Details

analyze709.0ms

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

sample45.0ms

Algorithm

intervals

Results

12.0ms	41×	body	1280	valid
12.0ms	41×	body	640	valid
7.0ms	142×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify523.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4820	15
1	4820	15

prune9.0ms

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

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite54.0ms

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))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
25.0ms	(* (tan x) (tan x))
13.0ms	(* (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)))
9.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify67.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4915	1205
1	4915	1205

prune255.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	101	15	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	15	117

Merged error: 0.0b

Counts

117 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (tan x) (sqrt 1.0))
0.2b	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
0.2b	(- (sqrt 1.0) (tan x))
0.3b	(* (tan x) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 86

Calls

4 calls:

4.0ms	(+ (tan x) (sqrt 1.0))
13.0ms	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
4.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series41.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (tan x) (sqrt 1.0))
17.0ms	(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
8.0ms	(- (sqrt 1.0) (tan x))
9.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4970	879
1	4970	879

prune212.0ms

Filtered

69 candidates to 98 candidates (-42.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	98	15	113

Merged error: 0.0b

Counts

113 → 15

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 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)

series57.0ms

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))))
9.0ms	(pow (tan x) 2)
9.0ms	(pow (tan x) 2)

simplify104.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4930	4413
1	4930	4413

prune369.0ms

Filtered

114 candidates to 240 candidates (-110.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	3	10	13
Picked	0	1	1
Done	0	1	1
Total	240	15	255

Merged error: 0.0b

Counts

255 → 15

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 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)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`associate-l`
17×	`add-cube-cbrt`
15×	`add-exp-log`
14×	`times-frac`
9×	`add-cbrt-cube`
8×	`pow1` `unpow-prod-down` `associate-r` `difference-of-squares`
6×	`pow-unpow` `add-log-exp`
4×	`prod-exp` `unpow2` `sqr-pow`
3×	`sub-neg` `flip3--` `flip--` `distribute-lft-out` `unswap-sqr`
2×	`frac-times` `pow-to-exp` `pow-pow` `associate-*r/` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `distribute-rgt-in` `rec-exp` `distribute-lft-in` `flip3-+` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 103

Calls

4 calls:

5.0ms	(- 1.0 (pow (tan x) 2))
17.0ms	(* (/ 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)

series59.0ms

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)))
9.0ms	(pow (tan x) 2)
11.0ms	(pow (tan x) 2)

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4891	1270
1	4891	1270

prune175.0ms

Filtered

77 candidates to 115 candidates (-49.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	115	15	130

Merged error: 0.0b

Counts

130 → 15

regimes177.0ms

Accuracy

0% (0.3b 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	56	19
1	56	19

end0.0ms

sample1.0s

Algorithm

intervals

Results

380.0ms	1437×	body	1280	valid
217.0ms	1248×	body	640	valid
178.0ms	4312×	body	80	valid
84.0ms	663×	body	320	valid
30.0ms	340×	body	160	valid

Details

analyze709.0ms

sample45.0ms

simplify523.0ms

prune9.0ms

localize19.0ms

rewrite54.0ms

series67.0ms

simplify67.0ms

prune255.0ms

localize10.0ms

rewrite29.0ms

series41.0ms

simplify47.0ms

prune212.0ms

localize9.0ms

rewrite41.0ms

series57.0ms

simplify104.0ms

prune369.0ms

localize9.0ms

rewrite30.0ms

series59.0ms

simplify66.0ms

prune175.0ms

regimes177.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling