Details

sample110.0ms

Algorithm

intervals

Results

11.0ms	43×	body	2560	valid
8.0ms	155×	body	80	valid
5.0ms	26×	body	1280	valid
4.0ms	94×	body	80	nan
3.0ms	19×	body	640	valid
2.0ms	13×	body	320	valid
2.0ms	5×	body	5120	valid
0.0ms	5×	body	160	valid

simplify343.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.6b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite184.0ms

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-cbrt-cube` `add-exp-log` `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` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

97.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
12.0ms	(- (* b_2 b_2) (* a c))
51.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
46.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1459
1	384
0	154

prune532.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

18.0ms

(* -1/2 (/ c b_2))

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(* -1/2 (/ c b_2))

simplify1.6s

Counts

35 → 35

Iterations

Iter	Nodes
done	5001
3	2505
2	572
1	178
0	68

prune191.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* -1/2 (/ c b_2))) (cbrt (* -1/2 (/ c b_2))))
15.1b	(cbrt (* -1/2 (/ c b_2)))
15.1b	(cbrt (* -1/2 (/ c b_2)))
15.1b	(cbrt (* -1/2 (/ c b_2)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`-un-lft-identity` `associate-r/` `add-cube-cbrt`
7×	`cbrt-prod` `cbrt-div`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

11.0ms	(* (cbrt (* -1/2 (/ c b_2))) (cbrt (* -1/2 (/ c b_2))))
4.0ms	(cbrt (* -1/2 (/ c b_2)))
4.0ms	(cbrt (* -1/2 (/ c b_2)))
5.0ms	(cbrt (* -1/2 (/ c b_2)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (cbrt (* -1/2 (/ c b_2))) (cbrt (* -1/2 (/ c b_2))))
144.0ms	(cbrt (* -1/2 (/ c b_2)))
148.0ms	(cbrt (* -1/2 (/ c b_2)))
121.0ms	(cbrt (* -1/2 (/ c b_2)))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	764
1	198
0	92

prune589.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ c (sqrt b_2))
0.1b	(* (/ -1/2 (sqrt b_2)) (/ c (sqrt b_2)))
0.2b	(/ -1/2 (sqrt b_2))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
84×	`times-frac`
59×	`*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
22×	`associate-r` `associate-l`
19×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
9×	`unswap-sqr`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv`
3×	`add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 151

Calls

3 calls:

9.0ms	(/ c (sqrt b_2))
46.0ms	(* (/ -1/2 (sqrt b_2)) (/ c (sqrt b_2)))
5.0ms	(/ -1/2 (sqrt b_2))

series157.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ c (sqrt b_2))
43.0ms	(* (/ -1/2 (sqrt b_2)) (/ c (sqrt b_2)))
51.0ms	(/ -1/2 (sqrt b_2))

simplify1.9s

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
2	2943
1	620
0	220

prune869.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.3b

regimes440.0ms

Accuracy

86% (4.7b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 39.0b

bsearch165.0ms

Steps

Iters	Range		Point
12	2.4919208328047006e-151	1.0529347607547997e-106	6.484072051994264e-107
8	-6.412561728939963e+28	-6.810701174428621e+25	-6.336287344206649e+28

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	1103×	body	2560	valid
506.0ms	5731×	body	80	valid
354.0ms	957×	body	1280	valid
173.0ms	2940×	body	80	nan
162.0ms	463×	body	640	valid
60.0ms	108×	body	5120	valid
48.0ms	228×	body	320	valid
14.0ms	118×	body	160	valid