Details

analyze11.0ms (0.4%)

Algorithm

1×

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

sample211.0ms (7%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

valid

simplify472.0ms (15.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	786	11
1	786	11

prune7.0ms (0.2%)

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 (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite22.0ms (0.7%)

Algorithm

1×	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:

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

series24.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

19.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(/ (- 1.0 x) (+ 1.0 x))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify35.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5097	1256

prune220.0ms (7.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
66×	`times-frac`
56×	`cbrt-prod`
42×	`add-cube-cbrt`
38×	`sqrt-prod`
17×	`distribute-lft-out`
11×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/l*`
6×	`add-exp-log` `cbrt-div`
5×	`pow1` `add-cbrt-cube`
4×	`associate-/r*` `associate-/r/` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `flip--`
2×	`flip3-+` `pow1/3` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 141

Calls

4 calls:

9.0ms	(sqrt (/ (cbrt (- 1.0 x)) (+ 1.0 x)))
8.0ms	(/ (cbrt (- 1.0 x)) (+ 1.0 x))
3.0ms	(cbrt (- 1.0 x))
3.0ms	(cbrt (- 1.0 x))

series43.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (/ (cbrt (- 1.0 x)) (+ 1.0 x)))
12.0ms	(/ (cbrt (- 1.0 x)) (+ 1.0 x))
8.0ms	(cbrt (- 1.0 x))
6.0ms	(cbrt (- 1.0 x))

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5552	2382

prune510.0ms (16.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	153	3	156

Merged error: 0b

Counts

156 → 3

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`*-un-lft-identity`
84×	`add-sqr-sqrt`
81×	`times-frac`
80×	`cbrt-prod`
46×	`add-cube-cbrt`
29×	`sqrt-prod`
21×	`distribute-lft-out`
17×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`flip3-+` `associate-/r*` `flip-+` `div-inv` `add-log-exp`
3×	`rem-sqrt-square` `cbrt-div` `pow1/3`
2×	`sqrt-pow1` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

4 → 159

Calls

4 calls:

9.0ms	(sqrt (cbrt (/ (- 1.0 x) (+ 1.0 x))))
9.0ms	(cbrt (/ (- 1.0 x) (+ 1.0 x)))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))
7.0ms	(cbrt (/ (- 1.0 x) (+ 1.0 x)))

series22.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(cbrt (/ (- 1.0 x) (+ 1.0 x)))
7.0ms	(sqrt (cbrt (/ (- 1.0 x) (+ 1.0 x))))
6.0ms	(cbrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify90.0ms (3%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4925	2445
1	4925	2445

prune570.0ms (18.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	171	3	174

Merged error: 0b

Counts

174 → 3

regimes156.0ms (5.2%)

Accuracy

Total 0.0b remaining (57%)

Threshold costs 0.0b (57%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	11
1	21	11

end0.0ms (0%)

sample485.0ms (16.1%)

Algorithm

1×

intervals

Results

383.0ms

8000×

body

valid

Details

analyze11.0ms (0.4%)

sample211.0ms (7%)

simplify472.0ms (15.7%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite22.0ms (0.7%)

series24.0ms (0.8%)

simplify35.0ms (1.2%)

prune220.0ms (7.3%)

localize11.0ms (0.4%)

rewrite29.0ms (1%)

series43.0ms (1.4%)

simplify36.0ms (1.2%)

prune510.0ms (16.9%)

localize11.0ms (0.4%)

rewrite39.0ms (1.3%)

series22.0ms (0.7%)

simplify90.0ms (3%)

prune570.0ms (18.9%)

regimes156.0ms (5.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample485.0ms (16.1%)

Profiling