Details

analyze940.0ms

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

sample69.0ms

Algorithm

intervals

Results

27.0ms	52×	body	1280	valid
16.0ms	55×	body	640	valid
9.0ms	125×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	invalid

simplify428.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	48	12
1	48	12

prune8.0ms

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

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (neg (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.1b	(/ 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)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (neg (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ 1.0 (tan B))
36.0ms	(* 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

prune190.0ms

Filtered

90 candidates to 115 candidates (-27.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Merged error: 0.0b

Counts

116 → 11

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (neg (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ 1.0 (sin B))

rewrite27.0ms

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:

15.0ms	(+ (neg (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
7.0ms	(/ (* x 1.0) (tan B))
4.0ms	(/ 1.0 (sin B))

series57.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (neg (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
24.0ms	(/ (* x 1.0) (tan B))
5.0ms	(/ 1.0 (sin B))

simplify58.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4988	718
1	4988	718

prune106.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 0.0b

Counts

85 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (neg (/ 1 (/ (tan B) (* 1.0 x)))) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (tan B) (* 1.0 x))
0.2b	(/ 1 (/ (tan B) (* 1.0 x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv` `add-log-exp`
5×	`pow1`
4×	`prod-exp` `distribute-lft-out`
3×	`rec-exp` `distribute-rgt-neg-in` `frac-2neg` `1-exp` `clear-num`
2×	`sum-log` `cbrt-unprod`
1×	`tan-quot` `+-commutative` `neg-sub0` `associate-+l-` `pow-flip` `flip3-+` `neg-log` `frac-add` `associate-/r/` `flip-+` `associate-/l/` `distribute-neg-frac` `inv-pow`

Counts

4 → 123

Calls

4 calls:

34.0ms	(+ (neg (/ 1 (/ (tan B) (* 1.0 x)))) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
5.0ms	(/ (tan B) (* 1.0 x))
8.0ms	(/ 1 (/ (tan B) (* 1.0 x)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (neg (/ 1 (/ (tan B) (* 1.0 x)))) (/ 1.0 (sin B)))
5.0ms	(/ 1.0 (sin B))
14.0ms	(/ (tan B) (* 1.0 x))
24.0ms	(/ 1 (/ (tan B) (* 1.0 x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5009	1334

prune159.0ms

Filtered

90 candidates to 135 candidates (-50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	135	9	144

Merged error: 0.0b

Counts

144 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* (cos B) (/ x (sin B)))))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ x (sin B))
19.0ms	(* (cos B) (/ x (sin B)))

simplify67.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5041	1013

prune108.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	113	8	121

Merged error: 0b

Counts

121 → 8

regimes114.0ms

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	11	11
1	11	11

end0.0ms

analyze730.0ms

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

751.0ms	1677×	body	1280	valid
427.0ms	1467×	body	640	valid
273.0ms	3827×	body	80	valid
140.0ms	703×	body	320	valid
47.0ms	326×	body	160	valid
11.0ms	159×	body	80	invalid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze940.0ms

sample69.0ms

simplify428.0ms

prune8.0ms

localize23.0ms

rewrite28.0ms

series85.0ms

simplify61.0ms

prune190.0ms

localize12.0ms

rewrite27.0ms

series57.0ms

simplify58.0ms

prune106.0ms

localize12.0ms

rewrite55.0ms

series71.0ms

simplify56.0ms

prune159.0ms

localize12.0ms

rewrite24.0ms

series61.0ms

simplify67.0ms

prune108.0ms

regimes114.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze730.0ms

sample1.8s

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