Details

sample201.0ms

Algorithm

intervals

Results

130.0ms	95×	body	2560	valid
50.0ms	88×	body	1280	valid
6.0ms	38×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	26×	body	320	valid
0.0ms	7×	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 (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: 60.1b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 130

Calls

2 calls:

7.0ms	(/ 1.0 (tan x))
18.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ 1.0 (tan x))
103.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify97.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	914	1367
1	4104	1312
2	5001	1309

prune183.0ms

Filtered

136 candidates to 92 candidates (32.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	1	137

Merged error: 0.4b

Counts

137 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`associate-r`
13×	`add-exp-log`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`unpow-prod-down`
7×	`pow1` `add-cbrt-cube`
6×	`prod-exp` `unswap-sqr`
5×	`add-log-exp`
4×	`distribute-lft-out` `sqr-pow`
2×	`pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `unpow3` `sum-log` `flip-+`

Counts

3 → 68

Calls

3 calls:

16.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
6.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))

series218.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
50.0ms	(* 0.0021164021164021165 (pow x 5))
36.0ms	(* 0.022222222222222223 (pow x 3))

simplify163.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	269	311
1	1082	290
2	4829	289
3	5002	289

prune132.0ms

Filtered

77 candidates to 47 candidates (39.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	5	78

Merged error: 0.3b

Counts

78 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
0.0b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
1.3b	(log (exp (* 0.022222222222222223 (pow x 3))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`-un-lft-identity` `associate-r*`
21×	`log-pow`
19×	`exp-prod`
15×	`add-exp-log` `add-cube-cbrt`
13×	`associate-l`
12×	`unpow-prod-down`
9×	`pow1` `unswap-sqr`
8×	`add-cbrt-cube`
7×	`add-log-exp`
6×	`prod-exp` `sqr-pow`
4×	`distribute-lft-out`
3×	`log-prod` `*-commutative`
2×	`pow-to-exp` `unpow3` `rem-log-exp` `pow-prod-down` `pow-exp` `cbrt-unprod`
1×	`+-commutative` `exp-to-pow` `flip3-+` `sum-log` `flip-+`

Counts

4 → 101

Calls

4 calls:

19.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
6.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))
7.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
47.0ms	(* 0.0021164021164021165 (pow x 5))
39.0ms	(* 0.022222222222222223 (pow x 3))
38.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	338	428
1	1237	397
2	5001	397

prune222.0ms

Filtered

113 candidates to 71 candidates (37.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	113	5	118

Merged error: 0.3b

Counts

118 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
0.6b	(log (exp (* 0.0021164021164021165 (pow x 5))))
1.3b	(log (exp (* 0.022222222222222223 (pow x 3))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

41×	`log-pow`
40×	`add-sqr-sqrt`
37×	`exp-prod`
30×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `unpow-prod-down`
12×	`associate-l` `unswap-sqr`
10×	`pow1`
8×	`add-cbrt-cube` `sqr-pow`
6×	`log-prod` `prod-exp` `add-log-exp`
4×	`rem-log-exp` `*-commutative`
2×	`pow-to-exp` `exp-to-pow` `unpow3` `pow-prod-down` `pow-exp` `cbrt-unprod`

Counts

4 → 118

Calls

4 calls:

6.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))
6.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))
6.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* 0.0021164021164021165 (pow x 5))
36.0ms	(* 0.022222222222222223 (pow x 3))
50.0ms	(log (exp (* 0.0021164021164021165 (pow x 5))))
36.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

simplify120.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	332	422
1	1106	386
2	4321	386
3	5002	386

prune292.0ms

Filtered

130 candidates to 86 candidates (33.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	130	5	135

Merged error: 0.3b

Counts

135 → 5

regimes27.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.3b 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

sample6.9s

Algorithm

intervals

Results

5.1s	3219×	body	2560	valid
1.3s	2519×	body	1280	valid
219.0ms	1291×	body	640	valid
102.0ms	8000×	pre	80	true
61.0ms	619×	body	320	valid
21.0ms	305×	body	160	valid
2.0ms	47×	body	80	valid