Details

sample57.0ms

Algorithm

intervals

Results

13.0ms	193×	body	80	valid
11.0ms	33×	body	2560	valid
8.0ms	30×	body	1280	valid
5.0ms	102×	body	80	nan
2.0ms	6×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize9.0ms

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))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

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:

36.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune626.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
4.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.0b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`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 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
25.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
55.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.4b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.4b	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
119×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
70×	`add-cube-cbrt`
32×	`add-exp-log`
25×	`associate-/r*`
24×	`difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp`
15×	`sqrt-prod`
12×	`distribute-lft-out--`
10×	`cbrt-undiv`
6×	`prod-exp` `div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `associate-/r/` `associate-/l/`

Counts

4 → 162

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
18.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
41.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	773	2158
1	3591	1999
2	5002	1976

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
32×	`add-exp-log`
26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
17×	`div-exp`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`1-exp` `associate-/r*`
6×	`pow1` `prod-exp`
5×	`cbrt-undiv` `div-inv`
4×	`rec-exp` `sqrt-prod`
3×	`flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `cbrt-unprod` `distribute-lft-out--` `inv-pow`

Counts

4 → 101

Calls

4 calls:

22.0ms	(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
20.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	504	1009
1	1998	871
2	5001	827

prune564.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.8b

regimes272.0ms

Accuracy

93.5% (1.5b remaining)

Error of 7.2b against oracle of 5.7b and baseline of 29.3b

bsearch91.0ms

Steps

Iters	Range		Point
7	7.8930669794294e+68	1.794276654474529e+70	1.7701741483501238e+70
8	1.1323007768539012e-246	2.166838235984046e-243	1.9220534958503673e-246
8	-2.75227652547193e+57	-2.8729039666377685e+54	-2.237522594933402e+57

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	20
1	43	20
2	43	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

360.0ms	1059×	body	2560	valid
331.0ms	5874×	body	80	valid
244.0ms	884×	body	1280	valid
156.0ms	2865×	body	80	nan
100.0ms	448×	body	640	valid
47.0ms	117×	body	5120	valid
34.0ms	208×	body	320	valid
16.0ms	126×	body	160	valid