Details

analyze1.1s

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
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample94.0ms

Algorithm

intervals

Results

51.0ms	93×	body	1280	valid
20.0ms	68×	body	640	valid
5.0ms	64×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series46.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

simplify59.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5018	783

prune130.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 0.2b

Counts

77 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 99

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
49.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify56.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5901	1692

prune193.0ms

Filtered

90 candidates to 111 candidates (-23.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	98	13	111
Fresh	8	2	10
Picked	0	1	1
Done	0	0	0
Total	106	16	122

Merged error: 0.0b

Counts

122 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
0.2b	(/ (cos a) (sin b))
0.2b	(* (/ (cos a) (sin b)) (cos b))
0.2b	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 99

Calls

4 calls:

6.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
4.0ms	(/ (cos a) (sin b))
7.0ms	(* (/ (cos a) (sin b)) (cos b))
9.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

series92.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
10.0ms	(/ (cos a) (sin b))
16.0ms	(* (/ (cos a) (sin b)) (cos b))
47.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4937	1443
1	4937	1443

prune174.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	5	9	14
Picked	1	0	1
Done	1	0	1
Total	114	13	127

Merged error: 0.0b

Counts

127 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos b) (sin b))
0.1b	(- (* (cos a) (/ (cos b) (sin b))) (sin a))
0.2b	(* (cos a) (/ (cos b) (sin b)))
0.2b	(/ r (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-r` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 99

Calls

4 calls:

4.0ms	(/ (cos b) (sin b))
6.0ms	(- (* (cos a) (/ (cos b) (sin b))) (sin a))
7.0ms	(* (cos a) (/ (cos b) (sin b)))
10.0ms	(/ r (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (cos b) (sin b))
23.0ms	(- (* (cos a) (/ (cos b) (sin b))) (sin a))
16.0ms	(* (cos a) (/ (cos b) (sin b)))
45.0ms	(/ r (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5088	1447

prune94.0ms

Filtered

82 candidates to 111 candidates (-35.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	111	13	124

Merged error: 0.0b

Counts

124 → 13

regimes307.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	2866×	body	1280	valid
731.0ms	1865×	body	640	valid
170.0ms	742×	body	320	valid
155.0ms	2197×	body	80	valid
61.0ms	330×	body	160	valid

Details

analyze1.1s

sample94.0ms

simplify3.0ms

prune8.0ms

localize11.0ms

rewrite17.0ms

series46.0ms

simplify59.0ms

prune130.0ms

localize17.0ms

rewrite34.0ms

series106.0ms

simplify56.0ms

prune193.0ms

localize16.0ms

rewrite29.0ms

series92.0ms

simplify49.0ms

prune174.0ms

localize15.0ms

rewrite31.0ms

series89.0ms

simplify60.0ms

prune94.0ms

regimes307.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling