Details

analyze2.0s

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

52.0ms	49×	body	1280	valid
33.0ms	52×	body	640	valid
19.0ms	129×	body	80	valid
6.0ms	14×	body	320	valid
4.0ms	12×	body	160	valid
2.0ms	15×	body	80	invalid
0.0ms	3×	body	80	nan

simplify445.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5148	27

prune25.0ms

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: 10.3b

Counts

2 → 2

localize24.0ms

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)))
0.3b	(/ (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))

rewrite55.0ms

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)))
12.0ms	(* x (/ (neg 1.0) (tan B)))
9.0ms	(/ (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))

series245.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
24.0ms	(* x (/ (neg 1.0) (tan B)))
90.0ms	(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
37.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5093	3935

prune543.0ms

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: 9.9b

Counts

214 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(* 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))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
79×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow-unpow`
28×	`associate-r`
25×	`add-exp-log` `unpow-prod-down`
16×	`associate-l` `add-cbrt-cube`
9×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`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` `distribute-frac-neg` `pow-prod-down` `*-commutative` `associate-/l/` `pow-sub`
1×	`pow-pow` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 177

Calls

4 calls:

7.0ms	(* (/ x (sin B)) (cos B))
13.0ms	(* 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))
11.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series219.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ x (sin B)) (cos B))
93.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
87.0ms	(/ (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))

simplify63.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5195	3698

prune442.0ms

Filtered

149 candidates to 189 candidates (-26.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	188	17	205

Merged error: 9.9b

Counts

205 → 17

localize22.0ms

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)))
16.4b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

rewrite47.0ms

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:

10.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
9.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
13.0ms	(* x (/ (neg 1.0) (tan B)))
9.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

series207.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (sin B))
70.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
23.0ms	(* x (/ (neg 1.0) (tan B)))
22.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5022	2585

prune355.0ms

Filtered

127 candidates to 171 candidates (-34.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	7	8	15
Picked	0	1	1
Done	0	1	1
Total	175	13	188

Merged error: 1.0b

Counts

188 → 13

localize24.0ms

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)))
16.4b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite50.0ms

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:

8.0ms	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
13.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
11.0ms	(* x (/ (neg 1.0) (tan B)))
7.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

series209.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
93.0ms	(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
22.0ms	(* x (/ (neg 1.0) (tan B)))
26.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4965	6182
1	4965	6182

prune593.0ms

Filtered

206 candidates to 259 candidates (-25.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	256	3	259
Fresh	4	6	10
Picked	1	0	1
Done	1	1	2
Total	262	10	272

Merged error: 1.0b

Counts

272 → 10

regimes368.0ms

Accuracy

98.1% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 10.3b

bsearch2.1s

Steps

Iters	Range		Point
8	6.558194580084462e+153	3.282777732482956e+158	1.3658377657683982e+154
9	-1.2117293533667276e+155	-1.8905499715095966e+149	-1.3308194757292465e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	118
1	85	118

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

sample3.6s

Algorithm

intervals

Results

1.5s	1653×	body	1280	valid
833.0ms	1364×	body	640	valid
538.0ms	3916×	body	80	valid
300.0ms	716×	body	320	valid
101.0ms	351×	body	160	valid
92.0ms	650×	body	80	invalid
13.0ms	126×	body	80	nan
1.0ms	1×	body	1280	invalid
1.0ms	1×	body	640	invalid
0.0ms	1×	body	320	invalid

Details

analyze2.0s

sample131.0ms

simplify445.0ms

prune25.0ms

localize24.0ms

rewrite55.0ms

series245.0ms

simplify63.0ms

prune543.0ms

localize24.0ms

rewrite46.0ms

series219.0ms

simplify63.0ms

prune442.0ms

localize22.0ms

rewrite47.0ms

series207.0ms

simplify52.0ms

prune355.0ms

localize24.0ms

rewrite50.0ms

series209.0ms

simplify105.0ms

prune593.0ms

regimes368.0ms

bsearch2.1s

simplify2.0ms

end0.0ms

analyze1.7s

sample3.6s

Profiling