Details

sample219.0ms

Algorithm

intervals

Results

82.0ms	105×	body	320	valid
58.0ms	144×	body	160	valid
47.0ms	275×	body	80	nan
1.0ms	7×	body	80	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3455
4	1170
3	353
2	116
1	46
0	19

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize49.0ms

Local error

Found 4 expressions with local error:

8.6b	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ g h))))))
9.6b	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
27.8b	(sqrt (* (- g h) (+ g h)))
27.8b	(sqrt (* (- g h) (+ g h)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
12×	`frac-times`
10×	`pow1` `cbrt-div`
8×	`flip3-+` `flip3--` `associate-*r/` `flip-+` `flip--`
6×	`associate-*l/`
4×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
2×	`cbrt-prod` `pow1/2` `pow1/3` `pow-prod-down` `sqrt-prod`

Counts

4 → 70

Calls

4 calls:

7.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ g h))))))
63.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
9.0ms	(sqrt (* (- g h) (+ g h)))
9.0ms	(sqrt (* (- g h) (+ g h)))

series981.0ms

Counts

4 → 12

Calls

4 calls:

411.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ g h))))))
383.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
106.0ms	(sqrt (* (- g h) (+ g h)))
81.0ms	(sqrt (* (- g h) (+ g h)))

simplify1.6s

Counts

82 → 82

Iterations

Iter	Nodes
done	5005
2	1571
1	437
0	189

prune855.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 28.2b

localize49.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (* (- g h) (+ g h))) g)
9.6b	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
27.8b	(sqrt (* (- g h) (+ g h)))
27.8b	(sqrt (* (- g h) (+ g h)))

rewrite100.0ms

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` `insert-posit16`
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 → 70

Calls

4 calls:

18.0ms	(- (sqrt (* (- g h) (+ g h))) g)
53.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
9.0ms	(sqrt (* (- g h) (+ g h)))
19.0ms	(sqrt (* (- g h) (+ g h)))

series740.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (sqrt (* (- g h) (+ g h))) g)
467.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
88.0ms	(sqrt (* (- g h) (+ g h)))
73.0ms	(sqrt (* (- g h) (+ g h)))

simplify1.6s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1249
1	333
0	155

prune964.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 27.4b

localize63.0ms

Local error

Found 4 expressions with local error:

2.1b	(+ g (sqrt (* (- g h) (+ g h))))
2.2b	(- (sqrt (* (- g h) (+ g h))) g)
27.8b	(sqrt (* (- g h) (+ g h)))
27.8b	(sqrt (* (- g h) (+ g h)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1`
8×	`frac-times` `*-un-lft-identity` `add-log-exp`
7×	`flip3-+` `flip3--` `flip-+` `flip--`
6×	`add-sqr-sqrt`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

4.0ms	(+ g (sqrt (* (- g h) (+ g h))))
17.0ms	(- (sqrt (* (- g h) (+ g h))) g)
9.0ms	(sqrt (* (- g h) (+ g h)))
24.0ms	(sqrt (* (- g h) (+ g h)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ g (sqrt (* (- g h) (+ g h))))
99.0ms	(- (sqrt (* (- g h) (+ g h))) g)
85.0ms	(sqrt (* (- g h) (+ g h)))
105.0ms	(sqrt (* (- g h) (+ g h)))

simplify1.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1127
1	251
0	106

prune842.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 26.8b

localize75.0ms

Local error

Found 4 expressions with local error:

2.1b	(+ g (sqrt (* (- g h) (+ g h))))
2.2b	(- (sqrt (* (- g h) (+ g h))) g)
27.8b	(sqrt (* (- g h) (+ g h)))
27.8b	(sqrt (* (- g h) (+ g h)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1`
8×	`frac-times` `*-un-lft-identity` `add-log-exp`
7×	`flip3-+` `flip3--` `flip-+` `flip--`
6×	`add-sqr-sqrt`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

4.0ms	(+ g (sqrt (* (- g h) (+ g h))))
18.0ms	(- (sqrt (* (- g h) (+ g h))) g)
17.0ms	(sqrt (* (- g h) (+ g h)))
9.0ms	(sqrt (* (- g h) (+ g h)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ g (sqrt (* (- g h) (+ g h))))
112.0ms	(- (sqrt (* (- g h) (+ g h))) g)
99.0ms	(sqrt (* (- g h) (+ g h)))
76.0ms	(sqrt (* (- g h) (+ g h)))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1127
1	251
0	106

prune682.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 26.8b

regimes679.0ms

Accuracy

82.3% (0.5b remaining)

Error of 29.4b against oracle of 29.0b and baseline of 31.5b

bsearch604.0ms

Steps

Iters	Range		Point
7	1.6133446259110393e-168	1.1834318527527503e-166	1.1669440241605785e-166
10	-1.7568584363366094e-151	-1.5754220496330615e-165	-6.3921017940024375e-161

simplify16.0ms

Iterations

Iter	Nodes
done	68
2	68
1	60
0	47

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.1s	3731×	body	320	valid
2.4s	8090×	body	80	nan
2.0s	4114×	body	160	valid
31.0ms	155×	body	80	valid