Details

sample25.0ms

Algorithm

intervals

Results

12.0ms	95×	body	1280	valid
4.0ms	135×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	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: 12.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

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:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (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))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

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

prune51.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

6.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify58.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune60.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.7b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 49

Calls

4 calls:

3.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (+ N 1.0))
1.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ N 1.0))
87.0ms	(cbrt (+ N 1.0))
89.0ms	(cbrt (+ N 1.0))
3.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify52.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	198	498
1	513	454
2	1617	445
3	5002	430

prune189.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (- N 1.0))
0.7b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
16.6b	(cbrt (- (* N N) (* 1.0 1.0)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
11×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`flip3--` `flip--` `difference-of-squares`
1×	`flip3-+` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 50

Calls

4 calls:

3.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (- N 1.0))
1.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
4.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ N 1.0))
98.0ms	(cbrt (- N 1.0))
9.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (/ (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
191.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	481	606
1	1462	551
2	5001	537

prune249.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes23.0ms

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

sample706.0ms

Algorithm

intervals

Results

382.0ms	2836×	body	1280	valid
120.0ms	4089×	body	80	valid
68.0ms	598×	body	640	valid
26.0ms	304×	body	320	valid
11.0ms	173×	body	160	valid