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

sample85.0ms

Algorithm

intervals

Results

41.0ms	85×	body	1280	valid
20.0ms	55×	body	640	valid
5.0ms	26×	body	320	valid
5.0ms	74×	body	80	valid
2.0ms	16×	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

prune12.0ms

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: 15.8b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ b a))))
0.2b	(/ (sin b) (cos (+ b a)))
3.1b	(cos (+ b a))

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 (+ b a))))
4.0ms	(/ (sin b) (cos (+ b a)))
4.0ms	(cos (+ b a))

series46.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* r (/ (sin b) (cos (+ b a))))
12.0ms	(/ (sin b) (cos (+ b a)))
6.0ms	(cos (+ b a))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4966	783
1	4966	783

prune101.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Merged error: 0.2b

Counts

78 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

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

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

series107.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
52.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
9.0ms	(* (sin b) (sin a))
29.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify68.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4927	1675
1	4927	1675

prune186.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sin b) r)
16.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
9.0ms	(* (sin b) (sin a))
55.0ms	(/ (* (sin b) r) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify38.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5242	1008

prune123.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	88	10	98

Merged error: 0.0b

Counts

98 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

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

series90.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
14.0ms	(* (cos b) (/ (cos a) (sin b)))
45.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))
12.0ms	(/ (cos a) (sin b))

simplify61.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5144	1445

prune110.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	112	9	121

Merged error: 0.0b

Counts

121 → 9

regimes241.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2830×	body	1280	valid
532.0ms	1851×	body	640	valid
169.0ms	779×	body	320	valid
158.0ms	2182×	body	80	valid
58.0ms	358×	body	160	valid
0.0ms	1×	body	1280	invalid

Details

analyze1.0s

sample85.0ms

simplify3.0ms

prune12.0ms

localize10.0ms

rewrite17.0ms

series46.0ms

simplify57.0ms

prune101.0ms

localize18.0ms

rewrite32.0ms

series107.0ms

simplify68.0ms

prune186.0ms

localize16.0ms

rewrite25.0ms

series88.0ms

simplify38.0ms

prune123.0ms

localize15.0ms

rewrite28.0ms

series90.0ms

simplify61.0ms

prune110.0ms

regimes241.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

Profiling