Details

sample28.0ms

Algorithm

intervals

Results

15.0ms	109×	body	1280	valid
4.0ms	120×	body	80	valid
1.0ms	10×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	5×	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: 14.2b

localize6.0ms

Local error

Found 1 expressions with local error:

1.9b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

5.0ms

(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(- (atan (+ N 1.0)) (atan N))

simplify75.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	72	123
1	142	114
2	286	112
3	678	111
4	2488	111
5	5001	111

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite21.0ms

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:

20.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series48.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

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

prune59.0ms

Pruning

6 alts after pruning (5 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))
0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite13.0ms

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:

4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ N 1.0))
86.0ms	(cbrt (+ N 1.0))
85.0ms	(cbrt (+ N 1.0))
4.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify55.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (49.0ms)

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

prune199.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow N 2) (+ (* 1.0 N) 1))
0.6b	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

rewrite25.0ms

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:

24.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
0.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

series27.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
3.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

simplify75.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (72.0ms)

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

prune56.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.6b

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	5
1	14	5

end0.0ms

sample737.0ms

Algorithm

intervals

Results

375.0ms	2851×	body	1280	valid
123.0ms	4049×	body	80	valid
65.0ms	614×	body	640	valid
27.0ms	328×	body	320	valid
10.0ms	158×	body	160	valid