Details

analyze699.0ms

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

sample39.0ms

Algorithm

intervals

Results

14.0ms	49×	body	1280	valid
8.0ms	47×	body	640	valid
5.0ms	130×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	14×	body	160	valid

simplify521.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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:

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

series70.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- 1.0 (* (tan x) (tan x)))
30.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 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

prune237.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	12	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Merged error: 0.0b

Counts

117 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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

series13.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5266	424

prune165.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	83	13	96

Merged error: 0.0b

Counts

96 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

8.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
5.0ms	(* (tan x) (tan x))

series70.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
10.0ms	(* (tan x) (sin x))
8.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5054	1679

prune162.0ms

Filtered

83 candidates to 121 candidates (-45.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	122	12	134

Merged error: 0.0b

Counts

134 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (tan x) 2)
0.3b	(pow (tan x) 2)
0.3b	(pow (tan x) 2)
0.4b	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
25×	`times-frac`
12×	`add-cube-cbrt`
11×	`unpow-prod-down`
10×	`difference-of-squares`
9×	`pow-unpow`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r/` `add-cbrt-cube` `distribute-lft-out`
3×	`pow-to-exp` `distribute-rgt-out--` `pow-pow` `pow-exp`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 87

Calls

4 calls:

3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)
41.0ms	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)
48.0ms	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

simplify32.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5194	1408

prune168.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	99	12	111

Merged error: 0.0b

Counts

111 → 12

regimes214.0ms

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	29	23
1	29	23

end0.0ms

sample981.0ms

Algorithm

intervals

Results

390.0ms	1509×	body	1280	valid
200.0ms	1192×	body	640	valid
164.0ms	4309×	body	80	valid
73.0ms	616×	body	320	valid
31.0ms	374×	body	160	valid

Details

analyze699.0ms

sample39.0ms

simplify521.0ms

prune4.0ms

localize10.0ms

rewrite24.0ms

series70.0ms

simplify53.0ms

prune237.0ms

localize13.0ms

rewrite13.0ms

series13.0ms

simplify37.0ms

prune165.0ms

localize14.0ms

rewrite26.0ms

series70.0ms

simplify43.0ms

prune162.0ms

localize10.0ms

rewrite52.0ms

series75.0ms

simplify32.0ms

prune168.0ms

regimes214.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample981.0ms

Profiling