Details

analyze903.0ms

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

sample63.0ms

Algorithm

intervals

Results

25.0ms	56×	body	1280	valid
9.0ms	34×	body	640	valid
8.0ms	122×	body	80	valid
6.0ms	31×	body	320	valid
2.0ms	13×	body	160	valid
0.0ms	6×	body	80	invalid

simplify417.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	48	12
1	48	12

prune25.0ms

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)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite29.0ms

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:

8.0ms	(+ (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:

32.0ms	(+ (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)))

simplify62.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4984	1028
1	4984	1028

prune176.0ms

Filtered

90 candidates to 115 candidates (-27.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	108	7	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	7	116

Merged error: 0.0b

Counts

116 → 7

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))
0.1b	(/ x (sin B))
0.2b	(* (cos B) (/ x (sin B)))

rewrite26.0ms

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:

9.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* (cos B) (/ x (sin B)))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ x (sin B))
7.0ms	(* (cos B) (/ x (sin B)))

series57.0ms

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))
16.0ms	(* (cos B) (/ x (sin B)))

simplify65.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5041	1013

prune128.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Merged error: 0.0b

Counts

119 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

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

series35.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(- 1.0 (* (cos B) (* x 1.0)))
8.0ms	(* (cos B) (* x 1.0))
18.0ms	(/ (- 1.0 (* (cos B) (* x 1.0))) (sin B))

simplify61.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4969	846
1	4969	846

prune86.0ms

Filtered

53 candidates to 68 candidates (-28.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	6	74

Merged error: 0.0b

Counts

74 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (neg (sin B))) (tan B))
0.1b	(* x (neg (sin B)))
0.2b	(* (tan B) (sin B))
9.4b	(/ (* 1.0 (+ (* x (neg (sin B))) (tan B))) (* (tan B) (sin B)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(+ (* x (neg (sin B))) (tan B))
5.0ms	(* x (neg (sin B)))
4.0ms	(* (tan B) (sin B))
10.0ms	(/ (* 1.0 (+ (* x (neg (sin B))) (tan B))) (* (tan B) (sin B)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (* x (neg (sin B))) (tan B))
8.0ms	(* x (neg (sin B)))
10.0ms	(* (tan B) (sin B))
39.0ms	(/ (* 1.0 (+ (* x (neg (sin B))) (tan B))) (* (tan B) (sin B)))

simplify38.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5006	941

prune85.0ms

Filtered

67 candidates to 92 candidates (-37.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	91	7	98

Merged error: 0.0b

Counts

98 → 7

regimes116.0ms

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	14
1	12	14

end0.0ms

analyze708.0ms

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

762.0ms	1716×	body	1280	valid
383.0ms	1414×	body	640	valid
264.0ms	3773×	body	80	valid
148.0ms	733×	body	320	valid
54.0ms	364×	body	160	valid
10.0ms	162×	body	80	invalid
0.0ms	1×	body	640	invalid

Details

analyze903.0ms

sample63.0ms

simplify417.0ms

prune25.0ms

localize14.0ms

rewrite29.0ms

series84.0ms

simplify62.0ms

prune176.0ms

localize12.0ms

rewrite26.0ms

series57.0ms

simplify65.0ms

prune128.0ms

localize10.0ms

rewrite14.0ms

series35.0ms

simplify61.0ms

prune86.0ms

localize13.0ms

rewrite26.0ms

series73.0ms

simplify38.0ms

prune85.0ms

regimes116.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze708.0ms

sample1.8s

Profiling