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

sample124.0ms

Algorithm

intervals

Results

50.0ms	53×	body	1280	valid
24.0ms	37×	body	640	valid
19.0ms	136×	body	80	valid
9.0ms	21×	body	320	valid
4.0ms	29×	body	80	invalid
3.0ms	9×	body	160	valid
0.0ms	3×	body	80	nan

simplify468.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5148	27

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: 8.2b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ (neg 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))
14.6b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite68.0ms

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:

11.0ms	(* x (/ (neg 1.0) (tan B)))
13.0ms	(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
23.0ms	(/ (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))

series243.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* x (/ (neg 1.0) (tan B)))
92.0ms	(* 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))

simplify63.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5093	3935

prune562.0ms

Filtered

166 candidates to 212 candidates (-27.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	196	16	212
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	197	17	214

Merged error: 7.9b

Counts

214 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (/ (neg 1.0) (tan B)))
0.3b	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
0.5b	(* (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (/ 1 (sin B)))
14.6b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

70×	`times-frac`
66×	`add-sqr-sqrt`
59×	`add-exp-log`
56×	`add-cube-cbrt` `*-un-lft-identity`
55×	`associate-r`
34×	`pow-unpow`
33×	`prod-exp`
23×	`add-cbrt-cube`
18×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`pow1` `div-exp` `cbrt-unprod`
8×	`associate-*r/` `distribute-frac-neg`
7×	`pow-neg` `unpow-prod-down` `associate-l`
6×	`pow-to-exp` `neg-mul-1` `pow-exp`
5×	`unswap-sqr`
4×	`neg-sub0` `rec-exp` `1-exp` `div-sub` `un-div-inv` `pow-sub` `add-log-exp`
3×	`cbrt-undiv` `frac-times` `associate-l/` `-commutative` `div-inv` `sqr-pow`
2×	`pow-prod-down`
1×	`tan-quot` `pow-pow` `associate-/r/` `distribute-rgt-neg-out`

Counts

4 → 184

Calls

4 calls:

11.0ms	(* x (/ (neg 1.0) (tan B)))
9.0ms	(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
13.0ms	(* (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (/ 1 (sin B)))
10.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

series204.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* x (/ (neg 1.0) (tan B)))
68.0ms	(* 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))) (/ 1 (sin B)))
21.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5611	3034

prune394.0ms

Filtered

131 candidates to 196 candidates (-49.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	4	12	16
Picked	0	1	1
Done	0	0	0
Total	198	15	213

Merged error: 7.9b

Counts

213 → 15

localize25.0ms

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 (/ (neg 1.0) (tan B)))
0.5b	(* (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (/ 1 (sin B)))
14.6b	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
108×	`times-frac`
74×	`*-un-lft-identity`
70×	`add-cube-cbrt`
59×	`add-exp-log`
48×	`associate-r`
28×	`associate-l`
27×	`unpow-prod-down`
24×	`div-exp`
23×	`add-cbrt-cube`
18×	`prod-exp`
14×	`unswap-sqr`
13×	`pow-unpow`
11×	`sqr-pow`
9×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`associate-/r*`
6×	`cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod`
5×	`div-inv`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`neg-mul-1` `associate-/l*`
2×	`associate-r/` `pow-prod-down` `-commutative`
1×	`tan-quot` `frac-times` `pow-pow` `frac-2neg` `distribute-frac-neg` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv` `distribute-rgt-neg-out`

Counts

4 → 210

Calls

4 calls:

7.0ms	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
11.0ms	(* x (/ (neg 1.0) (tan B)))
18.0ms	(* (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (/ 1 (sin B)))
7.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

series206.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
22.0ms	(* x (/ (neg 1.0) (tan B)))
91.0ms	(* (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (/ 1 (sin B)))
26.0ms	(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4985	4162
1	4985	4162

prune480.0ms

Filtered

161 candidates to 222 candidates (-37.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	5	8	13
Picked	0	1	1
Done	0	1	1
Total	225	12	237

Merged error: 0.8b

Counts

237 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos 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))
14.6b	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite44.0ms

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:

6.0ms	(* (/ 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))
9.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

series219.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (/ x (sin B)) (cos B))
91.0ms	(* 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))
25.0ms	(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5195	3698

prune372.0ms

Filtered

149 candidates to 189 candidates (-26.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	189	12	201

Merged error: 0.8b

Counts

201 → 12

regimes405.0ms

Accuracy

97.1% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 10.9b

bsearch2.1s

Steps

Iters	Range		Point
7	4.65419589716195e+140	1.9941198969251118e+142	1.968331059631482e+142
10	-1.0266082603837032e+159	-1.3583998552845537e+143	-1.3553598376870535e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	124
1	79	124

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	1650×	body	1280	valid
840.0ms	1404×	body	640	valid
536.0ms	3901×	body	80	valid
287.0ms	682×	body	320	valid
104.0ms	363×	body	160	valid
100.0ms	686×	body	80	invalid
13.0ms	128×	body	80	nan
1.0ms	1×	body	1280	invalid

Details

analyze1.9s

sample124.0ms

simplify468.0ms

prune16.0ms

localize25.0ms

rewrite68.0ms

series243.0ms

simplify63.0ms

prune562.0ms

localize23.0ms

rewrite50.0ms

series204.0ms

simplify60.0ms

prune394.0ms

localize25.0ms

rewrite51.0ms

series206.0ms

simplify64.0ms

prune480.0ms

localize23.0ms

rewrite44.0ms

series219.0ms

simplify60.0ms

prune372.0ms

regimes405.0ms

bsearch2.1s

simplify2.0ms

end0.0ms

analyze1.7s

sample3.6s

Profiling