Details

sample290.0ms

Algorithm

intervals

Results

7.0ms	182×	body	80	valid
6.0ms	33×	body	2560	valid
5.0ms	31×	body	1280	valid
3.0ms	85×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 35.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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:

23.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune227.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 7.9b

Counts

93 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.1b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `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 → 200

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
15.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
172.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	729	3368
1	3320	3193
2	5001	3167

prune451.0ms

Filtered

212 candidates to 142 candidates (67.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	211	11	222

Merged error: 7.8b

Counts

222 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.8b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.6b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 485

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
27.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
186.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
159.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1536	8628
1	5001	7982

prune948.0ms

Filtered

497 candidates to 298 candidates (60.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	496	1	497
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	499	9	508

Merged error: 7.8b

Counts

508 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
1.0b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

2862×	`times-frac`
1645×	`add-sqr-sqrt`
1644×	`*-un-lft-identity`
1136×	`add-cube-cbrt`
993×	`cbrt-prod`
254×	`distribute-lft-out--` `difference-of-squares`
155×	`associate-/l*`
130×	`sqrt-prod`
127×	`distribute-rgt-neg-in`
50×	`div-inv`
13×	`add-exp-log`
10×	`add-log-exp`
8×	`add-cbrt-cube`
7×	`associate-/r/`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`pow1`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 1153

Calls

4 calls:

8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
159.0ms	(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
33.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify275.0ms

Algorithm

egg-herbie

Counts

1165 → 1165

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	2926	27910
1	5003	26668

prune2.8s

Filtered

1165 candidates to 678 candidates (58.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1165	0	1165
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	1165	9	1174

Merged error: 7.8b

Counts

1174 → 9

regimes196.0ms

Accuracy

92.6% (1.8b remaining)

Error of 7.6b against oracle of 5.8b and baseline of 30.4b

bsearch134.0ms

Steps

Iters	Range	Point
7	6.184155830638016e+27	1.3306260697673677e+30	2.0732437802605094e+28
8	8.801855242554939e-263	2.6053624752067433e-259	8.94594987092143e-263
8	-1.109941606813071e+113	-3.739307379384431e+110	-2.7467723558510264e+111

Iters

Range

Point

6.184155830638016e+27

1.3306260697673677e+30

2.0732437802605094e+28

8.801855242554939e-263

2.6053624752067433e-259

8.94594987092143e-263

-1.109941606813071e+113

-3.739307379384431e+110

-2.7467723558510264e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	45	26
2	45	26

end0.0ms

sample980.0ms

Algorithm

intervals

Results

196.0ms	1067×	body	2560	valid
195.0ms	5875×	body	80	valid
141.0ms	883×	body	1280	valid
88.0ms	2893×	body	80	nan
52.0ms	445×	body	640	valid
27.0ms	223×	body	320	valid
24.0ms	103×	body	5120	valid
7.0ms	114×	body	160	valid