Details

sample1.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.140381%

Results

12.0ms	44×	body	1280	valid
9.0ms	126×	body	80	valid
8.0ms	42×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	16×	body	160	valid

simplify365.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

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:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (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 → 105

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))

series72.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- 1.0 (* (tan x) (tan x)))
38.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
8.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify41.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5002	824

prune193.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	103	14	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	14	118

Merged error: 0.0b

Counts

118 → 14

localize9.0ms

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
92×	`add-sqr-sqrt`
72×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
21×	`add-exp-log`
19×	`pow1`
16×	`difference-of-squares`
15×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`tan-quot` `div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow2` `frac-times` `rec-exp` `frac-2neg` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

6.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
8.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series79.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x))))
32.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	579	2593
1	2779	2384
2	5001	2279

prune214.0ms

Filtered

108 candidates to 199 candidates (-84.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	199	14	213

Merged error: 0.0b

Counts

213 → 14

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)

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 (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:

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

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1588	240
3	5001	236

prune158.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	83	15	98

Merged error: 0.0b

Counts

98 → 15

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))
0.4b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

7.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
13.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))
50.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	266	869
1	914	800
2	5002	784

prune109.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	2	10	12
Picked	1	0	1
Done	0	2	2
Total	119	14	133

Merged error: 0.0b

Counts

133 → 14

regimes305.0ms

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	12	10
1	12	10

end0.0ms

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.140381%

Results

384.0ms	1483×	body	1280	valid
229.0ms	1306×	body	640	valid
170.0ms	4259×	body	80	valid
78.0ms	637×	body	320	valid
27.0ms	315×	body	160	valid

Details

sample1.9s

simplify365.0ms

prune4.0ms

localize10.0ms

rewrite24.0ms

series72.0ms

simplify41.0ms

prune193.0ms

localize9.0ms

rewrite32.0ms

series79.0ms

simplify77.0ms

prune214.0ms

localize13.0ms

rewrite11.0ms

series13.0ms

simplify59.0ms

prune158.0ms

localize9.0ms

rewrite33.0ms

series76.0ms

simplify40.0ms

prune109.0ms

regimes305.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling