Details

sample47.0ms

Algorithm

intervals

Results

24.0ms	87×	body	1280	valid
10.0ms	136×	body	80	valid
4.0ms	18×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	7×	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: 15.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `diff-atan` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

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))

simplify48.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	126	328
1	342	227
2	1471	217
3	5001	161

prune49.0ms

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	(fma N (+ N 1.0) 1)
0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

2 → 19

Calls

2 calls:

0.0ms	(fma N (+ N 1.0) 1)
0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

series22.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma N (+ N 1.0) 1)
2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

simplify137.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	101
1	104	89
2	513	89
3	4531	89
4	5001	89

prune56.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1)))
13.3b	(cbrt (fma N (+ N 1.0) 1))
13.3b	(cbrt (fma N (+ N 1.0) 1))
13.3b	(cbrt (fma N (+ N 1.0) 1))

rewrite11.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

5.0ms	(* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1)))
0.0ms	(cbrt (fma N (+ N 1.0) 1))
0.0ms	(cbrt (fma N (+ N 1.0) 1))
3.0ms	(cbrt (fma N (+ N 1.0) 1))

series388.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1)))
89.0ms	(cbrt (fma N (+ N 1.0) 1))
102.0ms	(cbrt (fma N (+ N 1.0) 1))
89.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify89.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	192	663
1	610	604
2	2685	559
3	5001	554

prune263.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

13.3b	(cbrt (fma N (+ N 1.0) 1))
13.3b	(cbrt (fma N (+ N 1.0) 1))
13.3b	(cbrt (fma N (+ N 1.0) 1))
13.3b	(cbrt (fma N (+ N 1.0) 1))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

0.0ms	(cbrt (fma N (+ N 1.0) 1))
0.0ms	(cbrt (fma N (+ N 1.0) 1))
0.0ms	(cbrt (fma N (+ N 1.0) 1))
1.0ms	(cbrt (fma N (+ N 1.0) 1))

series356.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (fma N (+ N 1.0) 1))
90.0ms	(cbrt (fma N (+ N 1.0) 1))
88.0ms	(cbrt (fma N (+ N 1.0) 1))
88.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify111.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (106.0ms)

Iter	Nodes	Cost
0	90	380
1	218	344
2	636	336
3	2640	336
4	5001	328

prune286.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.1b

regimes51.0ms

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	9	3
1	9	3

end0.0ms

sample1.3s

Algorithm

intervals

Results

687.0ms	2813×	body	1280	valid
298.0ms	4099×	body	80	valid
128.0ms	621×	body	640	valid
51.0ms	303×	body	320	valid
22.0ms	164×	body	160	valid