Details

sample189.0ms

Algorithm

intervals

Results

84.0ms	122×	body	320	valid
32.0ms	280×	body	80	nan
30.0ms	130×	body	160	valid
1.0ms	4×	body	80	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4583
7	1834
6	1286
5	947
4	584
3	298
2	122
1	43
0	19

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize35.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
9.5b	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
26.5b	(sqrt (* (+ g h) (- g h)))
26.5b	(sqrt (* (+ g h) (- g h)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

550×	`times-frac`
312×	`add-sqr-sqrt` `*-un-lft-identity`
226×	`cbrt-prod`
224×	`add-cube-cbrt`
44×	`distribute-lft-out--` `difference-of-squares`
21×	`div-inv`
16×	`sqrt-div`
10×	`frac-times` `pow1`
8×	`flip3--` `flip--`
6×	`cbrt-div` `flip3-+` `associate-*r/` `associate-/r/` `flip-+`
5×	`associate-*l/`
4×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1/2` `pow1/3` `pow-prod-down` `sqrt-prod`

Counts

4 → 286

Calls

4 calls:

18.0ms	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
37.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
15.0ms	(sqrt (* (+ g h) (- g h)))
9.0ms	(sqrt (* (+ g h) (- g h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

491.0ms	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
363.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
92.0ms	(sqrt (* (+ g h) (- g h)))
77.0ms	(sqrt (* (+ g h) (- g h)))

simplify1.1s

Counts

298 → 298

Iterations

Iter	Nodes
done	5001
1	2242
0	976

prune3.1s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 28.9b

localize62.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (sqrt (* (+ h g) (- g h))) g)
7.6b	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
26.5b	(sqrt (* (+ h g) (- g h)))
26.5b	(sqrt (* (+ g h) (- g h)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`frac-times` `pow1`
9×	`flip3--` `flip--`
6×	`add-sqr-sqrt` `-un-lft-identity` `flip3-+` `associate-r/` `flip-+` `add-log-exp`
5×	`cbrt-div` `associate-*l/`
4×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

17.0ms	(- (sqrt (* (+ h g) (- g h))) g)
35.0ms	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
16.0ms	(sqrt (* (+ h g) (- g h)))
10.0ms	(sqrt (* (+ g h) (- g h)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (sqrt (* (+ h g) (- g h))) g)
500.0ms	(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
97.0ms	(sqrt (* (+ h g) (- g h)))
79.0ms	(sqrt (* (+ g h) (- g h)))

simplify793.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1785
1	450
0	209

prune1.0s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 28.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 2.0 (/ 1.0 a)))
2.6b	(- (sqrt (* (+ h g) (- g h))) g)
26.5b	(sqrt (* (+ h g) (- g h)))
26.5b	(sqrt (* (- g h) (+ h g)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
44×	`cbrt-prod`
41×	`add-sqr-sqrt` `*-un-lft-identity`
39×	`add-cube-cbrt`
16×	`sqrt-div`
10×	`pow1`
8×	`frac-times`
7×	`flip3--` `flip--`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `div-inv`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`cbrt-div` `sub-neg` `pow1/3` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 105

Calls

4 calls:

11.0ms	(cbrt (/ 2.0 (/ 1.0 a)))
35.0ms	(- (sqrt (* (+ h g) (- g h))) g)
15.0ms	(sqrt (* (+ h g) (- g h)))
16.0ms	(sqrt (* (- g h) (+ h g)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(cbrt (/ 2.0 (/ 1.0 a)))
134.0ms	(- (sqrt (* (+ h g) (- g h))) g)
99.0ms	(sqrt (* (+ h g) (- g h)))
104.0ms	(sqrt (* (- g h) (+ h g)))

simplify1.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	2459
1	636
0	327

prune1.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 28.6b

localize80.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (sqrt (* (+ h g) (- g h))) g)
7.6b	(cbrt (* (- (/ (+ g (sqrt (* (- g h) (+ h g)))) a)) (/ 1.0 2.0)))
26.5b	(sqrt (* (- g h) (+ h g)))
26.5b	(sqrt (* (+ h g) (- g h)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1`
9×	`frac-times`
7×	`flip3--` `flip--`
6×	`add-sqr-sqrt` `*-un-lft-identity` `flip3-+` `flip-+` `add-log-exp`
5×	`associate-l/` `associate-r/`
4×	`sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`cbrt-div`
2×	`pow1/2` `pow-prod-down` `sqrt-prod` `distribute-neg-frac`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

20.0ms	(- (sqrt (* (+ h g) (- g h))) g)
24.0ms	(cbrt (* (- (/ (+ g (sqrt (* (- g h) (+ h g)))) a)) (/ 1.0 2.0)))
19.0ms	(sqrt (* (- g h) (+ h g)))
18.0ms	(sqrt (* (+ h g) (- g h)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (sqrt (* (+ h g) (- g h))) g)
326.0ms	(cbrt (* (- (/ (+ g (sqrt (* (- g h) (+ h g)))) a)) (/ 1.0 2.0)))
76.0ms	(sqrt (* (- g h) (+ h g)))
113.0ms	(sqrt (* (+ h g) (- g h)))

simplify742.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
2	1721
1	457
0	217

prune1.1s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 28.6b

regimes1.1s

Accuracy

68.5% (0.9b remaining)

Error of 32.0b against oracle of 31.1b and baseline of 33.9b

bsearch336.0ms

Steps

Iters	Range		Point
11	-5.680280950886319e-157	-1.2554389614223213e-180	-1.5789647186735228e-162

simplify6.0ms

Iterations

Iter	Nodes
done	53
2	53
1	50
0	41

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	3683×	body	320	valid
1.6s	4170×	body	160	valid
1.5s	8083×	body	80	nan
21.0ms	147×	body	80	valid