Details

analyze1.0ms (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%	0%	50%	4

sample40.0ms (1.4%)

Algorithm

1×

intervals

Results

15.0ms	54×	body	1280	valid
9.0ms	50×	body	640	valid
6.0ms	125×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	12×	body	160	valid

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms (0.2%)

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: 30.5b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1.0))
2.8b	(- (log (+ N 1.0)) (log N))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series9.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5481	434

prune86.0ms (2.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.0b

Counts

47 → 2

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(log (/ (+ N 1.0) N))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series8.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4970	619
1	4970	619

prune96.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	2	68

Merged error: 0.0b

Counts

68 → 2

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.5b	(/ 0.5 (* N N))
0.6b	(/ 0.3333333333333333 (pow N 3))
13.2b	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite54.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`times-frac`
41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
31×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `unpow3` `difference-of-squares` `sqr-pow`
3×	`cbrt-undiv` `frac-add`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `associate-+r+` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 122

Calls

4 calls:

31.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))
10.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
5.0ms	(/ 0.3333333333333333 (pow N 3))
4.0ms	(/ 0.5 (* N N))

series16.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
4.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))
4.0ms	(/ 0.3333333333333333 (pow N 3))
3.0ms	(/ 0.5 (* N N))

simplify37.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5101	1475

prune243.0ms (8.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	131	5	136

Merged error: 0.0b

Counts

136 → 5

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

13.2b	(+ (/ 0.3333333333333333 (pow N 3)) (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))))
16.2b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
16.2b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
16.2b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite61.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`cbrt-div`
81×	`frac-times`
63×	`frac-add`
51×	`flip3--` `frac-sub` `flip--`
37×	`add-sqr-sqrt`
27×	`associate-*l/`
24×	`cbrt-prod`
15×	`associate-*r/`
13×	`*-un-lft-identity`
12×	`times-frac` `difference-of-squares`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `distribute-lft-out--`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 131

Calls

4 calls:

20.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))))
9.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
9.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
9.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

series40.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
11.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
10.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
8.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))))

simplify74.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5055	8187

prune804.0ms (27.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	143	5	148

Merged error: 0b

Counts

148 → 5

regimes48.0ms (1.6%)

Accuracy

Total 0.0b remaining (11.1%)

Threshold costs 0.0b (11.1%)

bsearch13.0ms (0.4%)

Steps

Iters	Range		Point
9	0.0006503813431540223	60978.321201749655	8131.4453676694275

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms (0%)

sample1.2s (39.4%)

Algorithm

1×

intervals

Results

498.0ms	1736×	body	1280	valid
245.0ms	1309×	body	640	valid
201.0ms	3981×	body	80	valid
82.0ms	637×	body	320	valid
28.0ms	337×	body	160	valid

Details

analyze1.0ms (0%)

sample40.0ms (1.4%)

simplify4.0ms (0.1%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite11.0ms (0.4%)

series9.0ms (0.3%)

simplify39.0ms (1.3%)

prune86.0ms (2.9%)

localize5.0ms (0.2%)

rewrite11.0ms (0.4%)

series8.0ms (0.3%)

simplify39.0ms (1.3%)

prune96.0ms (3.3%)

localize10.0ms (0.3%)

rewrite54.0ms (1.8%)

series16.0ms (0.6%)

simplify37.0ms (1.3%)

prune243.0ms (8.3%)

localize16.0ms (0.6%)

rewrite61.0ms (2.1%)

series40.0ms (1.4%)

simplify74.0ms (2.5%)

prune804.0ms (27.4%)

regimes48.0ms (1.6%)

bsearch13.0ms (0.4%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.2s (39.4%)

Profiling