Details

sample27.0ms

Algorithm

intervals

Results

14.0ms	100×	body	1280	valid
4.0ms	132×	body	80	valid
2.0ms	15×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	5×	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: 13.7b

localize6.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (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

prune37.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* (+ N 1.0) N))
0.0b	(* (+ N 1.0) N)
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite14.0ms

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:

2.0ms	(+ 1 (* (+ N 1.0) N))
10.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series74.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+ 1 (* (+ N 1.0) N))
51.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify120.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	177	222
1	766	193
2	4572	193
3	5001	193

prune91.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
16.3b	(cbrt (* (+ N 1.0) N))
16.3b	(cbrt (* (+ N 1.0) N))
16.3b	(cbrt (* (+ N 1.0) N))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
4.0ms	(cbrt (* (+ N 1.0) N))
3.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))

series354.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
113.0ms	(cbrt (* (+ N 1.0) N))
124.0ms	(cbrt (* (+ N 1.0) N))
108.0ms	(cbrt (* (+ N 1.0) N))

simplify72.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	208	572
1	609	524
2	2244	482
3	5002	474

prune187.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.2b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.2b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
7.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
19.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify104.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	110	649
1	391	565
2	2248	539
3	5001	520

prune128.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes21.0ms

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

sample739.0ms

Algorithm

intervals

Results

395.0ms	2845×	body	1280	valid
131.0ms	4041×	body	80	valid
69.0ms	617×	body	640	valid
30.0ms	342×	body	320	valid
10.0ms	155×	body	160	valid