Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample23.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	54×	body	1280	valid
5.0ms	47×	body	640	valid
3.0ms	118×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	15×	body	160	valid

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune9.0ms (0.3%)

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: 32.9b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 34

Calls

2 calls:

8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
3.0ms	(sqrt (+ x 1.0))

series14.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
4.0ms	(sqrt (+ x 1.0))

simplify53.0ms (2%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune86.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.2b

Counts

41 → 3

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
3.0ms	(sqrt (+ x 1.0))

series19.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
6.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
4.0ms	(sqrt (+ x 1.0))

simplify28.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5038	1051

prune178.0ms (6.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 0.0b

Counts

83 → 9

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

rewrite82.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

34.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
13.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series58.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
13.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify86.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4952	4249
1	4952	4249

prune802.0ms (29.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	262	9	271

Merged error: 0.0b

Counts

271 → 9

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
0.3b	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite65.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod`
74×	`*-un-lft-identity`
32×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
15×	`swap-sqr`
14×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `add-log-exp` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `-commutative` `div-inv`

Counts

4 → 135

Calls

4 calls:

23.0ms	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
20.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
8.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))

series43.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
11.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(/ 1.0 (* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))))
7.0ms	(* (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify55.0ms (2%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5254	2070

prune338.0ms (12.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	147	9	156

Merged error: 0.0b

Counts

156 → 9

regimes59.0ms (2.2%)

Accuracy

Total 0.1b remaining (85.2%)

Threshold costs 0.1b (85.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms (0%)

sample607.0ms (22.6%)

Algorithm

1×

intervals

Results

210.0ms	1712×	body	1280	valid
128.0ms	1278×	body	640	valid
118.0ms	4094×	body	80	valid
44.0ms	604×	body	320	valid
15.0ms	312×	body	160	valid

Details

analyze2.0ms (0.1%)

sample23.0ms (0.8%)

simplify6.0ms (0.2%)

prune9.0ms (0.3%)

localize6.0ms (0.2%)

rewrite12.0ms (0.4%)

series14.0ms (0.5%)

simplify53.0ms (2%)

prune86.0ms (3.2%)

localize7.0ms (0.2%)

rewrite22.0ms (0.8%)

series19.0ms (0.7%)

simplify28.0ms (1%)

prune178.0ms (6.6%)

localize10.0ms (0.4%)

rewrite82.0ms (3.1%)

series58.0ms (2.2%)

simplify86.0ms (3.2%)

prune802.0ms (29.9%)

localize10.0ms (0.4%)

rewrite65.0ms (2.4%)

series43.0ms (1.6%)

simplify55.0ms (2%)

prune338.0ms (12.6%)

regimes59.0ms (2.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample607.0ms (22.6%)

Profiling