Details

sample249.0ms

Algorithm

intervals

Results

85.0ms	128×	body	320	valid
82.0ms	122×	body	160	valid
53.0ms	251×	body	80	nan
1.0ms	6×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.5b

localize54.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
7.5b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite85.0ms

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:

33.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
28.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
15.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series800.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
304.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
61.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
3	3357
2	1069
1	426
0	208

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.3b

localize54.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
6.5b	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite45.0ms

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` `insert-posit16`
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 → 63

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
14.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
13.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* g g) (* h h))
369.0ms	(cbrt (* (+ g (sqrt (- (* g g) (* h h)))) (/ -1/2 a)))
69.0ms	(sqrt (- (* g g) (* h h)))
75.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

75 → 75

Iterations

Iter	Nodes
3	3296
2	908
1	330
0	157

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.9b

localize77.0ms

Local error

Found 4 expressions with local error:

30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

8.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (- (* g g) (* h h)))
92.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
5	3357
4	1098
3	468
2	203
1	97
0	45

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.9b

localize122.0ms

Local error

Found 4 expressions with local error:

30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))
30.3b	(sqrt (- (* g g) (* h h)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

15.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))
89.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
5	3357
4	1098
3	468
2	203
1	97
0	45

prune1.8s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 29.9b

regimes1.6s

Accuracy

60.4% (1.5b remaining)

Error of 31.2b against oracle of 29.7b and baseline of 33.5b

bsearch431.0ms

Steps

Iters	Range		Point
11	5.135401024806697e-156	2.027058670868406e-136	5.209462070880178e-156

simplify14.0ms

Iterations

Iter	Nodes
2	41
1	41
0	34

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.0s	3714×	body	320	valid
2.0s	7829×	body	80	nan
1.5s	4111×	body	160	valid
29.0ms	175×	body	80	valid