

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
8.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
47.0ms	(- (* g g) (* h h))
75.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))

simplify4.8s

Counts

74 → 74

Iterations

Iter	Nodes
4	9006
3	1622
2	376
1	127
0	57

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 32.3b

localize57.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
9.1b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
31.7b	(sqrt (- (* g g) (* h h)))
31.7b	(sqrt (- (* g g) (* h h)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`cbrt-prod` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `times-frac` `add-log-exp`
5×	`difference-of-squares`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `pow1/3` `diff-log` `div-inv` `distribute-lft-out--`

Counts

4 → 68

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
28.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
8.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* g g) (* h h))
309.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
87.0ms	(sqrt (- (* g g) (* h h)))
75.0ms	(sqrt (- (* g g) (* h h)))

simplify860.0ms

Counts

80 → 80

Iterations

Iter	Nodes
3	2664
2	767
1	322
0	158

prune1.4s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.3b

regimes911.0ms

Accuracy

55.2% (1.6b remaining)

Error of 31.4b against oracle of 29.9b and baseline of 33.4b

bsearch442.0ms

Steps

Iters	Range		Point
11	-4.5596823755857694e-157	-7.384045806005983e-186	-1.5974918824598454e-162

simplify13.0ms

Iterations

Iter	Nodes
2	43
1	43
0	35

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.4s	3746×	body	320	valid
2.0s	4124×	body	160	valid
1.6s	8203×	body	80	nan
61.0ms	130×	body	80	valid