Details

sample2.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results

16.0ms	37×	body	1280	invalid
16.0ms	35×	body	1280	valid
15.0ms	40×	body	640	valid
12.0ms	40×	body	640	invalid
12.0ms	150×	body	80	valid
5.0ms	21×	body	320	valid
5.0ms	21×	body	320	invalid
2.0ms	10×	body	160	valid
1.0ms	6×	body	160	invalid
1.0ms	11×	body	80	invalid

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

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))

rewrite21.0ms

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)))
4.0ms	(/ (cos th) (sqrt 2.0))

series48.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
38.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (43.0ms)

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

prune194.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	9	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Merged error: 0b

Counts

108 → 9

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:

3.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series63.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
23.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
34.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (36.0ms)

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

prune110.0ms

Filtered

49 candidates to 71 candidates (-44.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Merged error: 0b

Counts

80 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
34×	`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×	`flip3-+` `associate-r` `prod-exp` `cbrt-unprod` `flip-+`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `associate-/l/`

Counts

4 → 717

Calls

4 calls:

3.0ms	(+ (* a1 a1) (* a2 a2))
53.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
39.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify121.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.4s

Filtered

374 candidates to 729 candidates (-94.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	728	1	729
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	730	7	737

Merged error: 0b

Counts

737 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.3b	(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.3b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

3.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
13.0ms	(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
13.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series134.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
22.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
34.0ms	(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
72.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify84.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	594	2437
1	3183	2092
2	5001	2064

prune324.0ms

Filtered

102 candidates to 148 candidates (-45.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	148	7	155

Merged error: 0b

Counts

155 → 7

regimes457.0ms

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

sample5.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results

619.0ms	1384×	body	1280	valid
498.0ms	1110×	body	1280	invalid
351.0ms	4604×	body	80	valid
345.0ms	1112×	body	640	valid
312.0ms	999×	body	640	invalid
136.0ms	597×	body	320	valid
118.0ms	489×	body	320	invalid
48.0ms	303×	body	160	valid
40.0ms	262×	body	160	invalid
32.0ms	376×	body	80	invalid

Details

sample2.4s

simplify14.0ms

prune8.0ms

localize10.0ms

rewrite21.0ms

series48.0ms

simplify52.0ms

prune194.0ms

localize10.0ms

rewrite19.0ms

series63.0ms

simplify43.0ms

prune110.0ms

localize12.0ms

rewrite133.0ms

series58.0ms

simplify121.0ms

prune1.4s

localize18.0ms

rewrite40.0ms

series134.0ms

simplify84.0ms

prune324.0ms

regimes457.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.2s

Profiling