Details

analyze902.0ms

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

sample67.0ms

Algorithm

intervals

Results

27.0ms	61×	body	1280	valid
14.0ms	50×	body	640	valid
8.0ms	113×	body	80	valid
4.0ms	21×	body	320	valid
2.0ms	11×	body	160	valid
0.0ms	7×	body	80	invalid

simplify439.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	48	12
1	48	12

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r` `associate-/l`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `sum-log` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `pow-prod-down` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

7.0ms	(+ (neg (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (neg (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (tan B))
34.0ms	(* x (/ 1.0 (tan B)))

simplify61.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4984	1028
1	4984	1028

prune183.0ms

Filtered

90 candidates to 115 candidates (-27.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	10	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Merged error: 0.0b

Counts

116 → 10

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-/r*`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-neg-frac`

Counts

3 → 65

Calls

3 calls:

14.0ms	(+ (neg (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
5.0ms	(/ (* x 1.0) (tan B))
3.0ms	(/ 1.0 (sin B))

series57.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (neg (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
23.0ms	(/ (* x 1.0) (tan B))
5.0ms	(/ 1.0 (sin B))

simplify54.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4988	718
1	4988	718

prune105.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	74	10	84

Merged error: 0.0b

Counts

84 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (neg (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ (cos B) (sin B))
0.3b	(* x (* 1.0 (/ (cos B) (sin B))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
17×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
6×	`associate-/r` `associate-/l`
5×	`prod-exp` `cbrt-unprod`
4×	`associate-*r/`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down`
2×	`frac-2neg` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `associate-r` `neg-log` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

8.0ms	(+ (neg (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ (cos B) (sin B))
7.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (neg (* x (* 1.0 (/ (cos B) (sin B))))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
6.0ms	(/ (cos B) (sin B))
20.0ms	(* x (* 1.0 (/ (cos B) (sin B))))

simplify113.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4981	1060
1	4981	1060

prune173.0ms

Filtered

74 candidates to 102 candidates (-37.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 0.0b

Counts

112 → 9

localize15.0ms

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))

rewrite12.0ms

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)))
1.0ms	(cbrt (sin B))
2.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))

series81.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (cbrt (sin B)) (cbrt (sin B)))
20.0ms	(cbrt (sin B))
18.0ms	(cbrt (sin B))
20.0ms	(cbrt (sin B))

simplify64.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5456	490

prune77.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

regimes133.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms

analyze704.0ms

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

sample1.8s

Algorithm

intervals

Results

782.0ms	1766×	body	1280	valid
396.0ms	1431×	body	640	valid
267.0ms	3744×	body	80	valid
140.0ms	702×	body	320	valid
50.0ms	357×	body	160	valid
12.0ms	178×	body	80	invalid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze902.0ms

sample67.0ms

simplify439.0ms

prune9.0ms

localize14.0ms

rewrite28.0ms

series84.0ms

simplify61.0ms

prune183.0ms

localize15.0ms

rewrite24.0ms

series57.0ms

simplify54.0ms

prune105.0ms

localize15.0ms

rewrite24.0ms

series52.0ms

simplify113.0ms

prune173.0ms

localize15.0ms

rewrite12.0ms

series81.0ms

simplify64.0ms

prune77.0ms

regimes133.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze704.0ms

sample1.8s

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