Details

sample2.1s

Algorithm

intervals

sampling

Space saved by range analysis: 21.379927%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

24.0ms	53×	body	1280	invalid
20.0ms	40×	body	1280	valid
13.0ms	41×	body	640	valid
12.0ms	154×	body	80	valid
11.0ms	33×	body	640	invalid
4.0ms	18×	body	320	invalid
4.0ms	16×	body	320	valid
1.0ms	11×	body	80	invalid
1.0ms	5×	body	160	valid
1.0ms	5×	body	160	invalid

simplify15.0ms

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

prune8.0ms

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 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

3.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series50.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
39.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5001	791

prune344.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Merged error: 0b

Counts

108 → 8

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow a2 2) (pow a1 2))
0.1b	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.4b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
62×	`times-frac`
48×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
34×	`associate-r` `sqrt-prod`
28×	`unpow-prod-down` `distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `associate-/l*` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 122

Calls

3 calls:

7.0ms	(+ (pow a2 2) (pow a1 2))
17.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
11.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series56.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (pow a2 2) (pow a1 2))
38.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
12.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	1118
1	1557	1023
2	5001	1018

prune219.0ms

Filtered

70 candidates to 131 candidates (-87.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Merged error: 0b

Counts

139 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.4b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series67.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
25.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
36.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	309	564
1	1642	490
2	5001	481

prune99.0ms

Filtered

49 candidates to 71 candidates (-44.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	71	6	77

Merged error: 0b

Counts

77 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a2 2) (pow a1 2))
0.1b	(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.2b	(/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0)))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

1821×	`sqrt-prod`
1803×	`times-frac`
1534×	`*-un-lft-identity`
853×	`add-sqr-sqrt`
806×	`add-cube-cbrt`
445×	`associate-r`
364×	`unpow-prod-down` `distribute-lft-out`
54×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 1077

Calls

4 calls:

7.0ms	(+ (pow a2 2) (pow a1 2))
114.0ms	(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
27.0ms	(/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
15.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (pow a2 2) (pow a1 2))
37.0ms	(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
11.0ms	(/ (/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
15.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt (sqrt 2.0)))

simplify179.0ms

Algorithm

egg-herbie

Counts

1089 → 1089

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1817	16929
1	5001	14723

prune1.6s

Filtered

289 candidates to 1089 candidates (-276.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1088	1	1089
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	1089	6	1095

Merged error: 0b

Counts

1095 → 6

regimes431.0ms

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	14	7
1	14	7

end0.0ms

sample4.8s

Algorithm

intervals

sampling

Space saved by range analysis: 21.379927%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

613.0ms	1374×	body	1280	valid
551.0ms	1220×	body	1280	invalid
352.0ms	1130×	body	640	valid
346.0ms	4657×	body	80	valid
319.0ms	1011×	body	640	invalid
130.0ms	575×	body	320	valid
105.0ms	476×	body	320	invalid
41.0ms	264×	body	160	valid
40.0ms	242×	body	160	invalid
27.0ms	337×	body	80	invalid

Details

sample2.1s

simplify15.0ms

prune8.0ms

localize10.0ms

rewrite22.0ms

series50.0ms

simplify53.0ms

prune344.0ms

localize14.0ms

rewrite41.0ms

series56.0ms

simplify50.0ms

prune219.0ms

localize10.0ms

rewrite19.0ms

series67.0ms

simplify44.0ms

prune99.0ms

localize14.0ms

rewrite288.0ms

series68.0ms

simplify179.0ms

prune1.6s

regimes431.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.8s

Profiling