Details

sample87.0ms

Algorithm

intervals

Results

37.0ms	63×	body	1280	valid
16.0ms	47×	body	640	valid
13.0ms	151×	body	80	valid
4.0ms	17×	body	320	valid
3.0ms	15×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	6
2	39	6
3	50	6
4	53	6
5	53	6

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 101

Calls

4 calls:

6.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
8.0ms	(* x (/ 1.0 (tan B)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
18.0ms	(/ 1.0 (sin B))
35.0ms	(/ 1.0 (tan B))
117.0ms	(* x (/ 1.0 (tan B)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	386	627
1	1479	584
2	5001	584

prune273.0ms

Filtered

113 candidates to 88 candidates (77.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 0.0b

Counts

114 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (* x 1.0) (tan B))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `div-inv` `difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

11.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
3.0ms	(/ 1.0 (sin B))
5.0ms	(/ (* x 1.0) (tan B))

series263.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
19.0ms	(/ 1.0 (sin B))
116.0ms	(/ (* x 1.0) (tan B))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	316	461
1	1175	428
2	5001	428

prune162.0ms

Filtered

74 candidates to 56 candidates (75.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Merged error: 0.0b

Counts

85 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
0.1b	(/ (* x 1.0) (sin B))
0.2b	(/ 1.0 (sin B))
0.2b	(* (/ (* x 1.0) (sin B)) (cos B))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
7×	`associate-l`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/l*`
3×	`associate-r` `associate-*l/` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

7.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
5.0ms	(/ (* x 1.0) (sin B))
3.0ms	(/ 1.0 (sin B))
7.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

series304.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (/ 1.0 (sin B)) (* (/ (* x 1.0) (sin B)) (cos B)))
55.0ms	(/ (* x 1.0) (sin B))
23.0ms	(/ 1.0 (sin B))
107.0ms	(* (/ (* x 1.0) (sin B)) (cos B))

simplify56.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	393	673
1	1825	595
2	5002	595

prune202.0ms

Filtered

101 candidates to 73 candidates (72.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	102	7	109

Merged error: 0.0b

Counts

109 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin B)) (cbrt (sin B)))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
2.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))

series426.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
101.0ms	(cbrt (sin B))
101.0ms	(cbrt (sin B))
101.0ms	(cbrt (sin B))

simplify94.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	154	453
1	551	401
2	3082	369
3	5002	363

prune205.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Merged error: 0b

Counts

92 → 6

regimes51.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	8
1	12	8

end0.0ms

sample1.8s

Algorithm

intervals

Results

730.0ms	1717×	body	1280	valid
394.0ms	1407×	body	640	valid
326.0ms	4975×	body	80	valid
134.0ms	719×	body	320	valid
51.0ms	348×	body	160	valid