Details

analyze701.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample40.0ms

Algorithm

intervals

Results

12.0ms	44×	body	1280	valid
8.0ms	44×	body	640	valid
6.0ms	128×	body	80	valid
4.0ms	28×	body	320	valid
1.0ms	12×	body	160	valid

simplify505.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5284	15

prune4.0ms

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: 0.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series67.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune240.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	102	14	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	14	117

Merged error: 0.0b

Counts

117 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)
2.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (cos x) 2)
3.0ms	(pow (cos x) 2)
4.0ms	(pow (sin x) 2)
6.0ms	(pow (sin x) 2)

simplify37.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5266	424

prune173.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	84	14	98

Merged error: 0.0b

Counts

98 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (pow (tan x) 2) 1.0))
0.2b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ (pow (tan x) 2) 1.0)))
0.3b	(pow (tan x) 2)
0.3b	(* (tan x) (tan x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
26×	`times-frac`
21×	`associate-r`
20×	`add-exp-log`
15×	`pow1`
13×	`add-cbrt-cube`
7×	`associate-l` `distribute-lft-out`
5×	`prod-exp`
4×	`tan-quot` `div-exp` `associate-/r*` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`frac-times` `unpow-prod-down` `pow-unpow` `swap-sqr` `associate-l/` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `flip3--` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `flip--` `flip-+` `div-inv`
1×	`pow2` `pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `pow-plus` `pow-exp` `clear-num` `pow-sqr` `un-div-inv` `pow-prod-up` `unpow2` `inv-pow` `difference-of-squares` `sqr-pow`

Counts

4 → 129

Calls

4 calls:

7.0ms	(/ 1 (+ (pow (tan x) 2) 1.0))
14.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ (pow (tan x) 2) 1.0)))
3.0ms	(pow (tan x) 2)
5.0ms	(* (tan x) (tan x))

series68.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1 (+ (pow (tan x) 2) 1.0))
33.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ (pow (tan x) 2) 1.0)))
8.0ms	(pow (tan x) 2)
9.0ms	(* (tan x) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5004	1459

prune232.0ms

Filtered

86 candidates to 141 candidates (-64.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	141	14	155

Merged error: 0.0b

Counts

155 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (pow (tan x) 2))
0.2b	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
0.3b	(pow (tan x) 2)
0.3b	(pow (tan x) 2)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac`
201×	`add-sqr-sqrt`
197×	`*-un-lft-identity`
99×	`add-cube-cbrt`
68×	`difference-of-squares`
38×	`associate-/r*`
32×	`distribute-lft-out`
23×	`unpow-prod-down`
19×	`unpow2` `sqr-pow`
17×	`add-exp-log` `distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
7×	`pow1` `div-exp`
6×	`pow-unpow` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 228

Calls

4 calls:

5.0ms	(- 1.0 (pow (tan x) 2))
16.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series56.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- 1.0 (pow (tan x) 2))
31.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
8.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)

simplify88.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4972	4413
1	4972	4413

prune297.0ms

Filtered

112 candidates to 240 candidates (-114.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	239	15	254

Merged error: 0.0b

Counts

254 → 15

regimes182.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	20
1	27	20

end0.0ms

sample984.0ms

Algorithm

intervals

Results

378.0ms	1464×	body	1280	valid
214.0ms	1251×	body	640	valid
164.0ms	4353×	body	80	valid
73.0ms	596×	body	320	valid
28.0ms	336×	body	160	valid

Details

analyze701.0ms

sample40.0ms

simplify505.0ms

prune4.0ms

localize22.0ms

rewrite25.0ms

series67.0ms

simplify57.0ms

prune240.0ms

localize13.0ms

rewrite11.0ms

series15.0ms

simplify37.0ms

prune173.0ms

localize10.0ms

rewrite33.0ms

series68.0ms

simplify51.0ms

prune232.0ms

localize10.0ms

rewrite41.0ms

series56.0ms

simplify88.0ms

prune297.0ms

regimes182.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample984.0ms

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