Details

sample192.0ms

Algorithm

intervals

Results

17.0ms	38×	body	2560	valid
16.0ms	178×	body	80	valid
11.0ms	29×	body	1280	valid
6.0ms	79×	body	80	nan
3.0ms	11×	body	640	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

106.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
56.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

96 → 96

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	154	1624
1	361	1526
2	928	1426
3	2333	1418
done	5000	1410

prune387.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

222.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
58.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts

97 → 97

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	174	1603
1	415	1403
2	1167	1255
3	3468	1247
done	5001	1229

prune274.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.4b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.6b	(/ (- 0 (* c a)) a)
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`flip3--` `associate-/r` `sqrt-prod` `flip--` `associate-/l`
2×	`sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `sub0-neg` `pow1/2` `diff-log` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 70

Calls

4 calls:

18.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
29.0ms	(/ (- 0 (* c a)) a)
31.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b_2 b_2) (* a c))
133.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(/ (- 0 (* c a)) a)
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.6s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	140	1049
1	320	913
2	1004	805
3	3697	774
done	5000	774

prune319.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 0 c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.6b	(- (* b_2 b_2) (* a c))
1.4b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
20×	`times-frac`
16×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`distribute-lft-out`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`associate-/r*`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `sub0-neg` `pow1/2` `diff-log` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 86

Calls

4 calls:

67.0ms	(/ (- 0 c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(/ (- 0 c) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
65.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

98 → 98

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	152	1750
1	359	1560
2	944	1443
3	2596	1440
done	5000	1426

prune327.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.1b

regimes351.0ms

Accuracy

96.1% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 34.3b

bsearch228.0ms

Steps

Iters	Range	Point
4	9.936283634246925e+77	1.8488019868481542e+78	1.6082844052603056e+78
11	-1.0472779812871276e-269	-2.473343252086336e-295	-3.1400906193105714e-291
8	-6.990724105819741e+111	-2.6156774686163576e+108	-1.569310777886352e+111

Iters

Range

Point

9.936283634246925e+77

1.8488019868481542e+78

1.6082844052603056e+78

-1.0472779812871276e-269

-2.473343252086336e-295

-3.1400906193105714e-291

-6.990724105819741e+111

-2.6156774686163576e+108

-1.569310777886352e+111

simplify10.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	31	54
1	37	53
2	39	53
done	39	53

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.0s	1087×	body	2560	valid
812.0ms	936×	body	1280	valid
633.0ms	5805×	body	80	valid
218.0ms	2994×	body	80	nan
120.0ms	443×	body	640	valid
57.0ms	117×	body	5120	valid
44.0ms	113×	body	160	valid
36.0ms	211×	body	320	valid