Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	104×	body	1280	valid
6.0ms	118×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	1×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.5b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
4.0ms	(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
10.0ms	(- (atan (+ N 1.0)) (atan N))

simplify49.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	129	365
1	345	264
2	1480	254
3	5001	198

prune59.0ms

Filtered

44 candidates to 27 candidates (61.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	1	45

Merged error: 0.2b

Counts

45 → 1

localize5.0ms

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))

rewrite2.0ms

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:

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

series21.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(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

prune45.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Merged error: 0.1b

Counts

26 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1)))
16.9b	(cbrt (fma N (+ N 1.0) 1))
16.9b	(cbrt (fma N (+ N 1.0) 1))
16.9b	(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)))
1.0ms	(cbrt (fma N (+ N 1.0) 1))
1.0ms	(cbrt (fma N (+ N 1.0) 1))
1.0ms	(cbrt (fma N (+ N 1.0) 1))

series359.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1)))
86.0ms	(cbrt (fma N (+ N 1.0) 1))
84.0ms	(cbrt (fma N (+ N 1.0) 1))
84.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify93.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (79.0ms)

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

prune211.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	91	6	97

Merged error: 0.1b

Counts

97 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

16.3b	(sqrt (fma N (+ N 1.0) 1))
16.3b	(sqrt (fma N (+ N 1.0) 1))
16.9b	(cbrt (fma N (+ N 1.0) 1))
16.9b	(cbrt (fma N (+ N 1.0) 1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

1.0ms	(sqrt (fma N (+ N 1.0) 1))
2.0ms	(sqrt (fma N (+ N 1.0) 1))
1.0ms	(cbrt (fma N (+ N 1.0) 1))
1.0ms	(cbrt (fma N (+ N 1.0) 1))

series258.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (fma N (+ N 1.0) 1))
45.0ms	(sqrt (fma N (+ N 1.0) 1))
88.0ms	(cbrt (fma N (+ N 1.0) 1))
87.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	133	338
1	324	314
2	1036	310
3	5002	308

prune208.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	68	6	74

Merged error: 0.1b

Counts

74 → 6

regimes24.0ms

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

sample824.0ms

Algorithm

intervals

Results

445.0ms	2890×	body	1280	valid
146.0ms	4017×	body	80	valid
80.0ms	620×	body	640	valid
30.0ms	301×	body	320	valid
13.0ms	172×	body	160	valid