Details

sample317.0ms

Algorithm

intervals

Results

207.0ms	103×	body	2560	valid
63.0ms	69×	body	1280	valid
17.0ms	47×	body	640	valid
7.0ms	256×	pre	80	true
5.0ms	24×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	1×	body	80	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	220	8
1	220	8

prune5.0ms

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: 59.7b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

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:

6.0ms	(/ 1.0 (tan x))
25.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series63.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(/ 1.0 (tan x))
42.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4916	561
1	4916	561

prune144.0ms

Filtered

45 candidates to 56 candidates (-24.4%)

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

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
16.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
12.0ms	(* 0.0021164021164021165 (pow x 5))
11.0ms	(* 0.022222222222222223 (pow x 3))

series53.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))
12.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))
9.0ms	(* 0.0021164021164021165 (pow x 5))
8.0ms	(* 0.022222222222222223 (pow x 3))

simplify110.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4959	885
1	4959	885

prune297.0ms

Filtered

59 candidates to 92 candidates (-55.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 0.2b

Counts

93 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

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:

35.0ms	(* (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)))))
13.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
13.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
13.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (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)))))
36.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
36.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
37.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))

simplify65.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4987	3186
1	4987	3186

prune1.2s

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	92	15	107

Merged error: 0.2b

Counts

107 → 15

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

14.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
16.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
15.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
15.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333))))
42.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
41.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))
44.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* x 0.3333333333333333)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5554	2389

prune1.2s

Filtered

69 candidates to 73 candidates (-5.8%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	12	12
Picked	1	0	1
Done	0	2	2
Total	71	17	88

Merged error: 0.1b

Counts

88 → 17

regimes253.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample12.5s

Algorithm

intervals

Results

9.0s	3322×	body	2560	valid
2.4s	2486×	body	1280	valid
426.0ms	1240×	body	640	valid
218.0ms	8000×	pre	80	true
130.0ms	609×	body	320	valid
44.0ms	296×	body	160	valid
4.0ms	47×	body	80	valid

Details

sample317.0ms

simplify17.0ms

prune5.0ms

localize10.0ms

rewrite34.0ms

series63.0ms

simplify78.0ms

prune144.0ms

localize19.0ms

rewrite53.0ms

series53.0ms

simplify110.0ms

prune297.0ms

localize22.0ms

rewrite80.0ms

series154.0ms

simplify65.0ms

prune1.2s

localize40.0ms

rewrite63.0ms

series160.0ms

simplify53.0ms

prune1.2s

regimes253.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample12.5s

Profiling