Details

analyze688.0ms

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

18.0ms	47×	body	1280	valid
8.0ms	45×	body	640	valid
5.0ms	135×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid

simplify505.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

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: 0.4b

Counts

2 → 1

localize10.0ms

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))

rewrite35.0ms

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)))
14.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series66.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- 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))

simplify53.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune236.0ms

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: 0.1b

Counts

117 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.3b	(* (tan x) (tan x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (sin x))
6.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(* (tan x) (tan x))

series50.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (tan x) (sin x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
16.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
8.0ms	(* (tan x) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4977	791
1	4977	791

prune139.0ms

Filtered

63 candidates to 94 candidates (-49.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	95	14	109

Merged error: 0.1b

Counts

109 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

292×	`*-un-lft-identity`
264×	`times-frac`
208×	`add-sqr-sqrt`
104×	`add-cube-cbrt`
68×	`distribute-lft-out`
52×	`difference-of-squares`
36×	`associate-/r*`
26×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/r/`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`associate-/l*`
7×	`flip3--` `flip--` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`unpow-prod-down` `pow-unpow`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 253

Calls

4 calls:

4.0ms	(- (sqrt 1.0) (tan x))
11.0ms	(/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x)))
21.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x))))
3.0ms	(pow (tan x) 2)

series82.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
23.0ms	(/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x)))
44.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x))))
9.0ms	(pow (tan x) 2)

simplify90.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4953	6451
1	4953	6451

prune510.0ms

Filtered

142 candidates to 265 candidates (-86.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	258	7	265
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	264	15	279

Merged error: 0.1b

Counts

279 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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:

17.0ms	(* (/ 1 (+ (pow (tan x) 2) 1.0)) (- 1.0 (pow (tan x) 2)))
5.0ms	(- 1.0 (pow (tan x) 2))
4.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series55.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ 1 (+ (pow (tan x) 2) 1.0)) (- 1.0 (pow (tan x) 2)))
8.0ms	(- 1.0 (pow (tan x) 2))
8.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)

simplify38.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5367	1270

prune164.0ms

Filtered

78 candidates to 115 candidates (-47.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	115	15	130

Merged error: 0.1b

Counts

130 → 15

regimes184.0ms

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	22	15
1	22	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

390.0ms	1488×	body	1280	valid
221.0ms	1267×	body	640	valid
173.0ms	4284×	body	80	valid
86.0ms	659×	body	320	valid
26.0ms	302×	body	160	valid

Details

analyze688.0ms

sample45.0ms

simplify505.0ms

prune4.0ms

localize10.0ms

rewrite35.0ms

series66.0ms

simplify53.0ms

prune236.0ms

localize14.0ms

rewrite23.0ms

series50.0ms

simplify52.0ms

prune139.0ms

localize12.0ms

rewrite55.0ms

series82.0ms

simplify90.0ms

prune510.0ms

localize10.0ms

rewrite33.0ms

series55.0ms

simplify38.0ms

prune164.0ms

regimes184.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling