Details

sample298.0ms

Algorithm

intervals

Results

8.0ms	179×	body	80	valid
7.0ms	34×	body	2560	valid
5.0ms	30×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

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: 35.7b

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)
1.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

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)
9.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

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

prune218.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 4.9b

Counts

93 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.1b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
145.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune465.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	217	8	225

Merged error: 4.8b

Counts

225 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

14.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
31.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
158.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1582	8734
1	5001	8085

prune960.0ms

Filtered

503 candidates to 303 candidates (60.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	501	2	503
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	503	8	511

Merged error: 4.8b

Counts

511 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.0b	(- (* b_2 b_2) (* a c))
2.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 169

Calls

4 calls:

14.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
37.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	621	2276
1	2663	2085
2	5001	1950

prune226.0ms

Filtered

181 candidates to 82 candidates (45.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	181	8	189

Merged error: 4.8b

Counts

189 → 8

regimes155.0ms

Accuracy

90.7% (2.3b remaining)

Error of 7.6b against oracle of 5.3b and baseline of 29.7b

bsearch163.0ms

Steps

Iters	Range		Point
9	14028.172733867412	3007116902181.375	2947728123750.7354
11	-7.158612012333694e-224	-2.980406596944262e-243	-5.266108209623796e-239
10	-1.552489725432399e+46	-8.211399685419546e+34	-1.310778137866809e+45

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	22
1	39	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

225.0ms	1100×	body	2560	valid
202.0ms	5800×	body	80	valid
148.0ms	889×	body	1280	valid
95.0ms	2951×	body	80	nan
64.0ms	468×	body	640	valid
32.0ms	119×	body	5120	valid
22.0ms	212×	body	320	valid
7.0ms	112×	body	160	valid

Details

sample298.0ms

simplify15.0ms

prune4.0ms

localize11.0ms

rewrite45.0ms

series271.0ms

simplify48.0ms

prune218.0ms

localize12.0ms

rewrite57.0ms

series451.0ms

simplify115.0ms

prune465.0ms

localize11.0ms

rewrite101.0ms

series473.0ms

simplify109.0ms

prune960.0ms

localize14.0ms

rewrite38.0ms

series278.0ms

simplify75.0ms

prune226.0ms

regimes155.0ms

bsearch163.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling