Details

sample138.0ms

Algorithm

intervals

Results

29.0ms	31×	body	2560	valid
26.0ms	173×	body	80	valid
26.0ms	35×	body	1280	valid
12.0ms	82×	body	80	nan
12.0ms	20×	body	640	valid
6.0ms	5×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	2×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	109
5	109
4	101
3	80
2	42
1	21
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
0.4b	(- (* b b) (* (* 3 a) c))
0.9b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

22.0ms	(* (* 3 a) c)
15.0ms	(- (* b b) (* (* 3 a) c))
38.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 3 a) c)
51.0ms	(- (* b b) (* (* 3 a) c))
108.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
102.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1556
1	306
0	123

prune429.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
0.9b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
22.2b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt c)
1.0ms	(cbrt c)
55.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
10.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt c)
331.0ms	(cbrt c)
143.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
106.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
2	1013
1	246
0	106

prune434.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
0.9b	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
22.2b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `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` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

56.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
47.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
14.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
7.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
157.0ms	(- (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
122.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
126.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify874.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	860
1	207
0	85

prune674.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.5b

localize95.0ms

Local error

Found 4 expressions with local error:

22.2b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
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`

Counts

4 → 64

Calls

4 calls:

13.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
15.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
8.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
8.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
115.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
134.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
108.0ms	(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify2.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	4224
2	598
1	144
0	55

prune679.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.5b

regimes714.0ms

Accuracy

85.5% (3.2b remaining)

Error of 15.0b against oracle of 11.7b and baseline of 33.9b

bsearch179.0ms

Steps

Iters	Range		Point
6	1.6664801848567985e-94	1.3864776888564433e-93	1.3635892865650846e-93
9	-2.409563002992963e+162	-2.0274263258127503e+155	-2.0519886074223697e+155

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.3s	1055×	body	2560	valid
990.0ms	5742×	body	80	valid
633.0ms	978×	body	1280	valid
619.0ms	138×	body	5120	valid
336.0ms	2913×	body	80	nan
260.0ms	455×	body	640	valid
112.0ms	257×	body	320	valid
27.0ms	118×	body	160	valid