Details

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample201.0ms

Algorithm

intervals

Results

115.0ms	48×	body	2560	valid
49.0ms	95×	body	1280	valid
17.0ms	64×	body	640	valid
6.0ms	28×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	10×	body	80	valid

simplify473.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	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: 29.7b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.4b	(- x (sin x))
0.6b	(- x (tan 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 → 78

Calls

3 calls:

7.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series51.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
20.0ms	(- x (tan x))

simplify62.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune84.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0b

Counts

88 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
0.4b	(- x (sin x))
0.6b	(- x (tan 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 → 226

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify71.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4944	3904
1	4944	3904

prune153.0ms

Filtered

137 candidates to 238 candidates (-73.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	238	3	241

Merged error: 0b

Counts

241 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x 9/40))
0.1b	(* (pow x 4) -27/2800)
0.2b	(* x 9/40)
17.1b	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* x (* x 9/40))
7.0ms	(* (pow x 4) -27/2800)
3.0ms	(* x 9/40)
8.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

series14.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* x (* x 9/40))
4.0ms	(* (pow x 4) -27/2800)
2.0ms	(* x 9/40)
6.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4903	646
1	4903	646

prune95.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	86	3	89

Merged error: 0b

Counts

89 → 3

regimes72.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch44.0ms

Steps

Iters	Range		Point
9	4.00253050412063e-05	126458.98420069004	0.026051316717657508
11	-1613.211003907984	-5.934790107255817e-26	-0.02787034415248285

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	41
1	48	41

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.9s	1615×	body	2560	valid
1.7s	2790×	body	1280	valid
523.0ms	1874×	body	640	valid
178.0ms	902×	body	320	valid
64.0ms	485×	body	160	valid
27.0ms	334×	body	80	valid

Details

analyze1.4s

sample201.0ms

simplify473.0ms

prune4.0ms

localize11.0ms

rewrite20.0ms

series51.0ms

simplify62.0ms

prune84.0ms

localize10.0ms

rewrite40.0ms

series40.0ms

simplify71.0ms

prune153.0ms

localize9.0ms

rewrite24.0ms

series14.0ms

simplify55.0ms

prune95.0ms

regimes72.0ms

bsearch44.0ms

simplify2.0ms

end0.0ms

sample6.6s

Profiling