Details

analyze753.0ms

Algorithm: search

sample92.0ms

Algorithm

intervals

Results

24.0ms	46×	body	1280	valid
15.0ms	34×	body	1280	invalid
12.0ms	41×	body	640	valid
11.0ms	150×	body	80	valid
6.0ms	21×	body	640	invalid
4.0ms	17×	body	320	valid
3.0ms	16×	body	320	invalid
2.0ms	10×	body	160	invalid
1.0ms	16×	body	80	invalid
0.0ms	2×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.5b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

2 → 87

Calls

2 calls:

10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series45.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	479	795
1	2384	738
2	5003	725

prune169.0ms

Filtered

64 candidates to 93 candidates (-45.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	8	94

Merged error: 0.0b

Counts

94 → 8

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.4b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series62.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
38.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	300	487
1	1619	424
2	5001	417

prune96.0ms

Filtered

39 candidates to 57 candidates (-46.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	58	7	65

Merged error: 0b

Counts

65 → 7

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
1×	`frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+`

Counts

2 → 83

Calls

2 calls:

10.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series49.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	314	880
1	1523	816
2	5001	800

prune123.0ms

Filtered

58 candidates to 89 candidates (-53.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	89	7	96

Merged error: 0b

Counts

96 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
0.7b	(/ (cos th) (sqrt 2.0))
5.6b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.6b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
35×	`sqrt-prod`
22×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `sqrt-div`
6×	`associate-r` `associate-/r*` `unswap-sqr`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 121

Calls

4 calls:

12.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms	(/ (cos th) (sqrt 2.0))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	352	1093
1	1256	1042
2	5001	1028

prune159.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	133	7	140

Merged error: 0b

Counts

140 → 7

regimes486.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

end0.0ms

analyze743.0ms

Algorithm: search

sample2.8s

Algorithm

intervals

Results

594.0ms	1332×	body	1280	valid
500.0ms	1137×	body	1280	invalid
363.0ms	4744×	body	80	valid
338.0ms	1088×	body	640	valid
285.0ms	938×	body	640	invalid
131.0ms	564×	body	320	valid
127.0ms	541×	body	320	invalid
41.0ms	272×	body	160	valid
40.0ms	485×	body	80	invalid
39.0ms	242×	body	160	invalid

Details

analyze753.0ms

sample92.0ms

simplify14.0ms

prune9.0ms

localize10.0ms

rewrite18.0ms

series45.0ms

simplify51.0ms

prune169.0ms

localize10.0ms

rewrite15.0ms

series62.0ms

simplify42.0ms

prune96.0ms

localize10.0ms

rewrite20.0ms

series49.0ms

simplify44.0ms

prune123.0ms

localize13.0ms

rewrite28.0ms

series50.0ms

simplify43.0ms

prune159.0ms

regimes486.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze743.0ms

sample2.8s

Profiling