Details

sample90.0ms

Algorithm

intervals

Results

10.0ms	37×	body	2560	valid
8.0ms	185×	body	80	valid
7.0ms	33×	body	1280	valid
5.0ms	81×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Counts: 1 → 1

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite122.0ms

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:

8.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
81.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Counts: 103 → 103

prune275.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

42.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
97.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
64.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
174.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
210.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Counts: 199 → 199

prune543.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
3.8b	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

15078×	`times-frac`
9183×	`add-sqr-sqrt`
7371×	`*-un-lft-identity`
6341×	`sqrt-prod`
5561×	`add-cube-cbrt`
1810×	`difference-of-squares`
986×	`associate-/l*`
905×	`distribute-lft-out--`
190×	`div-inv`
56×	`associate-/r/`
27×	`add-exp-log` `add-cbrt-cube`
16×	`cbrt-undiv` `div-exp`
14×	`sqrt-div`
12×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`pow1`
4×	`add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 4612

Calls

4 calls:

356.0ms	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
142.0ms	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (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)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
197.0ms	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts: 4624 → 4624

prune12.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.4b	(/ a (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-exp-log`
60×	`div-exp`
41×	`add-cbrt-cube`
34×	`times-frac`
29×	`prod-exp`
26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`1-exp`
18×	`cbrt-undiv`
16×	`associate-/l*`
9×	`cbrt-unprod`
8×	`rec-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
4×	`flip3--` `sqrt-prod` `flip--` `div-inv`
2×	`frac-times` `frac-2neg` `sqrt-div` `associate-r/` `clear-num` `associate-/r` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*l/` `associate-/l/` `distribute-lft-out--`

Counts

4 → 130

Calls

4 calls:

66.0ms	(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
49.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(/ a (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
92.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(/ a (* a c))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify93.0ms

Counts: 142 → 142

prune251.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes221.0ms

Accuracy

85.5% (3.9b remaining)

Error of 9.4b against oracle of 5.6b and baseline of 32.1b

bsearch200.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	6.326287366549383e+74
9	-7.826064039423189e-132	-1.1138670077130767e-140	-5.358830408552925e-132
6	-3.4377365604695865e-95	-7.852755480555329e-96	-7.975591029427467e-96
7	-8.794280737794768e+42	-4.315177351158757e+40	-3.628086182808922e+42

simplify3.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

703.0ms	5846×	body	80	valid
389.0ms	1058×	body	2560	valid
193.0ms	921×	body	1280	valid
192.0ms	2929×	body	80	nan
111.0ms	503×	body	640	valid
53.0ms	210×	body	320	valid
34.0ms	109×	body	5120	valid
9.0ms	109×	body	160	valid