Details

analyze1.0s

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
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

sample86.0ms

Algorithm

intervals

Results

46.0ms	87×	body	1280	valid
14.0ms	51×	body	640	valid
6.0ms	32×	body	320	valid
5.0ms	74×	body	80	valid
2.0ms	12×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	119	9
1	119	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: 13.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.3b	(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))

series45.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4966	783
1	4966	783

prune119.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.1b

Counts

77 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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)))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4942	1675
1	4942	1675

prune194.0ms

Filtered

90 candidates to 111 candidates (-23.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	107	12	119

Merged error: 0.0b

Counts

119 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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:

6.0ms	(- (* (cos a) (/ (cos b) (sin b))) (sin a))
4.0ms	(/ (cos b) (sin b))
7.0ms	(* (cos a) (/ (cos b) (sin b)))
8.0ms	(/ r (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (* (cos a) (/ (cos b) (sin b))) (sin a))
6.0ms	(/ (cos b) (sin b))
18.0ms	(* (cos a) (/ (cos b) (sin b)))
45.0ms	(/ r (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5113	1453

prune158.0ms

Filtered

83 candidates to 111 candidates (-33.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
7.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
5.0ms	(/ (* (cos a) (cos b)) (sin b))
9.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
19.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
16.0ms	(/ (* (cos a) (cos b)) (sin b))
48.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4955	1426
1	4955	1426

prune94.0ms

Filtered

73 candidates to 103 candidates (-41.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	10	10
Picked	0	1	1
Done	1	0	1
Total	103	12	115

Merged error: 0.0b

Counts

115 → 12

regimes372.0ms

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	57	13
1	57	13

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2894×	body	1280	valid
660.0ms	1786×	body	640	valid
166.0ms	803×	body	320	valid
159.0ms	2154×	body	80	valid
54.0ms	363×	body	160	valid
1.0ms	3×	body	1280	invalid
0.0ms	1×	body	160	invalid

Details

analyze1.0s

sample86.0ms

simplify4.0ms

prune8.0ms

localize9.0ms

rewrite17.0ms

series45.0ms

simplify62.0ms

prune119.0ms

localize15.0ms

rewrite32.0ms

series105.0ms

simplify47.0ms

prune194.0ms

localize16.0ms

rewrite28.0ms

series88.0ms

simplify53.0ms

prune158.0ms

localize14.0ms

rewrite28.0ms

series91.0ms

simplify54.0ms

prune94.0ms

regimes372.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling