Details

analyze1.2s

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

sample88.0ms

Algorithm

intervals

Results

42.0ms	87×	body	1280	valid
20.0ms	51×	body	640	valid
7.0ms	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

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: 13.2b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

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

24.0ms	(* r (/ (sin b) (cos (+ b a))))
12.0ms	(/ (sin b) (cos (+ b a)))
9.0ms	(cos (+ b a))

simplify66.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4896	783
1	4896	783

prune127.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	9	78

Merged error: 0.1b

Counts

78 → 9

localize15.0ms

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))))

rewrite35.0ms

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)))))
5.0ms	(* (sin b) (sin a))
11.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
53.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
9.0ms	(* (sin b) (sin a))
30.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify58.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4951	1675
1	4951	1675

prune187.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Merged error: 0.0b

Counts

120 → 10

localize15.0ms

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))))

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:

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))))

series87.0ms

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))))

simplify39.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5259	1023

prune129.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
0.2b	(* (cos b) (/ (cos a) (sin b)))
0.2b	(/ (cos a) (sin b))
0.2b	(/ r (- (* (cos b) (/ (cos a) (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 b) (/ (cos a) (sin b))) (sin a))
7.0ms	(* (cos b) (/ (cos a) (sin b)))
4.0ms	(/ (cos a) (sin b))
8.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))

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)))
12.0ms	(/ (cos a) (sin b))
44.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5086	1449

prune111.0ms

Filtered

84 candidates to 111 candidates (-32.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Merged error: 0.0b

Counts

121 → 9

regimes229.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	15
1	59	15

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2894×	body	1280	valid
535.0ms	1786×	body	640	valid
166.0ms	803×	body	320	valid
160.0ms	2154×	body	80	valid
59.0ms	363×	body	160	valid
1.0ms	3×	body	1280	invalid
0.0ms	1×	body	160	invalid

Details

analyze1.2s

sample88.0ms

simplify4.0ms

prune12.0ms

localize10.0ms

rewrite17.0ms

series46.0ms

simplify66.0ms

prune127.0ms

localize15.0ms

rewrite35.0ms

series109.0ms

simplify58.0ms

prune187.0ms

localize15.0ms

rewrite24.0ms

series87.0ms

simplify39.0ms

prune129.0ms

localize16.0ms

rewrite28.0ms

series90.0ms

simplify55.0ms

prune111.0ms

regimes229.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling