Details

sample317.0ms

Algorithm

intervals

Results

40.0ms	95×	body	1280	valid
17.0ms	68×	body	640	valid
4.0ms	22×	body	320	valid
3.0ms	58×	body	80	valid
2.0ms	13×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune4.0ms

Filtered

1 candidates to 0 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: 12.6b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite37.0ms

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)))
6.0ms	(cos (+ a b))

series165.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune192.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 0.2b

Counts

77 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
11.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos a) (cos b))
214.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
47.0ms	(* (sin a) (sin b))
112.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify60.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	428	1219
1	1858	1103
2	5001	1098

prune354.0ms

Filtered

117 candidates to 87 candidates (74.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	115	12	127

Merged error: 0.0b

Counts

127 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
4.0ms	(* r (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
8.0ms	(* (sin a) (sin b))

series344.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos a) (cos b))
38.0ms	(* r (sin b))
221.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
45.0ms	(* (sin a) (sin b))

simplify50.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	367	682
1	1616	594
2	5001	593

prune249.0ms

Filtered

93 candidates to 64 candidates (68.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	92	13	105

Merged error: 0b

Counts

105 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
30.0b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/r/` `associate-/l`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-exp` `clear-num` `cos-mult` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
10.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
5.0ms	(pow (* (sin a) (sin b)) 3)
3.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series276.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin a) (sin b))
115.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
65.0ms	(pow (* (sin a) (sin b)) 3)
46.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	338	899
1	1422	821
2	5001	809

prune280.0ms

Filtered

102 candidates to 72 candidates (70.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	103	12	115

Merged error: 0b

Counts

115 → 12

regimes298.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2843×	body	1280	valid
473.0ms	1872×	body	640	valid
126.0ms	734×	body	320	valid
124.0ms	2212×	body	80	valid
47.0ms	339×	body	160	valid