Details

sample458.0ms

Algorithm

intervals

Results

59.0ms	64×	body	1280	valid
24.0ms	147×	body	80	valid
23.0ms	37×	body	640	valid
9.0ms	19×	body	320	valid
4.0ms	41×	body	80	nan
3.0ms	10×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.5b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
7.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
16.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 155

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
15.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
13.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
25.0ms	(* x (/ 1.0 (tan B)))
64.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
33.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	817	1480
1	3336	1390
2	5001	1389

prune1.6s

Filtered

167 candidates to 128 candidates (23.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	155	12	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	12	168

Merged error: 1.2b

Counts

168 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

7.0ms	(* x (/ 1.0 (tan B)))
12.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
11.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series204.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (/ 1.0 (tan B)))
98.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
62.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
22.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	703	1170
1	3086	1048
2	5001	1048

prune992.0ms

Filtered

120 candidates to 90 candidates (25.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 1.2b

Counts

132 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
16.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
7×	`unpow-prod-down` `associate-r` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
10.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series202.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* x 1.0) (tan B))
97.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
61.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
21.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	657	1115
1	2821	993
2	5001	993

prune833.0ms

Filtered

109 candidates to 83 candidates (23.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	109	11	120

Merged error: 1.2b

Counts

120 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ 1.0 (tan B)))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.4b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
16.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

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

series136.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (/ 1.0 (tan B)))
31.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
59.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	773	1380
1	3290	1264
2	5001	1264

prune1.3s

Filtered

145 candidates to 108 candidates (25.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	145	11	156

Merged error: 1.2b

Counts

156 → 11

regimes353.0ms

Accuracy

97.8% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 10.7b

bsearch295.0ms

Steps

Iters	Range		Point
8	3.7787022717182464e+149	3.260050336703768e+152	3.220323072834628e+152
8	-5.108778053722052e+157	-1.638752705635939e+154	-1.6692299645252848e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	62
1	74	62

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	1737×	body	1280	valid
807.0ms	1374×	body	640	valid
617.0ms	4737×	body	80	valid
292.0ms	707×	body	320	valid
154.0ms	1640×	body	80	nan
94.0ms	344×	body	160	valid

Details

sample458.0ms

simplify44.0ms

prune17.0ms

localize26.0ms

rewrite52.0ms

series133.0ms

simplify87.0ms

prune1.6s

localize22.0ms

rewrite41.0ms

series204.0ms

simplify76.0ms

prune992.0ms

localize22.0ms

rewrite38.0ms

series202.0ms

simplify68.0ms

prune833.0ms

localize23.0ms

rewrite44.0ms

series136.0ms

simplify86.0ms

prune1.3s

regimes353.0ms

bsearch295.0ms

simplify2.0ms

end0.0ms

sample3.9s

Profiling