Details

analyze1.9s

Algorithm: search

sample120.0ms

Algorithm

intervals

Results

37.0ms	40×	body	1280	valid
26.0ms	147×	body	80	valid
23.0ms	36×	body	640	valid
10.0ms	23×	body	320	valid
4.0ms	26×	body	80	invalid
3.0ms	10×	body	160	valid
0.0ms	3×	body	80	nan

simplify411.0ms

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

prune14.0ms

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: 15.1b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
8.8b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite43.0ms

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

series141.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1.0 (tan B))
28.0ms	(* x (/ 1.0 (tan B)))
59.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
42.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	817	1482
1	3341	1390
2	5002	1389

prune383.0ms

Filtered

128 candidates to 167 candidates (-30.5%)

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

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite39.0ms

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:

10.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
8.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series206.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
99.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
23.0ms	(* x (/ 1.0 (tan B)))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	703	1170
1	3086	1048
2	5002	1048

prune283.0ms

Filtered

90 candidates to 120 candidates (-33.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 1.2b

Counts

132 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite36.0ms

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

series205.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (* x 1.0) (tan B))
61.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
99.0ms	(/ F (* (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))

simplify66.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

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

prune243.0ms

Filtered

81 candidates to 109 candidates (-34.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	110	12	122

Merged error: 1.2b

Counts

122 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
0.4b	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
75×	`times-frac`
56×	`add-exp-log`
53×	`*-un-lft-identity`
49×	`add-cube-cbrt`
39×	`associate-r`
23×	`add-cbrt-cube`
22×	`div-exp`
18×	`prod-exp`
16×	`associate-l`
15×	`unpow-prod-down`
14×	`unswap-sqr`
13×	`pow-unpow`
9×	`pow1`
7×	`sqr-pow`
6×	`cbrt-undiv` `cbrt-unprod`
5×	`pow-to-exp` `pow-exp` `div-inv`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`tan-quot` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative`
1×	`frac-times` `pow-pow` `frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 170

Calls

4 calls:

3.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
19.0ms	(* (/ 1 (sin B)) (/ F (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))

series164.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1.0 (tan B))
23.0ms	(* x (/ 1.0 (tan B)))
108.0ms	(* (/ 1 (sin B)) (/ F (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))

simplify107.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	986	1851
1	4644	1682
2	5001	1682

prune323.0ms

Filtered

130 candidates to 182 candidates (-40.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	181	13	194

Merged error: 1.2b

Counts

194 → 13

regimes338.0ms

Accuracy

96.7% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 10.7b

bsearch2.0s

Steps

Iters	Range		Point
10	8.351670587972746e+148	1.2703133248204668e+162	1.356758820112869e+154
6	-1.8577766019447153e+139	-2.8848989608440314e+138	-1.8333827337343462e+139

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	65
1	77	65

end0.0ms

analyze1.7s

Algorithm: search

sample3.6s

Algorithm

intervals

Results

1.5s	1611×	body	1280	valid
827.0ms	1388×	body	640	valid
564.0ms	3933×	body	80	valid
303.0ms	723×	body	320	valid
103.0ms	345×	body	160	valid
98.0ms	684×	body	80	invalid
14.0ms	142×	body	80	nan
1.0ms	1×	body	640	invalid

Details

analyze1.9s

sample120.0ms

simplify411.0ms

prune14.0ms

localize25.0ms

rewrite43.0ms

series141.0ms

simplify83.0ms

prune383.0ms

localize21.0ms

rewrite39.0ms

series206.0ms

simplify78.0ms

prune283.0ms

localize21.0ms

rewrite36.0ms

series205.0ms

simplify66.0ms

prune243.0ms

localize22.0ms

rewrite47.0ms

series164.0ms

simplify107.0ms

prune323.0ms

regimes338.0ms

bsearch2.0s

simplify2.0ms

end0.0ms

analyze1.7s

sample3.6s

Profiling