Details

sample244.0ms

Algorithm

intervals

Results

181.0ms	109×	body	2560	valid
40.0ms	78×	body	1280	valid
6.0ms	36×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	19×	body	320	valid
1.0ms	12×	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 (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

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.1b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

4.0ms	(/ 1.0 (tan x))
13.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ 1.0 (tan x))
103.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	232	342
1	610	327
2	1894	327
3	5001	326

prune107.0ms

Filtered

56 candidates to 46 candidates (82.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	1	57

Merged error: 0.4b

Counts

57 → 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))

rewrite28.0ms

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:

4.0ms	(+ (* 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))
9.0ms	(* 0.022222222222222223 (pow x 3))

series275.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
61.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
50.0ms	(* 0.0021164021164021165 (pow x 5))
35.0ms	(* 0.022222222222222223 (pow x 3))

simplify55.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (11.0ms)

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

prune184.0ms

Filtered

92 candidates to 59 candidates (64.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	7	93

Merged error: 0.3b

Counts

93 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:

12.0ms	(* (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)))

series3.9s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
930.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.1s	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
940.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (44.0ms)

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

prune399.0ms

Filtered

99 candidates to 75 candidates (75.8%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	86	13	99
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	87	19	106

Merged error: 0.2b

Counts

106 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-div`
16×	`cbrt-prod`
9×	`flip3-+` `flip-+`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `associate-l/`

Counts

4 → 59

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 (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
10.0ms	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))

series4.1s

Counts

4 → 12

Calls

4 calls:

938.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
937.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.1s	(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.2s	(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	589	1393
1	1963	1320
2	5001	1211

prune347.0ms

Filtered

71 candidates to 63 candidates (88.7%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	3	13	16
Picked	1	0	1
Done	0	2	2
Total	70	20	90

Merged error: 0.2b

Counts

90 → 20

regimes101.0ms

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

sample7.4s

Algorithm

intervals

Results

5.2s	3208×	body	2560	valid
1.4s	2522×	body	1280	valid
424.0ms	1277×	body	640	valid
138.0ms	8000×	pre	80	true
71.0ms	633×	body	320	valid
25.0ms	308×	body	160	valid
2.0ms	52×	body	80	valid

Details

sample244.0ms

simplify5.0ms

prune2.0ms

localize9.0ms

rewrite18.0ms

series137.0ms

simplify57.0ms

prune107.0ms

localize10.0ms

rewrite28.0ms

series275.0ms

simplify55.0ms

prune184.0ms

localize14.0ms

rewrite26.0ms

series3.9s

simplify61.0ms

prune399.0ms

localize19.0ms

rewrite25.0ms

series4.1s

simplify59.0ms

prune347.0ms

regimes101.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.4s

Profiling