Details

analyze279.0ms (8.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

sample69.0ms (2.1%)

Algorithm

1×

intervals

Results

20.0ms	100×	body	1280	nan
18.0ms	91×	body	2560	nan
11.0ms	256×	body	80	valid
6.0ms	43×	body	640	nan
2.0ms	24×	body	320	nan
0.0ms	6×	body	160	nan
0.0ms	6×	body	80	nan

simplify82.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5257	9

prune5.0ms (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: 30.6b

Counts

2 → 1

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
28.5b	(sqrt (- (* x x) 1.0))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))

series21.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

12.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))

simplify57.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5188	615

prune104.0ms (3.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0b

Counts

53 → 2

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
0.0b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b	(sqrt (- x (sqrt 1.0)))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`sqrt-prod`
19×	`*-un-lft-identity`
16×	`sqrt-div`
11×	`pow1` `add-cube-cbrt`
9×	`associate-r`
7×	`add-exp-log` `associate-l`
6×	`add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`frac-times` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `add-log-exp` `difference-of-squares` `unswap-sqr`
3×	`log-prod` `pow-prod-down`
2×	`rem-sqrt-square` `log-div` `associate-r/` `associate-l/` `distribute-lft-out` `distribute-lft-out--`
1×	`sqrt-unprod` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

15.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
4.0ms	(sqrt (- x (sqrt 1.0)))
4.0ms	(sqrt (+ x (sqrt 1.0)))
3.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

series37.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
5.0ms	(sqrt (- x (sqrt 1.0)))
5.0ms	(sqrt (+ x (sqrt 1.0)))

simplify34.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5142	1478

prune291.0ms (8.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	102	2	104

Merged error: 0b

Counts

104 → 2

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt (- (* x x) 1.0)))
0.0b	(log (+ x (exp (log (sqrt (- (* x x) 1.0))))))
5.7b	(exp (log (sqrt (- (* x x) 1.0))))
28.5b	(sqrt (- (* x x) 1.0))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`log-prod`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`add-cube-cbrt`
10×	`pow1`
7×	`exp-sum` `log-pow`
6×	`add-exp-log` `log-div` `exp-prod` `sqrt-div`
4×	`add-cbrt-cube` `add-log-exp`
3×	`flip3--` `sqrt-pow1` `pow1/2` `flip--` `difference-of-squares`
2×	`exp-diff` `rem-log-exp`
1×	`rem-sqrt-square` `flip3-+` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

11.0ms	(log (+ x (exp (log (sqrt (- (* x x) 1.0))))))
6.0ms	(exp (log (sqrt (- (* x x) 1.0))))
5.0ms	(log (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series26.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(log (+ x (exp (log (sqrt (- (* x x) 1.0))))))
8.0ms	(log (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))
4.0ms	(exp (log (sqrt (- (* x x) 1.0))))

simplify49.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5001	958

prune183.0ms (5.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	86	2	88

Merged error: 0b

Counts

88 → 2

regimes27.0ms (0.8%)

Accuracy

Total 0.0b remaining (2.4%)

Threshold costs 0.0b (2.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	14
1	23	14

end0.0ms (0%)

sample1.9s (58.3%)

Algorithm

1×

intervals

Results

637.0ms	3062×	body	2560	nan
433.0ms	2540×	body	1280	nan
343.0ms	8000×	body	80	valid
166.0ms	1223×	body	640	nan
71.0ms	665×	body	320	nan
22.0ms	308×	body	160	nan
10.0ms	287×	body	80	nan

Details

analyze279.0ms (8.5%)

sample69.0ms (2.1%)

simplify82.0ms (2.5%)

prune5.0ms (0.2%)

localize8.0ms (0.2%)

rewrite18.0ms (0.5%)

series21.0ms (0.6%)

simplify57.0ms (1.7%)

prune104.0ms (3.2%)

localize11.0ms (0.3%)

rewrite29.0ms (0.9%)

series37.0ms (1.1%)

simplify34.0ms (1%)

prune291.0ms (8.8%)

localize12.0ms (0.4%)

rewrite29.0ms (0.9%)

series26.0ms (0.8%)

simplify49.0ms (1.5%)

prune183.0ms (5.5%)

regimes27.0ms (0.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.9s (58.3%)

Profiling