Details

sample38.0ms

Algorithm

intervals

Results

20.0ms	88×	body	1280	valid
6.0ms	131×	body	80	valid
4.0ms	24×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	7×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.6b	(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

0.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify73.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune56.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* (+ N 1.0) N))
0.0b	(* (+ N 1.0) N)
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
4×	`associate-l`
3×	`associate-r`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 39

Calls

3 calls:

2.0ms	(+ 1 (* (+ N 1.0) N))
9.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series66.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ 1 (* (+ N 1.0) N))
46.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify111.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	177	222
1	766	193
2	4572	193
3	5001	193

prune87.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ N 1.0))
0.2b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.5b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 88

Calls

4 calls:

2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
19.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ N 1.0))
90.0ms	(cbrt (+ N 1.0))
105.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
3.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify158.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	330	806
1	1079	745
2	4794	696
3	5001	692

prune246.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow N 2) (+ (* 1.0 N) 1))
0.5b	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
4×	`*-un-lft-identity`
3×	`sum-log`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `distribute-lft-out`

Counts

2 → 21

Calls

2 calls:

12.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
0.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

series22.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
3.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

simplify74.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	114	181
1	447	156
2	2686	155
3	5001	152

prune55.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes21.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample1.1s

Algorithm

intervals

Results

648.0ms	2872×	body	1280	valid
197.0ms	4067×	body	80	valid
106.0ms	604×	body	640	valid
39.0ms	291×	body	320	valid
16.0ms	166×	body	160	valid