Details

sample28.0ms

Algorithm

intervals

Results

14.0ms	102×	body	1280	valid
4.0ms	131×	body	80	valid
2.0ms	12×	body	640	valid
1.0ms	6×	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: 12.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.5b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

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))
6.0ms	(- (atan (+ N 1.0)) (atan N))

series10.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
9.0ms	(- (atan (+ N 1.0)) (atan N))

simplify75.0ms

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

prune49.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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:

6.0ms	(+ 1 (* (+ N 1.0) N))
23.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series61.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+ 1 (* (+ N 1.0) N))
39.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify114.0ms

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

prune82.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
17.8b	(cbrt (* (+ N 1.0) N))
17.8b	(cbrt (* (+ N 1.0) N))
17.8b	(cbrt (* (+ N 1.0) N))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

21.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series393.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
91.0ms	(cbrt (* (+ N 1.0) N))
92.0ms	(cbrt (* (+ N 1.0) N))
90.0ms	(cbrt (* (+ N 1.0) N))

simplify44.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	353	803
1	1280	743
2	5001	669

prune254.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite20.0ms

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:

11.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
5.0ms	(cbrt N)

series711.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (cbrt N) (cbrt N))
171.0ms	(cbrt N)
172.0ms	(cbrt N)
171.0ms	(cbrt N)

simplify87.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune200.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes49.0ms

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

sample766.0ms

Algorithm

intervals

Results

390.0ms	2852×	body	1280	valid
126.0ms	4071×	body	80	valid
65.0ms	595×	body	640	valid
26.0ms	306×	body	320	valid
11.0ms	176×	body	160	valid