Details

analyze17.0ms

Algorithm

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

sample287.0ms

Algorithm

intervals

Results

219.0ms	115×	body	2560	valid
47.0ms	76×	body	1280	valid
6.0ms	33×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	4×	body	80	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	220	8
1	220	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: 59.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.3b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite19.0ms

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 → 49

Calls

2 calls:

3.0ms	(/ 1.0 (tan x))
14.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series33.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/ 1.0 (tan x))
23.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4916	556
1	4916	556

prune88.0ms

Filtered

45 candidates to 55 candidates (-22.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	3	56

Merged error: 0.3b

Counts

56 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

9.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
5.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
5.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4959	885
1	4959	885

prune147.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	87	8	95

Merged error: 0.2b

Counts

95 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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:

15.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
5.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
5.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
58.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
59.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
59.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4987	2218
1	4987	2218

prune433.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	91	16	107

Merged error: 0.1b

Counts

107 → 16

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

4.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt x)

series127.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
22.0ms	(cbrt x)
22.0ms	(cbrt x)
24.0ms	(cbrt x)

simplify32.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4962	504
1	4962	504

prune237.0ms

Filtered

44 candidates to 58 candidates (-31.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	1	12	13
Picked	1	0	1
Done	0	2	2
Total	59	15	74

Merged error: 0.1b

Counts

74 → 15

regimes97.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample7.2s

Algorithm

intervals

Results

5.3s	3279×	body	2560	valid
1.4s	2527×	body	1280	valid
218.0ms	1192×	body	640	valid
128.0ms	8000×	pre	80	true
73.0ms	654×	body	320	valid
24.0ms	301×	body	160	valid
2.0ms	47×	body	80	valid

Details

analyze17.0ms

sample287.0ms

simplify9.0ms

prune2.0ms

localize5.0ms

rewrite19.0ms

series33.0ms

simplify46.0ms

prune88.0ms

localize10.0ms

rewrite28.0ms

series25.0ms

simplify61.0ms

prune147.0ms

localize14.0ms

rewrite32.0ms

series238.0ms

simplify50.0ms

prune433.0ms

localize34.0ms

rewrite9.0ms

series127.0ms

simplify32.0ms

prune237.0ms

regimes97.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.2s

Profiling