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

sample160.0ms

Algorithm

intervals

Results

45.0ms	95×	body	1280	valid
14.0ms	48×	body	640	valid
7.0ms	18×	body	160	valid
5.0ms	27×	body	320	valid
4.0ms	68×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune11.0ms

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: 14.3b

Counts

2 → 2

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
14.3b	(cos (+ a b))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

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

series40.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
9.0ms	(cos (+ a b))

simplify56.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5357	439

prune99.0ms

Filtered

43 candidates to 56 candidates (-30.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	49	9	58

Merged error: 0.2b

Counts

58 → 9

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite24.0ms

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:

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify38.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4979	974
1	4979	974

prune147.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	12	87
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	83	13	96

Merged error: 0.0b

Counts

96 → 13

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
0.2b	(* (sin b) (sin a))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (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 a) (cos b)) (* (sin b) (sin a)))
4.0ms	(* (sin b) (sin a))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series105.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
10.0ms	(* (sin b) (sin a))
52.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6025	1735

prune166.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	110	14	124

Merged error: 0.0b

Counts

124 → 14

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
0.1b	(* (/ (cos b) (sin b)) (cos a))
0.2b	(/ (cos b) (sin b))
0.2b	(/ r (- (* (/ (cos b) (sin b)) (cos a)) (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 b) (sin b)) (cos a)) (sin a))
7.0ms	(* (/ (cos b) (sin b)) (cos a))
4.0ms	(/ (cos b) (sin b))
10.0ms	(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
14.0ms	(* (/ (cos b) (sin b)) (cos a))
6.0ms	(/ (cos b) (sin b))
43.0ms	(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4939	1437
1	4939	1437

prune106.0ms

Filtered

84 candidates to 111 candidates (-32.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	112	13	125

Merged error: 0.0b

Counts

125 → 13

regimes301.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b 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

sample4.4s

Algorithm

intervals

Results

1.4s	2841×	body	1280	valid
543.0ms	1863×	body	640	valid
162.0ms	778×	body	320	valid
140.0ms	2151×	body	80	valid
57.0ms	367×	body	160	valid

Details

analyze1.1s

sample160.0ms

simplify3.0ms

prune11.0ms

localize27.0ms

rewrite13.0ms

series40.0ms

simplify56.0ms

prune99.0ms

localize48.0ms

rewrite24.0ms

series86.0ms

simplify38.0ms

prune147.0ms

localize47.0ms

rewrite32.0ms

series105.0ms

simplify57.0ms

prune166.0ms

localize46.0ms

rewrite29.0ms

series83.0ms

simplify48.0ms

prune106.0ms

regimes301.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.4s

Profiling