Details

sample277.0ms

Algorithm

intervals

Results

17.0ms	41×	body	2560	valid
12.0ms	186×	body	80	valid
10.0ms	28×	body	1280	valid
7.0ms	108×	body	80	nan
5.0ms	17×	body	640	valid
4.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

68.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
50.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
48.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

103 → 103

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	156	1821
1	366	1727
2	1005	1611
3	2773	1595
done	5001	1593

prune414.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.1b	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.3b	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`sqrt-prod` `associate-/r/`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

62.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
160.0ms	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
72.0ms	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series721.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
266.0ms	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
262.0ms	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

139 → 139

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	239	3118
1	593	2899
2	1941	2569
done	5000	2563

prune530.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite169.0ms

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` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 83

Calls

4 calls:

63.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
42.0ms	(- (* b_2 b_2) (* a c))
107.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
115.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.3s

Counts

95 → 95

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	147	1588
1	311	1491
2	773	1393
3	1814	1389
4	4582	1375
done	5000	1375

prune304.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune1.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.1b

regimes230.0ms

Accuracy

77.2% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 30.0b

bsearch132.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
5	-2.3823986784004295e+101	-6.644598008915225e+100	-1.8696623466311214e+101

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	38
1	33	36
done	33	36

end0.0ms

sample3.2s

Algorithm

intervals

Results

717.0ms	5894×	body	80	valid
495.0ms	226×	body	320	valid
444.0ms	1051×	body	2560	valid
373.0ms	835×	body	1280	valid
245.0ms	2996×	body	80	nan
152.0ms	450×	body	640	valid
113.0ms	135×	body	5120	valid
16.0ms	119×	body	160	valid