Details

sample26.0ms

Algorithm

intervals

Results

10.0ms	72×	body	1280	valid
5.0ms	139×	body	80	valid
3.0ms	27×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	9×	body	160	valid

simplify5.0ms

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: 16.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.3b	(- (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))

simplify77.0ms

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

prune55.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.1b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite11.0ms

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:

10.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series51.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify57.0ms

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

prune68.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.5b	(cbrt N)
0.5b	(cbrt N)
0.5b	(cbrt N)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt N) (cbrt N))
0.0ms	(cbrt N)
0.0ms	(cbrt N)
1.0ms	(cbrt N)

series782.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cbrt N) (cbrt N))
187.0ms	(cbrt N)
186.0ms	(cbrt N)
194.0ms	(cbrt N)

simplify89.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	236

prune217.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ N 1.0) (cbrt (pow N 2)))
0.2b	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
0.5b	(cbrt N)
25.9b	(cbrt (pow N 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-prod`
21×	`add-sqr-sqrt`
17×	`associate-r`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`pow1` `add-exp-log`
7×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-*l/`
5×	`associate-l` `unswap-sqr`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`unpow2` `sqr-pow`
2×	`flip3-+` `pow1/3` `*-commutative` `flip-+`
1×	`distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

14.0ms	(* (+ N 1.0) (cbrt (pow N 2)))
21.0ms	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
0.0ms	(cbrt N)
1.0ms	(cbrt (pow N 2))

series760.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (+ N 1.0) (cbrt (pow N 2)))
64.0ms	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
182.0ms	(cbrt N)
186.0ms	(cbrt (pow N 2))

simplify46.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	304	533
1	1417	473
2	5001	445

prune251.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes53.0ms

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

sample763.0ms

Algorithm

intervals

Results

421.0ms	2919×	body	1280	valid
125.0ms	3973×	body	80	valid
72.0ms	634×	body	640	valid
28.0ms	312×	body	320	valid
11.0ms	162×	body	160	valid