Details

sample74.0ms

Algorithm

intervals

Results

20.0ms	66×	body	1280	valid
13.0ms	282×	body	80	valid
13.0ms	64×	body	640	valid
6.0ms	38×	body	320	valid
2.0ms	23×	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

localize14.0ms

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)))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite59.0ms

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:

10.0ms	(+ (* a1 a1) (* a2 a2))
35.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
10.0ms	(/ (cos th) (sqrt 2.0))

series302.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* a1 a1) (* a2 a2))
212.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

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

prune277.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

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))

rewrite51.0ms

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:

9.0ms	(+ (* a1 a1) (* a2 a2))
22.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
18.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series353.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* a1 a1) (* a2 a2))
111.0ms	(* (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 (39.0ms)

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

prune194.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
0.4b	(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`sqrt-div`
16×	`sqrt-prod`
15×	`add-exp-log` `add-cbrt-cube`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/`
9×	`flip3-+` `flip-+`
8×	`pow1` `associate-/l/`
6×	`times-frac` `associate-r` `associate-/r*`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 91

Calls

4 calls:

25.0ms	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
53.0ms	(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
7.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
8.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cos th) (sqrt (+ (* a1 a1) (* a2 a2))))
215.0ms	(/ (* (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt (+ (* a1 a1) (* a2 a2)))) (sqrt 2.0))
36.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
40.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	336	968
1	1658	827
2	5001	815

prune307.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.2b	(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))
5.8b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
107×	`add-sqr-sqrt` `sqrt-prod`
85×	`add-cube-cbrt` `*-un-lft-identity`
82×	`cbrt-prod`
58×	`associate-r`
47×	`add-exp-log`
33×	`add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
8×	`pow1`
7×	`unswap-sqr`
6×	`sqrt-div` `associate-/l*`
5×	`associate-l`
4×	`add-log-exp`
3×	`flip3-+` `flip-+` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 215

Calls

4 calls:

17.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
97.0ms	(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
7.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
8.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
216.0ms	(* (/ (* (cos th) (sqrt (+ (* a1 a1) (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (sqrt (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
37.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
42.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify138.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	750	4004
1	4535	3552
2	5001	3378

prune585.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes194.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms

sample2.2s

Algorithm

intervals

Results

748.0ms	2422×	body	1280	valid
442.0ms	2129×	body	640	valid
386.0ms	7959×	body	80	valid
156.0ms	1061×	body	320	valid
54.0ms	549×	body	160	valid