Details

analyze2.0ms (0%)

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

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

7.0ms	54×	body	1280	valid
5.0ms	50×	body	640	valid
3.0ms	125×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms (0%)

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: 31.0b

Counts

2 → 1

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

2.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 18

Calls

1 calls:

13.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series10.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

10.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify30.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5102	335

prune54.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	3	22

Merged error: 0.1b

Counts

22 → 3

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 55

Calls

2 calls:

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

series15.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5138	866

prune130.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 0.0b

Counts

64 → 7

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite94.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

28.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))

series64.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
18.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify129.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5073	11200

prune2.0s (20.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	451	6	457
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	453	11	464

Merged error: 0b

Counts

464 → 11

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)))
0.2b	(cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))
0.3b	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.4b	(pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)

rewrite217.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

1822×	`*-un-lft-identity`
1674×	`times-frac`
1600×	`sqrt-prod`
840×	`cbrt-prod`
702×	`add-sqr-sqrt` `add-cube-cbrt`
640×	`distribute-lft-out`
324×	`unpow-prod-down` `cube-prod`
90×	`associate-/l*`
36×	`cube-mult` `unpow3` `associate-/r*` `sqr-pow`
28×	`sqrt-div`
26×	`cube-div`
24×	`cbrt-div` `associate-/r/`
14×	`flip3-+` `flip-+`
12×	`add-exp-log` `div-inv`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 1096

Calls

4 calls:

49.0ms	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
16.0ms	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)))
10.0ms	(pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)
10.0ms	(cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))

series67.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)
19.0ms	(/ (/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
18.0ms	(/ 1.0 (cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3)))
11.0ms	(cbrt (pow (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))) 3))

simplify323.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1108 → 1108

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4968	26812
1	4968	26812

prune6.0s (60%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1106	2	1108
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	1111	8	1119

Merged error: 0b

Counts

1119 → 8

regimes50.0ms (0.5%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

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%)

sample623.0ms (6.3%)

Algorithm

1×

intervals

Results

218.0ms	1715×	body	1280	valid
137.0ms	1304×	body	640	valid
111.0ms	3997×	body	80	valid
48.0ms	643×	body	320	valid
17.0ms	341×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze2.0ms (0%)

sample22.0ms (0.2%)

simplify5.0ms (0%)

prune5.0ms (0%)

localize5.0ms (0.1%)

rewrite14.0ms (0.1%)

series10.0ms (0.1%)

simplify30.0ms (0.3%)

prune54.0ms (0.5%)

localize6.0ms (0.1%)

rewrite19.0ms (0.2%)

series15.0ms (0.1%)

simplify26.0ms (0.3%)

prune130.0ms (1.3%)

localize13.0ms (0.1%)

rewrite94.0ms (1%)

series64.0ms (0.6%)

simplify129.0ms (1.3%)

prune2.0s (20.4%)

localize18.0ms (0.2%)

rewrite217.0ms (2.2%)

series67.0ms (0.7%)

simplify323.0ms (3.3%)

prune6.0s (60%)

regimes50.0ms (0.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample623.0ms (6.3%)

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