Details

sample131.0ms

Algorithm

intervals

Results

22.0ms	31×	body	2560	valid
21.0ms	35×	body	1280	valid
20.0ms	173×	body	80	valid
9.0ms	20×	body	640	valid
9.0ms	82×	body	80	nan
4.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify424.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
7	94
6	93
5	91
4	83
3	68
2	39
1	21
0	12

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
0.9b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite204.0ms

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:

41.0ms	(* (* 3.0 a) c)
18.0ms	(- (* b b) (* (* 3.0 a) c))
117.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
25.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* 3.0 a) c)
80.0ms	(- (* b b) (* (* 3.0 a) c))
157.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
171.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify7.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5003
3	3583
2	916
1	298
0	124

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.8b

localize155.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
0.9b	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
22.2b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite164.0ms

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:

2.0ms	(cbrt c)
2.0ms	(cbrt c)
128.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
29.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series1.1s

Counts

4 → 12

Calls

4 calls:

347.0ms	(cbrt c)
342.0ms	(cbrt c)
186.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
195.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify7.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5005
3	3250
2	746
1	240
0	107

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.7b

localize313.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
0.9b	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
22.2b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite370.0ms

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:

133.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
162.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
31.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
41.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
199.0ms	(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
175.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
161.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify6.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2742
2	646
1	201
0	86

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.7b

localize687.0ms

Local error

Found 4 expressions with local error:

22.2b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
22.2b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite168.0ms

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:

40.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
40.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
41.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
41.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
201.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
189.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))
178.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify5.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2249
2	467
1	138
0	56

prune1.5s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 11.7b

regimes1.4s

Accuracy

85.6% (3.3b remaining)

Error of 15.2b against oracle of 11.9b and baseline of 34.6b

bsearch243.0ms

Steps

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

simplify16.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample3.4s

Algorithm

intervals

Results

987.0ms	1055×	body	2560	valid
601.0ms	5742×	body	80	valid
576.0ms	978×	body	1280	valid
333.0ms	2913×	body	80	nan
157.0ms	455×	body	640	valid
114.0ms	138×	body	5120	valid
66.0ms	257×	body	320	valid
48.0ms	118×	body	160	valid