Details

analyze11.0ms

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

sample21.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify676.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	786	11
1	786	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	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite22.0ms

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:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
7.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
9.0ms	(/ (- 1.0 x) (+ 1.0 x))

series17.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
5.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify62.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5097	1256

prune163.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

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

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
130×	`sqrt-prod`
124×	`add-sqr-sqrt`
121×	`times-frac`
71×	`add-cube-cbrt`
64×	`cbrt-prod`
58×	`unpow-prod-down` `cube-prod`
31×	`distribute-lft-out`
25×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r/`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv`
5×	`associate-/l*`
4×	`associate-/r*` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-div`
2×	`cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `flip3--` `frac-2neg` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 237

Calls

4 calls:

7.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
12.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
7.0ms	(/ (- 1.0 x) (+ 1.0 x))
11.0ms	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

series24.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
9.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
3.0ms	(/ (- 1.0 x) (+ 1.0 x))
8.0ms	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

simplify69.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5148	3732

prune321.0ms

Filtered

119 candidates to 249 candidates (-109.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	249	3	252

Merged error: 0b

Counts

252 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 112

Calls

3 calls:

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

series10.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(sqrt (- 1.0 x))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
5.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5050	1754

prune165.0ms

Filtered

66 candidates to 121 candidates (-83.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	121	3	124

Merged error: 0b

Counts

124 → 3

regimes139.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample480.0ms

Algorithm

intervals

Results

385.0ms

8000×

body

valid

Details

analyze11.0ms

sample21.0ms

simplify676.0ms

prune5.0ms

localize10.0ms

rewrite22.0ms

series17.0ms

simplify62.0ms

prune163.0ms

localize11.0ms

rewrite48.0ms

series24.0ms

simplify69.0ms

prune321.0ms

localize9.0ms

rewrite24.0ms

series10.0ms

simplify51.0ms

prune165.0ms

regimes139.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample480.0ms

Profiling