Details

sample175.0ms

Algorithm

intervals

Results

92.0ms	86×	body	1280	valid
38.0ms	59×	body	640	valid
12.0ms	81×	body	80	valid
9.0ms	19×	body	320	valid
3.0ms	11×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	30
1	182	30
2	657	30
3	2727	30
4	5001	30

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1` `associate-r/` `associate-r` `associate-l*`
5×	`sqrt-prod` `difference-of-squares`
4×	`sub-neg` `times-frac` `associate-/r/`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `associate-*l/` `frac-add` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `diff-cos`

Counts

4 → 88

Calls

4 calls:

11.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series1.4s

Counts

4 → 10

Calls

4 calls:

1.3s	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
87.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
54.0ms	(- (cos x) (cos y))

simplify92.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	852	1769
1	3560	1553
2	5002	1553

prune551.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`diff-cos`
1×	`sqrt-prod`

Counts

4 → 60

Calls

4 calls:

4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))
4.0ms	(- (cos x) (cos y))
5.0ms	(- (cos x) (cos y))

series162.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
55.0ms	(- (cos x) (cos y))
55.0ms	(- (cos x) (cos y))
53.0ms	(- (cos x) (cos y))

simplify94.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	244	454
1	687	428
2	3117	424
3	5002	424

prune513.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`diff-cos`
1×	`sqrt-prod`

Counts

4 → 60

Calls

4 calls:

4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))
5.0ms	(- (cos x) (cos y))
5.0ms	(- (cos x) (cos y))

series161.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
54.0ms	(- (cos x) (cos y))
54.0ms	(- (cos x) (cos y))
52.0ms	(- (cos x) (cos y))

simplify95.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	251	435
1	716	428
2	3229	424
3	5003	424

prune570.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.0b	(- 3.0 (sqrt 5.0))
1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
7×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`sqrt-prod`
1×	`diff-cos`

Counts

4 → 60

Calls

4 calls:

5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series54.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
0.0ms	(- 3.0 (sqrt 5.0))
0.0ms	(- 3.0 (sqrt 5.0))
54.0ms	(- (cos x) (cos y))

simplify60.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	228	409
1	606	387
2	2256	383
3	5001	383

prune435.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes309.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	69
1	56	69

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	2709×	body	1280	valid
1.3s	1829×	body	640	valid
386.0ms	793×	body	320	valid
346.0ms	2309×	body	80	valid
114.0ms	360×	body	160	valid