Details

sample40.0ms

Algorithm

intervals

Results

19.0ms	87×	body	1280	valid
9.0ms	136×	body	80	valid
4.0ms	18×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	7×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 15.1b

localize6.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

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:

3.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify79.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (11.0ms)

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

prune228.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.2b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite10.0ms

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:

9.0ms	(* (+ 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)))

simplify59.0ms

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

prune65.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ N 1.0))
0.2b	(cbrt (+ N 1.0))
0.2b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `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 → 95

Calls

4 calls:

2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
22.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ N 1.0))
85.0ms	(cbrt (+ N 1.0))
86.0ms	(cbrt (+ N 1.0))
102.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

simplify152.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	305	792
1	1006	747
2	4433	693
3	5002	689

prune279.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ N 1.0))
0.2b	(cbrt (+ N 1.0))
0.2b	(cbrt (- N 1.0))
13.3b	(cbrt (- (* N N) (* 1.0 1.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
14×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`flip3--` `flip3-+` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 57

Calls

4 calls:

2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (+ N 1.0))
2.0ms	(cbrt (- N 1.0))
2.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ N 1.0))
91.0ms	(cbrt (+ N 1.0))
99.0ms	(cbrt (- N 1.0))
191.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

simplify152.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	421	522
1	1298	493
2	4467	476
3	5002	476

prune293.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.1b

regimes58.0ms

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	12	4
1	12	4

end0.0ms

sample1.2s

Algorithm

intervals

Results

618.0ms	2813×	body	1280	valid
275.0ms	4099×	body	80	valid
113.0ms	621×	body	640	valid
43.0ms	303×	body	320	valid
18.0ms	164×	body	160	valid