Details

sample336.0ms

Algorithm

intervals

Results

7.0ms	206×	body	80	valid
5.0ms	28×	body	2560	valid
5.0ms	28×	body	1280	valid
4.0ms	105×	body	80	nan
2.0ms	13×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid
0.0ms	4×	body	320	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (31.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

64.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

92 → 92

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	151	1534
1	355	1440
2	1001	1266
3	2792	1252
done	5000	1249

prune239.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

57.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
37.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

174 → 174

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	258	3976
1	553	3485
2	1282	3208
3	3344	3128
done	5000	3098

prune271.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

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×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

43.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	78	1064
1	182	944
2	496	884
3	1172	876
4	2461	864
done	5000	862

prune215.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
17.6b	(/ (- 0 (* a c)) a)
21.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

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:

32.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(/ (- 0 (* a c)) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- 0 (* a c)) a)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	138	1049
1	312	913
2	981	835
3	3975	774
done	5001	774

prune196.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.2b

regimes219.0ms

Accuracy

92.9% (1.7b remaining)

Error of 7.0b against oracle of 5.3b and baseline of 29.5b

bsearch89.0ms

Steps

Iters	Range	Point
6	2.0335150395734557e+19	1.0746392320557105e+20	1.0610691325078738e+20
9	-1.1485903349781853e-287	-4.3901224953656154e-293	-8.600451188821801e-288
2	-2.2142651020916072e+95	-1.9471150030455292e+95	-2.1808713397108476e+95

Iters

Range

Point

2.0335150395734557e+19

1.0746392320557105e+20

1.0610691325078738e+20

-1.1485903349781853e-287

-4.3901224953656154e-293

-8.600451188821801e-288

-2.2142651020916072e+95

-1.9471150030455292e+95

-2.1808713397108476e+95

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	58
1	41	58
done	41	58

end0.0ms

sample1.1s

Algorithm

intervals

Results

195.0ms	1044×	body	2560	valid
191.0ms	5929×	body	80	valid
135.0ms	905×	body	1280	valid
84.0ms	2855×	body	80	nan
54.0ms	466×	body	640	valid
23.0ms	102×	body	5120	valid
19.0ms	223×	body	320	valid
5.0ms	92×	body	160	valid