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

sample81.0ms

Algorithm

intervals

Results

44.0ms	97×	body	1280	valid
17.0ms	62×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	67×	body	80	valid
1.0ms	5×	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

prune15.0ms

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

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))

rewrite16.0ms

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))

series40.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(* r (/ (sin b) (cos (+ b a))))
11.0ms	(/ (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

prune97.0ms

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

localize14.0ms

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))
0.3b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

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 b) (cos a)) (* (sin b) (sin a)))
14.0ms	(* 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))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
50.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
9.0ms	(* (sin b) (sin a))
27.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify67.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4927	1675
1	4927	1675

prune157.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

localize14.0ms

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

series85.0ms

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))
53.0ms	(/ (* (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

prune112.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	5	5	10
Picked	1	0	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:

0.1b	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
0.1b	(/ (sin b) (cos a))
0.2b	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))
0.3b	(/ (cos b) (/ (sin b) (cos a)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

223×	`add-sqr-sqrt`
211×	`times-frac`
118×	`*-un-lft-identity`
73×	`add-cube-cbrt`
45×	`difference-of-squares`
30×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/r/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `frac-sub` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 194

Calls

4 calls:

35.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
4.0ms	(/ (sin b) (cos a))
35.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))
6.0ms	(/ (cos b) (/ (sin b) (cos a)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1))
13.0ms	(/ (sin b) (cos a))
43.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (/ (sin a) 1)))
14.0ms	(/ (cos b) (/ (sin b) (cos a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4929	3685
1	4929	3685

prune150.0ms

Filtered

147 candidates to 206 candidates (-40.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	206	10	216

Merged error: 0.0b

Counts

216 → 10

regimes225.0ms

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	24	13
1	24	13

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2914×	body	1280	valid
522.0ms	1822×	body	640	valid
162.0ms	801×	body	320	valid
142.0ms	2150×	body	80	valid
45.0ms	313×	body	160	valid
0.0ms	1×	body	1280	invalid

Details

analyze1.2s

sample81.0ms

simplify3.0ms

prune15.0ms

localize10.0ms

rewrite16.0ms

series40.0ms

simplify57.0ms

prune97.0ms

localize14.0ms

rewrite34.0ms

series103.0ms

simplify67.0ms

prune157.0ms

localize14.0ms

rewrite24.0ms

series85.0ms

simplify38.0ms

prune112.0ms

localize15.0ms

rewrite91.0ms

series88.0ms

simplify71.0ms

prune150.0ms

regimes225.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

Profiling