Details

sample204.0ms

Algorithm

intervals

Results

132.0ms	95×	body	2560	valid
50.0ms	88×	body	1280	valid
7.0ms	38×	body	640	valid
3.0ms	256×	pre	80	true
3.0ms	26×	body	320	valid
0.0ms	7×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 60.1b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
256×	`add-sqr-sqrt`
252×	`*-un-lft-identity`
244×	`add-cube-cbrt`
182×	`prod-diff`
81×	`frac-sub`
57×	`associate-/r` `associate-/l`
31×	`div-inv`
19×	`frac-2neg` `clear-num`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `flip--`

Counts

2 → 329

Calls

2 calls:

4.0ms	(/ 1.0 (tan x))
26.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series142.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ 1.0 (tan x))
107.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

335 → 335

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1552	6949
1	5001	5476

prune385.0ms

Filtered

335 candidates to 172 candidates (48.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	334	1	335
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	335	1	336

Merged error: 0.4b

Counts

336 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(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 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))

series124.0ms

Counts

1 → 3

Calls

1 calls:

124.0ms

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

simplify50.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	27	59
1	65	52
2	228	52
3	978	52
4	5001	52

prune40.0ms

Filtered

13 candidates to 11 candidates (15.4%)

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

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`
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 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series3.9s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.0s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
934.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
908.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	405	1266
1	1425	1158
2	5001	964

prune301.0ms

Filtered

96 candidates to 72 candidates (25.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	89	11	100

Merged error: 0.2b

Counts

100 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

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:

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

series4.0s

Counts

4 → 12

Calls

4 calls:

997.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
973.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.1s	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
943.0ms	(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	201	848
1	621	800
2	2771	668
3	5001	652

prune291.0ms

Filtered

64 candidates to 60 candidates (6.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	64	11	75

Merged error: 0.2b

Counts

75 → 11

regimes55.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample7.0s

Algorithm

intervals

Results

5.2s	3219×	body	2560	valid
1.3s	2519×	body	1280	valid
221.0ms	1291×	body	640	valid
96.0ms	8000×	pre	80	true
64.0ms	619×	body	320	valid
22.0ms	305×	body	160	valid
2.0ms	47×	body	80	valid