Details

sample369.0ms

Algorithm

intervals

Results

241.0ms	98×	body	1280	valid
75.0ms	27×	body	2560	valid
16.0ms	64×	body	640	valid
8.0ms	36×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	11×	body	80	valid

simplify280.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 16.1b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.1b	(- x (tan x))
0.1b	(- x (sin x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series37.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify158.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune88.0ms

Filtered

89 candidates to 63 candidates (29.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 0.1b

Counts

90 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.0b	(/ (- x (tan x)) (- x (sin x)))
0.1b	(- x (tan x))
0.1b	(- x (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 228

Calls

4 calls:

11.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
7.0ms	(/ (- x (tan x)) (- x (sin x)))
3.0ms	(- x (tan x))
3.0ms	(- x (sin x))

series39.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
12.0ms	(/ (- x (tan x)) (- x (sin x)))
10.0ms	(- x (tan x))
5.0ms	(- x (sin x))

simplify89.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	744	2645
1	3445	2437
2	5001	2274

prune131.0ms

Filtered

240 candidates to 116 candidates (51.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	239	1	240
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	241	3	244

Merged error: 0.1b

Counts

244 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
0.1b	(- x (sin x))
0.1b	(- x (sin x))
0.2b	(/ (tan x) (- x (sin x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`tan-quot` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `associate-/l/` `sub-div`

Counts

4 → 95

Calls

4 calls:

24.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
3.0ms	(- x (sin x))
3.0ms	(- x (sin x))
6.0ms	(/ (tan x) (- x (sin x)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- (/ x (- x (sin x))) (/ (tan x) (- x (sin x))))
5.0ms	(- x (sin x))
5.0ms	(- x (sin x))
13.0ms	(/ (tan x) (- x (sin x)))

simplify119.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	359	902
1	1107	860
2	4250	855
3	5003	855

prune102.0ms

Filtered

107 candidates to 80 candidates (25.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Merged error: 0.0b

Counts

110 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (tan x) (- x (sin x))) (/ (tan x) (- x (sin x))))
0.2b	(/ (tan x) (- x (sin x)))
0.2b	(/ (tan x) (- x (sin x)))
0.2b	(/ (tan x) (- x (sin x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
134×	`add-sqr-sqrt`
121×	`times-frac`
74×	`add-cube-cbrt`
30×	`distribute-lft-out--`
27×	`swap-sqr`
24×	`difference-of-squares`
22×	`add-exp-log` `add-cbrt-cube`
21×	`associate-r` `associate-l`
15×	`associate-/r*`
14×	`associate-/r/`
11×	`pow1`
9×	`associate-/l*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `div-inv`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`tan-quot` `frac-2neg` `clear-num` `associate-/l/`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 211

Calls

4 calls:

21.0ms	(* (/ (tan x) (- x (sin x))) (/ (tan x) (- x (sin x))))
6.0ms	(/ (tan x) (- x (sin x)))
6.0ms	(/ (tan x) (- x (sin x)))
6.0ms	(/ (tan x) (- x (sin x)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (/ (tan x) (- x (sin x))) (/ (tan x) (- x (sin x))))
10.0ms	(/ (tan x) (- x (sin x)))
10.0ms	(/ (tan x) (- x (sin x)))
11.0ms	(/ (tan x) (- x (sin x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	606	2421
1	3043	2207
2	5001	2136

prune185.0ms

Filtered

223 candidates to 155 candidates (30.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	222	5	227

Merged error: 0.0b

Counts

227 → 5

regimes53.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.4b

bsearch108.0ms

Steps

Iters	Range		Point
11	9.244429547692074e-24	0.06968268467981475	0.03063986986674429
15	-163.36048396326007	3.867226923396042e-305	-0.03379767516090271

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	43
1	45	43

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	772×	body	2560	valid
1.4s	2904×	body	1280	valid
535.0ms	2184×	body	640	valid
184.0ms	1076×	body	320	valid
72.0ms	579×	body	160	valid
35.0ms	485×	body	80	valid

Details

sample369.0ms

simplify280.0ms

prune4.0ms

localize12.0ms

rewrite20.0ms

series37.0ms

simplify158.0ms

prune88.0ms

localize10.0ms

rewrite40.0ms

series39.0ms

simplify89.0ms

prune131.0ms

localize11.0ms

rewrite40.0ms

series44.0ms

simplify119.0ms

prune102.0ms

localize18.0ms

rewrite48.0ms

series45.0ms

simplify90.0ms

prune185.0ms

regimes53.0ms

bsearch108.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling