Details

sample307.0ms

Algorithm

intervals

Results

24.0ms	59×	body	1280	valid
16.0ms	59×	body	640	valid
9.0ms	150×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune9.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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))))
4.0ms	(/ 1.0 (tan B))
16.0ms	(/ 1.0 (sin B))
9.0ms	(* x (/ 1.0 (tan B)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
39.0ms	(/ 1.0 (tan B))
18.0ms	(/ 1.0 (sin B))
121.0ms	(* x (/ 1.0 (tan B)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (10.0ms)

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

prune262.0ms

Filtered

113 candidates to 88 candidates (77.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
12×	`times-frac`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

10.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
5.0ms	(/ (* x (cos B)) (sin B))
4.0ms	(/ 1.0 (sin B))
4.0ms	(* x (cos B))

series261.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (/ 1.0 (sin B)) (* 1.0 (/ (* x (cos B)) (sin B))))
93.0ms	(/ (* x (cos B)) (sin B))
18.0ms	(/ 1.0 (sin B))
35.0ms	(* x (cos B))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	333	572
1	1375	511
2	5001	511

prune183.0ms

Filtered

93 candidates to 68 candidates (73.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 0.0b

Counts

101 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.3b	(* x (/ 1.0 (sin B)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 107

Calls

4 calls:

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

series195.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1.0 (sin B))
18.0ms	(/ 1.0 (sin B))
106.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
53.0ms	(* x (/ 1.0 (sin B)))

simplify49.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	315	645
1	1562	560
2	5001	560

prune224.0ms

Filtered

119 candidates to 84 candidates (70.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	119	8	127

Merged error: 0.0b

Counts

127 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
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` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

7.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))

series478.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
112.0ms	(cbrt (tan B))
118.0ms	(cbrt (tan B))
114.0ms	(cbrt (tan B))

simplify77.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	168	505
1	527	468
2	2101	436
3	5001	432

prune215.0ms

Filtered

91 candidates to 65 candidates (71.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	91	8	99

Merged error: 0.0b

Counts

99 → 8

regimes62.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	8
1	12	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

707.0ms	1754×	body	1280	valid
353.0ms	1374×	body	640	valid
295.0ms	4991×	body	80	valid
121.0ms	683×	body	320	valid
46.0ms	350×	body	160	valid