Details

sample254.0ms

Algorithm

intervals

Results

181.0ms	99×	body	2560	valid
50.0ms	92×	body	1280	valid
5.0ms	27×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	21×	body	320	valid
1.0ms	15×	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: 60.0b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

4.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
54×	`associate-/r` `associate-/l`
51×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
39×	`add-cube-cbrt`
18×	`frac-2neg` `clear-num`
10×	`times-frac`
5×	`distribute-lft-out--`
4×	`difference-of-squares`
3×	`add-log-exp`
2×	`div-inv`
1×	`pow1` `add-exp-log` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`

Counts

1 → 102

Calls

1 calls:

20.0ms

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

series111.0ms

Counts

1 → 3

Calls

1 calls:

111.0ms

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

simplify88.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	856	1221
1	3713	1171
2	5001	1168

prune143.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	1	106

Merged error: 0.4b

Counts

106 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

34.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
7.0ms	(* 0.0021164021164021165 (pow x 5))
7.0ms	(* 0.022222222222222223 (pow x 3))

series164.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
56.0ms	(* 0.0021164021164021165 (pow x 5))
46.0ms	(* 0.022222222222222223 (pow x 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	291	442
1	1207	415
2	5002	415

prune145.0ms

Filtered

86 candidates to 49 candidates (57.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Merged error: 0.3b

Counts

87 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
23×	`associate-l`
22×	`distribute-lft-out`
20×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`pow1` `unpow-prod-down` `add-cbrt-cube`
6×	`prod-exp` `unswap-sqr`
4×	`sum-log` `sqr-pow`
3×	`+-commutative`
2×	`pow-to-exp` `associate-+l+` `flip3-+` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`unpow3`

Counts

4 → 92

Calls

4 calls:

37.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
26.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
7.0ms	(* 0.0021164021164021165 (pow x 5))
7.0ms	(* 0.022222222222222223 (pow x 3))

series313.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
154.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
55.0ms	(* 0.0021164021164021165 (pow x 5))
39.0ms	(* 0.022222222222222223 (pow x 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	334	566
1	1412	541
2	5001	541

prune179.0ms

Filtered

104 candidates to 59 candidates (56.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	104	5	109

Merged error: 0.3b

Counts

109 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

791×	`*-un-lft-identity`
486×	`distribute-lft-out`
367×	`associate-l`
315×	`cbrt-prod`
126×	`swap-sqr`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
16×	`associate-r`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cbrt-cube`
6×	`add-exp-log`
4×	`frac-times` `cbrt-unprod` `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`

Counts

4 → 260

Calls

4 calls:

81.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
35.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
33.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
36.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

315.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
493.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
280.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
296.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify100.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	505	5268
1	1972	5092
2	5002	3592

prune309.0ms

Filtered

272 candidates to 75 candidates (27.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	260	12	272
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	260	17	277

Merged error: 0.2b

Counts

277 → 17

regimes93.0ms

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

sample6.8s

Algorithm

intervals

Results

5.0s	3168×	body	2560	valid
1.3s	2546×	body	1280	valid
218.0ms	1253×	body	640	valid
110.0ms	8000×	pre	80	true
66.0ms	645×	body	320	valid
25.0ms	345×	body	160	valid
2.0ms	43×	body	80	valid