Details

sample28.0ms

Algorithm

intervals

Results

14.0ms	99×	body	1280	valid
4.0ms	123×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	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: 16.0b

localize7.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (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:

6.0ms

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

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

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

simplify76.0ms

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

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.4b	(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)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* (+ 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

prune61.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(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))
9.0ms	(cbrt (* (+ N 1.0) N))

series382.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
89.0ms	(cbrt (* (+ N 1.0) N))
88.0ms	(cbrt (* (+ N 1.0) N))
89.0ms	(cbrt (* (+ N 1.0) N))

simplify45.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (36.0ms)

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

prune247.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (* (cbrt N) (cbrt (* (+ N 1.0) N)))) (cbrt (* (+ N 1.0) N)))))
0.5b	(cbrt N)
16.0b	(cbrt (* (+ N 1.0) N))
16.0b	(cbrt (* (+ N 1.0) N))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

5×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `associate-*l/` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (* (cbrt N) (cbrt (* (+ N 1.0) N)))) (cbrt (* (+ N 1.0) N)))))
1.0ms	(cbrt N)
10.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series363.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (* (cbrt N) (cbrt (* (+ N 1.0) N)))) (cbrt (* (+ N 1.0) N)))))
173.0ms	(cbrt N)
91.0ms	(cbrt (* (+ N 1.0) N))
92.0ms	(cbrt (* (+ N 1.0) N))

simplify77.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	247	482
1	724	436
2	2568	416
3	5001	416

prune190.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes27.0ms

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

sample769.0ms

Algorithm

intervals

Results

411.0ms	2971×	body	1280	valid
119.0ms	3953×	body	80	valid
65.0ms	597×	body	640	valid
26.0ms	307×	body	320	valid
11.0ms	172×	body	160	valid