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

sample122.0ms

Algorithm

intervals

Results

42.0ms	44×	body	1280	valid
24.0ms	38×	body	640	valid
20.0ms	138×	body	80	valid
10.0ms	23×	body	320	valid
4.0ms	29×	body	80	invalid
4.0ms	13×	body	160	valid
0.0ms	2×	body	80	nan

simplify468.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5148	27

prune17.0ms

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: 10.9b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.3b	(* x (/ (neg 1.0) (tan B)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
18.1b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 200

Calls

4 calls:

13.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
11.0ms	(* x (/ (neg 1.0) (tan B)))
22.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
11.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series239.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
24.0ms	(* x (/ (neg 1.0) (tan B)))
91.0ms	(/ (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))

simplify64.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5093	3935

prune552.0ms

Filtered

166 candidates to 212 candidates (-27.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	197	15	212
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	198	16	214

Merged error: 10.6b

Counts

214 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x (neg 1.0)) (tan B))
0.2b	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.4b	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
18.1b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

5.0ms	(/ (* x (neg 1.0)) (tan B))
15.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
9.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
8.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series219.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* x (neg 1.0)) (tan B))
90.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
86.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
21.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4983	3619
1	4983	3619

prune428.0ms

Filtered

141 candidates to 180 candidates (-27.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	177	3	180
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	178	18	196

Merged error: 10.6b

Counts

196 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
0.3b	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
0.3b	(* x (/ (neg 1.0) (tan B)))
18.1b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac`
61×	`add-sqr-sqrt`
51×	`add-cube-cbrt` `*-un-lft-identity`
42×	`associate-r`
34×	`pow-unpow`
25×	`add-exp-log`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
16×	`add-cbrt-cube`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`neg-mul-1` `distribute-frac-neg` `associate-l`
5×	`pow-neg` `associate-*r/` `div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `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/` `distribute-rgt-neg-out` `associate-/l*`

Counts

4 → 159

Calls

4 calls:

11.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
8.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
10.0ms	(* x (/ (neg 1.0) (tan B)))
8.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

series200.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
67.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
22.0ms	(* x (/ (neg 1.0) (tan B)))
21.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5022	2585

prune346.0ms

Filtered

127 candidates to 171 candidates (-34.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	11	5	16
Picked	0	1	1
Done	0	1	1
Total	178	11	189

Merged error: 1.1b

Counts

189 → 11

localize22.0ms

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	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
0.3b	(* x (/ (neg 1.0) (tan B)))
18.0b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

220×	`times-frac`
136×	`add-sqr-sqrt`
131×	`add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
35×	`associate-r`
28×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow`
11×	`div-exp`
10×	`associate-/r*`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`div-inv`
7×	`pow1`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `neg-mul-1` `associate-l` `pow-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`tan-quot` `pow-pow` `associate-r/` `distribute-frac-neg` `pow-prod-down` `associate-/r/` `-commutative` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 247

Calls

4 calls:

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

series201.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
90.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
25.0ms	(* x (/ (neg 1.0) (tan B)))
20.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4965	6182
1	4965	6182

prune591.0ms

Filtered

206 candidates to 259 candidates (-25.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	260	10	270

Merged error: 1.1b

Counts

270 → 10

regimes268.0ms

Accuracy

95.6% (0.4b remaining)

Error of 1.5b against oracle of 1.1b and baseline of 10.7b

bsearch2.1s

Steps

Iters	Range		Point
9	2.5357018836827442e+147	2.0741555018436638e+154	1.3316745337714515e+154
8	-9.508913031192838e+161	-2.8172658888476748e+159	-2.8462823683330226e+159

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	119
1	88	119

end0.0ms

analyze1.7s

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

sample3.7s

Algorithm

intervals

Results

1.5s	1677×	body	1280	valid
873.0ms	1440×	body	640	valid
543.0ms	3899×	body	80	valid
282.0ms	667×	body	320	valid
92.0ms	317×	body	160	valid
91.0ms	653×	body	80	invalid
15.0ms	127×	body	80	nan

Details

analyze1.9s

sample122.0ms

simplify468.0ms

prune17.0ms

localize26.0ms

rewrite66.0ms

series239.0ms

simplify64.0ms

prune552.0ms

localize23.0ms

rewrite43.0ms

series219.0ms

simplify58.0ms

prune428.0ms

localize24.0ms

rewrite44.0ms

series200.0ms

simplify51.0ms

prune346.0ms

localize22.0ms

rewrite49.0ms

series201.0ms

simplify104.0ms

prune591.0ms

regimes268.0ms

bsearch2.1s

simplify2.0ms

end0.0ms

analyze1.7s

sample3.7s

Profiling