Details

analyze599.0ms

Algorithm: search

sample44.0ms

Algorithm

intervals

Results

11.0ms	40×	body	2560	valid
7.0ms	150×	body	80	valid
6.0ms	30×	body	1280	valid
2.0ms	14×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	8×	body	320	valid
1.0ms	19×	body	80	nan
1.0ms	7×	body	160	valid
0.0ms	7×	body	80	invalid

simplify384.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

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: 36.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.6b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

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:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify139.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune129.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	7	93

Merged error: 5.6b

Counts

93 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.8b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.7b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

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	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
50.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	716	3474
1	3237	3299
2	5002	3273

prune231.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	218	7	225

Merged error: 5.5b

Counts

225 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.7b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.8b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

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:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
29.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
43.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune312.0ms

Filtered

303 candidates to 503 candidates (-66.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	501	2	503
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	503	7	510

Merged error: 5.5b

Counts

510 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.4b	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
11.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	618	2273
1	2704	2086
2	5001	1951

prune98.0ms

Filtered

81 candidates to 181 candidates (-123.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	181	7	188

Merged error: 5.5b

Counts

188 → 7

regimes326.0ms

Accuracy

92.7% (1.8b remaining)

Error of 6.9b against oracle of 5.1b and baseline of 29.6b

bsearch624.0ms

Steps

Iters	Range	Point
9	1.1344596947434557e+44	3.2474682024327674e+52	1.3502405774646824e+48
9	-1.2961144270936513e-160	-8.824316923191854e-166	-3.6345679597105963e-163
6	-2.0638477527809012e+79	-3.5828367223779936e+78	-2.0353790449559682e+79

Iters

Range

Point

1.1344596947434557e+44

3.2474682024327674e+52

1.3502405774646824e+48

-1.2961144270936513e-160

-8.824316923191854e-166

-3.6345679597105963e-163

-2.0638477527809012e+79

-3.5828367223779936e+78

-2.0353790449559682e+79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	41
1	43	41

end0.0ms

analyze394.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

270.0ms	1092×	body	2560	valid
221.0ms	5055×	body	80	valid
197.0ms	954×	body	1280	valid
77.0ms	467×	body	640	valid
33.0ms	759×	body	80	nan
33.0ms	101×	body	5120	valid
25.0ms	214×	body	320	valid
13.0ms	266×	body	80	invalid
10.0ms	117×	body	160	valid

Details

analyze599.0ms

sample44.0ms

simplify384.0ms

prune6.0ms

localize12.0ms

rewrite50.0ms

series64.0ms

simplify139.0ms

prune129.0ms

localize12.0ms

rewrite51.0ms

series124.0ms

simplify109.0ms

prune231.0ms

localize12.0ms

rewrite100.0ms

series125.0ms

simplify107.0ms

prune312.0ms

localize11.0ms

rewrite40.0ms

series67.0ms

simplify74.0ms

prune98.0ms

regimes326.0ms

bsearch624.0ms

simplify2.0ms

end0.0ms

analyze394.0ms

sample1.1s

Profiling