Details

sample217.0ms

Algorithm

intervals

Results

154.0ms	108×	body	2560	valid
40.0ms	79×	body	1280	valid
7.0ms	42×	body	640	valid
4.0ms	256×	pre	80	true
1.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	3×	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

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: 59.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.6b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
60×	`add-sqr-sqrt`
57×	`associate-/r` `associate-/l`
56×	`*-un-lft-identity`
48×	`add-cube-cbrt`
19×	`frac-2neg` `times-frac` `clear-num`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`div-inv`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `associate-/r/` `flip--`

Counts

2 → 130

Calls

2 calls:

8.0ms	(/ 1.0 (tan x))
19.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series143.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ 1.0 (tan x))
107.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	920	1367
1	4146	1312
2	5001	1309

prune253.0ms

Filtered

136 candidates to 92 candidates (67.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	1	137

Merged error: 0.4b

Counts

137 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
19×	`associate-r` `associate-l`
18×	`distribute-lft-out`
13×	`add-exp-log`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-log-exp`
7×	`pow1` `add-cbrt-cube` `unswap-sqr`
6×	`prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`sum-log`
2×	`+-commutative` `pow-to-exp` `associate-+r+` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`cube-mult` `flip3-+` `unpow3` `flip-+`

Counts

3 → 82

Calls

3 calls:

35.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
7.0ms	(* 0.0021164021164021165 (pow x 5))
8.0ms	(* 0.022222222222222223 (pow x 3))

series155.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
56.0ms	(* 0.0021164021164021165 (pow x 5))
38.0ms	(* 0.022222222222222223 (pow x 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	302	459
1	1297	426
2	5001	426

prune203.0ms

Filtered

91 candidates to 50 candidates (54.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	6	92

Merged error: 0.3b

Counts

92 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

791×	`*-un-lft-identity`
486×	`distribute-lft-out`
367×	`associate-l`
315×	`cbrt-prod`
126×	`swap-sqr`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
16×	`associate-r`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cbrt-cube`
6×	`add-exp-log`
4×	`frac-times` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 260

Calls

4 calls:

84.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
38.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
35.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
39.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
273.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
283.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
277.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify92.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	511	5268
1	2022	5092
2	5001	3625

prune416.0ms

Filtered

272 candidates to 75 candidates (27.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	260	12	272
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	263	15	278

Merged error: 0.2b

Counts

278 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

793×	`*-un-lft-identity`
498×	`cbrt-prod`
486×	`distribute-lft-out`
367×	`associate-l`
126×	`swap-sqr`
28×	`cbrt-div`
25×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`associate-r`
9×	`flip3-+` `flip-+`
4×	`pow1` `add-exp-log` `frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `associate-l/`
1×	`*-commutative`

Counts

4 → 255

Calls

4 calls:

33.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
38.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
35.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
92.0ms	(cbrt (* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

432.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
282.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
319.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
356.0ms	(cbrt (* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))))

simplify119.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	650	5986
1	2345	5883
2	5001	5251

prune437.0ms

Filtered

267 candidates to 74 candidates (27.7%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	262	5	267
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	262	20	282

Merged error: 0.1b

Counts

282 → 20

regimes119.0ms

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	18	7
1	18	7

end0.0ms

sample7.1s

Algorithm

intervals

Results

5.2s	3250×	body	2560	valid
1.3s	2531×	body	1280	valid
218.0ms	1233×	body	640	valid
110.0ms	8000×	pre	80	true
66.0ms	618×	body	320	valid
27.0ms	335×	body	160	valid
1.0ms	33×	body	80	valid