Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample131.0ms

Algorithm

intervals

Results

55.0ms	58×	body	1280	valid
26.0ms	40×	body	640	valid
20.0ms	130×	body	80	valid
11.0ms	25×	body	320	valid
3.0ms	22×	body	80	invalid
1.0ms	3×	body	160	valid
1.0ms	5×	body	80	nan

simplify455.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4951	26
1	4951	26

prune16.0ms

Filtered

1 candidates to 1 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: 10.0b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.3b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
16.4b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
79×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
34×	`pow-unpow`
25×	`add-exp-log` `unpow-prod-down`
16×	`add-cbrt-cube`
9×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `neg-mul-1` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `div-sub` `associate-r/` `distribute-frac-neg` `pow-prod-down` `-commutative` `associate-/l/` `pow-sub`
1×	`tan-quot` `pow-pow` `frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 178

Calls

4 calls:

7.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
22.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
12.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series241.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* x (/ 1.0 (tan B)))
93.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
92.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
32.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4957	3681
1	4957	3681

prune544.0ms

Filtered

150 candidates to 190 candidates (-26.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	171	19	190
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	172	20	192

Merged error: 9.6b

Counts

192 → 20

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
0.2b	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
0.2b	(* x (/ 1.0 (tan B)))
16.4b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
43×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`pow-neg` `associate-*r/` `distribute-frac-neg` `div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `neg-mul-1` `div-sub` `pow-exp` `associate-/r*` `div-inv` `associate-/l/` `pow-sub` `sqr-pow`
2×	`un-div-inv` `*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 137

Calls

4 calls:

10.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
10.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
7.0ms	(* x (/ 1.0 (tan B)))
11.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

series204.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
92.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
22.0ms	(* x (/ 1.0 (tan B)))
21.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4958	2360
1	4958	2360

prune341.0ms

Filtered

111 candidates to 149 candidates (-34.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	3	16	19
Picked	0	1	1
Done	0	0	0
Total	150	19	169

Merged error: 9.6b

Counts

169 → 19

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
0.2b	(* x (/ 1.0 (tan B)))
16.4b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

187×	`times-frac`
115×	`add-sqr-sqrt`
110×	`add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down`
28×	`associate-/l*`
22×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`associate-r`
13×	`pow-unpow` `sqr-pow`
9×	`div-exp`
8×	`div-inv`
7×	`pow1`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`associate-l`
2×	`tan-quot` `pow-to-exp` `frac-2neg` `pow-exp` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`pow-pow` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/`

Counts

4 → 208

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
13.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
7.0ms	(* x (/ 1.0 (tan B)))
7.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

series151.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
92.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
27.0ms	(* x (/ 1.0 (tan B)))
21.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4972	5017
1	4972	5017

prune580.0ms

Filtered

177 candidates to 220 candidates (-24.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	208	12	220
Fresh	10	7	17
Picked	1	0	1
Done	0	1	1
Total	219	20	239

Merged error: 9.6b

Counts

239 → 20

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
0.2b	(* (/ x (sin B)) (cos B))
0.2b	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
16.4b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

199×	`times-frac`
123×	`add-sqr-sqrt`
118×	`add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
28×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow` `associate-l`
11×	`div-exp`
10×	`associate-/r*`
8×	`div-inv`
7×	`pow1`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`pow-pow` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 224

Calls

4 calls:

8.0ms	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
6.0ms	(* (/ x (sin B)) (cos B))
13.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
7.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

series202.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
17.0ms	(* (/ x (sin B)) (cos B))
92.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
24.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5046	5963

prune517.0ms

Filtered

186 candidates to 236 candidates (-26.9%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	232	4	236
Fresh	3	15	18
Picked	0	1	1
Done	0	1	1
Total	235	21	256

Merged error: 9.6b

Counts

256 → 21

regimes427.0ms

Accuracy

0% (0.3b remaining)

Error of 10.3b against oracle of 10.0b and baseline of 10.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	28
1	73	28

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1639×	body	1280	valid
801.0ms	1312×	body	640	valid
548.0ms	3975×	body	80	valid
302.0ms	716×	body	320	valid
101.0ms	358×	body	160	valid
95.0ms	654×	body	80	invalid
12.0ms	116×	body	80	nan
1.0ms	1×	body	1280	invalid

Details

analyze1.9s

sample131.0ms

simplify455.0ms

prune16.0ms

localize25.0ms

rewrite62.0ms

series241.0ms

simplify76.0ms

prune544.0ms

localize23.0ms

rewrite42.0ms

series204.0ms

simplify61.0ms

prune341.0ms

localize24.0ms

rewrite39.0ms

series151.0ms

simplify67.0ms

prune580.0ms

localize23.0ms

rewrite44.0ms

series202.0ms

simplify99.0ms

prune517.0ms

regimes427.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling