Details

analyze12.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample22.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify623.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	11
1	14	11

prune5.0ms

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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 91

Calls

3 calls:

7.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

series18.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify58.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5147	1251

prune175.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
0.0b	(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
0.0b	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

567×	`times-frac`
514×	`*-un-lft-identity`
348×	`add-sqr-sqrt`
336×	`sqrt-prod`
234×	`add-cube-cbrt`
84×	`distribute-lft-out`
56×	`distribute-lft-out--` `difference-of-squares`
41×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
11×	`flip3-+` `flip-+`
9×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`associate-/r*`
6×	`pow1`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 392

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
3.0ms	(sqrt (+ 1.0 x))
1.0ms	(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
22.0ms	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
4.0ms	(sqrt (+ 1.0 x))
2.0ms	(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
3.0ms	(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

simplify122.0ms

Algorithm

egg-herbie

Counts

404 → 404

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	6347	8037

prune442.0ms

Filtered

138 candidates to 404 candidates (-192.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	404	3	407

Merged error: 0b

Counts

407 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- 1.0 x))
0.0b	(cbrt (- 1.0 x))
0.0b	(/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x)))
0.0b	(/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

146×	`*-un-lft-identity`
112×	`times-frac`
110×	`add-sqr-sqrt`
90×	`cbrt-prod`
74×	`add-cube-cbrt`
72×	`sqrt-prod`
18×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
16×	`associate-/l*`
14×	`associate-/r*`
8×	`add-exp-log` `cbrt-div`
6×	`add-cbrt-cube`
4×	`pow1` `flip3--` `sqrt-div` `associate-/r/` `flip--` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `pow1/3` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 204

Calls

4 calls:

3.0ms	(cbrt (- 1.0 x))
3.0ms	(cbrt (- 1.0 x))
10.0ms	(/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x)))
10.0ms	(/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (- 1.0 x))
6.0ms	(cbrt (- 1.0 x))
21.0ms	(/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x)))
19.0ms	(/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5192	3576

prune602.0ms

Filtered

136 candidates to 216 candidates (-58.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	216	3	219

Merged error: 0b

Counts

219 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (log (exp (/ (- 1.0 x) (+ 1.0 x)))))
0.0b	(atan (sqrt (log (exp (/ (- 1.0 x) (+ 1.0 x))))))
0.0b	(log (exp (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
60×	`times-frac`
54×	`log-pow`
52×	`exp-prod`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
16×	`distribute-lft-out`
13×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
5×	`associate-/l*`
4×	`associate-/r*` `add-log-exp`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`div-sub` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `log-div` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 132

Calls

4 calls:

11.0ms	(sqrt (log (exp (/ (- 1.0 x) (+ 1.0 x)))))
1.0ms	(atan (sqrt (log (exp (/ (- 1.0 x) (+ 1.0 x))))))
10.0ms	(log (exp (/ (- 1.0 x) (+ 1.0 x))))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))

series12.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt (log (exp (/ (- 1.0 x) (+ 1.0 x)))))
2.0ms	(atan (sqrt (log (exp (/ (- 1.0 x) (+ 1.0 x))))))
3.0ms	(log (exp (/ (- 1.0 x) (+ 1.0 x))))
3.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5125	1662

prune231.0ms

Filtered

99 candidates to 144 candidates (-45.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	144	3	147

Merged error: 0b

Counts

147 → 3

regimes64.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample495.0ms

Algorithm

intervals

Results

394.0ms

8000×

body

valid

Details

analyze12.0ms

sample22.0ms

simplify623.0ms

prune5.0ms

localize10.0ms

rewrite23.0ms

series18.0ms

simplify58.0ms

prune175.0ms

localize10.0ms

rewrite63.0ms

series13.0ms

simplify122.0ms

prune442.0ms

localize14.0ms

rewrite36.0ms

series53.0ms

simplify73.0ms

prune602.0ms

localize15.0ms

rewrite36.0ms

series12.0ms

simplify48.0ms

prune231.0ms

regimes64.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze5.0ms

sample495.0ms

Profiling