Details

sample74.0ms

Algorithm

intervals

Results

25.0ms	80×	body	1280	valid
13.0ms	58×	body	640	valid
12.0ms	257×	body	80	valid
5.0ms	35×	body	320	valid
2.0ms	20×	body	160	valid

simplify16.0ms

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 (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.5b

Counts

2 → 2

localize16.0ms

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))

rewrite23.0ms

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:

4.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series306.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
215.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5003	791

prune275.0ms

Filtered

107 candidates to 74 candidates (69.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 0.0b

Counts

109 → 8

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))

rewrite20.0ms

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))

series352.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
112.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
213.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (38.0ms)

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

prune364.0ms

Filtered

71 candidates to 49 candidates (69.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	72	7	79

Merged error: 0b

Counts

79 → 7

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow a2 2) (pow a1 2))
0.2b	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.4b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite40.0ms

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))

series336.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (pow a2 2) (pow a1 2))
214.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
95.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (39.0ms)

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

prune232.0ms

Filtered

131 candidates to 69 candidates (52.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	131	7	138

Merged error: 0b

Counts

138 → 7

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))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite143.0ms

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:

4.0ms	(+ (* a1 a1) (* a2 a2))
55.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a1 a1) (* a2 a2))
215.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
65.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
101.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify128.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.5s

Filtered

729 candidates to 374 candidates (51.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	729	0	729
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	729	7	736

Merged error: 0b

Counts

736 → 7

regimes215.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

822.0ms	2559×	body	1280	valid
468.0ms	2124×	body	640	valid
408.0ms	7995×	body	80	valid
165.0ms	1067×	body	320	valid
65.0ms	585×	body	160	valid

Details

sample74.0ms

simplify16.0ms

prune8.0ms

localize16.0ms

rewrite23.0ms

series306.0ms

simplify54.0ms

prune275.0ms

localize10.0ms

rewrite20.0ms

series352.0ms

simplify45.0ms

prune364.0ms

localize12.0ms

rewrite40.0ms

series336.0ms

simplify52.0ms

prune232.0ms

localize12.0ms

rewrite143.0ms

series415.0ms

simplify128.0ms

prune1.5s

regimes215.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling