Details

sample95.0ms

Algorithm

intervals

Results

28.0ms	69×	body	1280	valid
23.0ms	287×	body	80	valid
17.0ms	62×	body	640	valid
6.0ms	27×	body	320	valid
4.0ms	26×	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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite29.0ms

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))
19.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms	(/ (cos th) (sqrt 2.0))

series288.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
202.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
61.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (46.0ms)

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

prune275.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (/ (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)))

rewrite205.0ms

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))
111.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
18.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
210.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
97.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
59.0ms	(/ (/ (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

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite299.0ms

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:

3.0ms	(+ (* a1 a1) (* a2 a2))
195.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
23.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a1 a1) (* a2 a2))
223.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
294.0ms	(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
99.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify117.0ms

Algorithm

egg-herbie

Counts

666 → 666

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1788	11355
1	5001	10480

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (/ 1 (sqrt (sqrt 2.0))))
0.3b	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (* (cos th) (/ 1 (sqrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
0.3b	(* (* (cos th) (/ 1 (sqrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

1437×	`sqrt-prod`
972×	`times-frac`
525×	`add-sqr-sqrt`
511×	`*-un-lft-identity`
508×	`add-cube-cbrt`
488×	`associate-l`
172×	`add-exp-log`
88×	`prod-exp`
74×	`add-cbrt-cube`
52×	`div-exp`
35×	`associate-r`
34×	`cbrt-unprod`
24×	`associate-*r/`
23×	`pow1`
20×	`frac-times`
18×	`cbrt-undiv`
15×	`div-inv`
14×	`rec-exp` `1-exp`
10×	`pow-prod-down` `un-div-inv`
9×	`flip3-+` `associate-/r*` `flip-+`
7×	`associate-*l/` `unswap-sqr`
5×	`distribute-rgt-in` `pow-flip` `distribute-lft-in`
4×	`sqrt-pow1` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`pow1/2`
1×	`frac-2neg` `clear-num` `inv-pow`

Counts

4 → 708

Calls

4 calls:

18.0ms	(* (cos th) (/ 1 (sqrt (sqrt 2.0))))
269.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (* (cos th) (/ 1 (sqrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
41.0ms	(* (* (cos th) (/ 1 (sqrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series623.0ms

Counts

4 → 10

Calls

4 calls:

99.0ms	(* (cos th) (/ 1 (sqrt (sqrt 2.0))))
216.0ms	(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (* (cos th) (/ 1 (sqrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2))))
308.0ms	(* (* (cos th) (/ 1 (sqrt (sqrt 2.0)))) (+ (* a1 a1) (* a2 a2)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify137.0ms

Algorithm

egg-herbie

Counts

718 → 718

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1927	12002
1	5002	10985

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes192.0ms

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	24	18
1	24	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	2509×	body	1280	valid
657.0ms	8199×	body	80	valid
595.0ms	2088×	body	640	valid
219.0ms	987×	body	320	valid
82.0ms	539×	body	160	valid