Details

sample210.0ms

Algorithm

intervals

Results

140.0ms	93×	body	2560	valid
47.0ms	92×	body	1280	valid
7.0ms	40×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	2×	body	80	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	8
1	11	8

prune2.0ms

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

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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:

14.0ms

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

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

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

simplify47.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5316	327

prune48.0ms

Filtered

21 candidates to 25 candidates (-19.0%)

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

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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:

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* x 0.3333333333333333) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))
13.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
4.0ms	(* 0.022222222222222223 (pow x 3))

simplify38.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4948	920
1	4948	920

prune161.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	5	93

Merged error: 0.1b

Counts

93 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

rewrite43.0ms

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:

19.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
22.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
22.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
25.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5001	3117

prune580.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	94	10	104

Merged error: 0.1b

Counts

104 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
24.0ms	(cbrt x)
22.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
24.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

simplify35.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5223	1026

prune306.0ms

Filtered

48 candidates to 60 candidates (-25.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	59	11	70

Merged error: 0.1b

Counts

70 → 11

regimes103.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample7.1s

Algorithm

intervals

Results

5.2s	3271×	body	2560	valid
1.3s	2515×	body	1280	valid
224.0ms	1195×	body	640	valid
128.0ms	8000×	pre	80	true
73.0ms	617×	body	320	valid
30.0ms	356×	body	160	valid
2.0ms	46×	body	80	valid

Details

sample210.0ms

simplify2.0ms

prune2.0ms

localize6.0ms

rewrite15.0ms

series23.0ms

simplify47.0ms

prune48.0ms

localize13.0ms

rewrite27.0ms

series29.0ms

simplify38.0ms

prune161.0ms

localize15.0ms

rewrite43.0ms

series95.0ms

simplify50.0ms

prune580.0ms

localize33.0ms

rewrite18.0ms

series95.0ms

simplify35.0ms

prune306.0ms

regimes103.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.1s

Profiling