Details

sample78.0ms

Algorithm

intervals

Results

24.0ms	77×	body	1280	valid
14.0ms	67×	body	640	valid
13.0ms	264×	body	80	valid
7.0ms	44×	body	320	valid
1.0ms	13×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.5b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite32.0ms

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))
22.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series296.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
213.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
56.0ms	(/ (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

prune286.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.5b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite195.0ms

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:

2.0ms	(+ (* a1 a1) (* a2 a2))
103.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
22.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
216.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
98.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
69.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify122.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
0.5b	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

1434×	`sqrt-prod`
969×	`times-frac`
518×	`add-sqr-sqrt`
515×	`associate-l`
507×	`add-cube-cbrt` `*-un-lft-identity`
71×	`add-exp-log`
47×	`add-cbrt-cube`
27×	`prod-exp`
25×	`div-exp`
17×	`cbrt-unprod`
15×	`div-inv`
14×	`cbrt-undiv`
11×	`pow1` `frac-times` `associate-*r/`
9×	`associate-/r*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `associate-*l/` `unswap-sqr`
3×	`rec-exp` `1-exp` `associate-/l*`
2×	`*-commutative`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 654

Calls

4 calls:

2.0ms	(+ (* a1 a1) (* a2 a2))
184.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
22.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series842.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
215.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
493.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
106.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify121.0ms

Algorithm

egg-herbie

Counts

666 → 666

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1788	11355
1	5001	10480

prune2.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

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))
7.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
7.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite38.0ms

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:

23.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
4.0ms	(/ (cos th) (sqrt 2.0))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
67.0ms	(/ (cos th) (sqrt 2.0))
34.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
35.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify45.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (33.0ms)

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

prune381.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.3b

regimes249.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

831.0ms	2511×	body	1280	valid
458.0ms	2041×	body	640	valid
424.0ms	8164×	body	80	valid
170.0ms	1027×	body	320	valid
61.0ms	537×	body	160	valid