Details

sample250.0ms

Algorithm

intervals

Results

181.0ms	99×	body	2560	valid
47.0ms	92×	body	1280	valid
5.0ms	27×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid
0.0ms	2×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4

prune6.0ms

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: 60.0b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

4.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

262×	`times-frac`
247×	`add-sqr-sqrt`
243×	`*-un-lft-identity`
235×	`add-cube-cbrt`
182×	`prod-diff`
81×	`frac-sub`
54×	`associate-/r` `associate-/l`
30×	`div-inv`
18×	`frac-2neg` `clear-num`
13×	`tan-quot` `fma-neg` `associate-/r/`
5×	`distribute-lft-out--`
4×	`difference-of-squares`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 299

Calls

1 calls:

24.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

series113.0ms

Counts

1 → 3

Calls

1 calls:

113.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1516	6798
1	5002	5330

prune359.0ms

Filtered

302 candidates to 145 candidates (48.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	1	303

Merged error: 0.4b

Counts

303 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series62.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	49	89
1	147	78
2	832	78
3	5001	78

prune39.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	10	3	13
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	4	14

Merged error: 0.3b

Counts

14 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))) (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 84

Calls

4 calls:

6.0ms	(* (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))) (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

284.0ms	(* (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))) (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
278.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
277.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
275.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

simplify66.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	414	1572
1	1477	1429
2	5001	1200

prune315.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	86	14	100

Merged error: 0.2b

Counts

100 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.6b	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b	(cbrt (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
9×	`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 → 55

Calls

4 calls:

1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
2.0ms	(cbrt (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

285.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
283.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
272.0ms	(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
280.0ms	(cbrt (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	340	1051
1	1100	984
2	4731	863
3	5001	858

prune301.0ms

Filtered

67 candidates to 63 candidates (94.0%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	2	9	11
Picked	1	0	1
Done	0	2	2
Total	65	16	81

Merged error: 0.2b

Counts

81 → 16

regimes86.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.9s	3168×	body	2560	valid
1.3s	2546×	body	1280	valid
211.0ms	1253×	body	640	valid
114.0ms	8000×	pre	80	true
65.0ms	645×	body	320	valid
24.0ms	345×	body	160	valid
2.0ms	43×	body	80	valid