Details

sample262.0ms

Algorithm

intervals

Results

190.0ms	115×	body	2560	valid
46.0ms	75×	body	1280	valid
7.0ms	39×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	19×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	3×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 59.9b

Counts

2 → 1

localize10.0ms

Local error

Found 1 expressions with local error:

1.6b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`times-frac`
5×	`distribute-lft-out--`
4×	`difference-of-squares`
3×	`add-cube-cbrt` `add-log-exp`
2×	`div-inv`
1×	`pow1` `add-exp-log` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--`

Counts

1 → 22

Calls

1 calls:

13.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify97.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	163	196
1	351	186
2	1151	186
3	3993	185
4	5001	185

prune72.0ms

Filtered

25 candidates to 21 candidates (16.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	1	26

Merged error: 0.3b

Counts

26 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

203.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
7.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))

series26.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
6.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	355	465
1	1532	436
2	5001	436

prune320.0ms

Filtered

92 candidates to 59 candidates (35.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	6	93

Merged error: 0.2b

Counts

93 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `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` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

11.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
55.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
57.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
59.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	480	1634
1	1767	1548
2	5001	1352

prune670.0ms

Filtered

99 candidates to 75 candidates (24.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	93	12	105

Merged error: 0.1b

Counts

105 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
56.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
57.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify127.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	260	1036
1	886	992
2	4352	852
3	5001	852

prune492.0ms

Filtered

64 candidates to 60 candidates (6.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	65	11	76

Merged error: 0.1b

Counts

76 → 11

regimes86.0ms

Accuracy

0% (0.1b 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

sample7.2s

Algorithm

intervals

Results

5.2s	3236×	body	2560	valid
1.3s	2513×	body	1280	valid
242.0ms	1327×	body	640	valid
119.0ms	8000×	pre	80	true
63.0ms	578×	body	320	valid
24.0ms	306×	body	160	valid
2.0ms	40×	body	80	valid

Details

sample262.0ms

simplify4.0ms

prune3.0ms

localize10.0ms

rewrite14.0ms

series19.0ms

simplify97.0ms

prune72.0ms

localize10.0ms

rewrite223.0ms

series26.0ms

simplify53.0ms

prune320.0ms

localize15.0ms

rewrite25.0ms

series234.0ms

simplify58.0ms

prune670.0ms

localize20.0ms

rewrite17.0ms

series227.0ms

simplify127.0ms

prune492.0ms

regimes86.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.2s

Profiling