Details

analyze810.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

sample203.0ms (1.9%)

Algorithm

1×

intervals

Results

87.0ms	94×	body	1280	valid
61.0ms	27×	body	2560	valid
23.0ms	55×	body	640	valid
5.0ms	19×	body	320	valid
5.0ms	6×	body	1280	invalid
3.0ms	7×	body	640	invalid
3.0ms	50×	body	80	valid
2.0ms	5×	body	320	invalid
1.0ms	11×	body	160	valid
1.0ms	9×	body	80	invalid
1.0ms	14×	body	80	nan
0.0ms	2×	body	160	invalid

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5281	15

prune10.0ms (0.1%)

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: 47.8b

Counts

2 → 2

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
9.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite87.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 280

Calls

4 calls:

31.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
19.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)

series184.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
58.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
33.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms	(pow (+ 1.0 (/ i n)) n)

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4988	5853
1	4988	5853

prune680.0ms (6.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	286	6	292
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Merged error: 18.3b

Counts

294 → 6

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
0.1b	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
10.9b	(* (* i i) (* 0.5 (log 1.0)))
19.1b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac`
95×	`add-sqr-sqrt`
86×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
13×	`associate-/r*` `add-log-exp`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `div-inv`
6×	`cbrt-undiv` `div-exp`
5×	`sum-log`
4×	`associate-+r-` `associate-l`
3×	`associate-/l*` `unswap-sqr`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `frac-2neg` `diff-log` `div-sub` `associate-*r/` `clear-num`

Counts

4 → 188

Calls

4 calls:

20.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
14.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))
12.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
7.0ms	(* (* i i) (* 0.5 (log 1.0)))

series62.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
18.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))
13.0ms	(* (* i i) (* 0.5 (log 1.0)))
10.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5701	5673

prune694.0ms (6.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	190	10	200
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	191	15	206

Merged error: 7.5b

Counts

206 → 15

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* i (+ 1.0 (* i 0.5)))
0.0b	(* n (/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i))
0.1b	(* 100.0 (- (* n (/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i)) (* n (/ (* i (* (log 1.0) 0.5)) 1))))
10.2b	(/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i)

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-*r/`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `div-exp` `flip-+` `div-inv` `associate-/l/`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 107

Calls

4 calls:

10.0ms	(* 100.0 (- (* n (/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i)) (* n (/ (* i (* (log 1.0) 0.5)) 1))))
8.0ms	(* n (/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i))
6.0ms	(/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i)
5.0ms	(* i (+ 1.0 (* i 0.5)))

series50.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(* 100.0 (- (* n (/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i)) (* n (/ (* i (* (log 1.0) 0.5)) 1))))
13.0ms	(* n (/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i))
12.0ms	(/ (+ (* n (log 1.0)) (* i (+ 1.0 (* i 0.5)))) i)
8.0ms	(* i (+ 1.0 (* i 0.5)))

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4981	2243
1	4981	2243

prune369.0ms (3.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	118	16	134

Merged error: 7.5b

Counts

134 → 16

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ 1.0 (* i 0.5)))
0.2b	(cbrt (+ 1.0 (* i 0.5)))
0.2b	(* (cbrt (+ 1.0 (* i 0.5))) (cbrt (+ 1.0 (* i 0.5))))
10.2b	(/ (+ (* n (log 1.0)) (* (* i (* (cbrt (+ 1.0 (* i 0.5))) (cbrt (+ 1.0 (* i 0.5))))) (cbrt (+ 1.0 (* i 0.5))))) i)

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
16×	`cbrt-div`
11×	`pow1`
9×	`flip3-+` `times-frac` `flip-+`
8×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
4×	`frac-times` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 103

Calls

4 calls:

16.0ms	(* (cbrt (+ 1.0 (* i 0.5))) (cbrt (+ 1.0 (* i 0.5))))
14.0ms	(/ (+ (* n (log 1.0)) (* (* i (* (cbrt (+ 1.0 (* i 0.5))) (cbrt (+ 1.0 (* i 0.5))))) (cbrt (+ 1.0 (* i 0.5))))) i)
5.0ms	(cbrt (+ 1.0 (* i 0.5)))
4.0ms	(cbrt (+ 1.0 (* i 0.5)))

series36.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (+ (* n (log 1.0)) (* (* i (* (cbrt (+ 1.0 (* i 0.5))) (cbrt (+ 1.0 (* i 0.5))))) (cbrt (+ 1.0 (* i 0.5))))) i)
7.0ms	(* (cbrt (+ 1.0 (* i 0.5))) (cbrt (+ 1.0 (* i 0.5))))
7.0ms	(cbrt (+ 1.0 (* i 0.5)))
7.0ms	(cbrt (+ 1.0 (* i 0.5)))

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4930	1907
1	4930	1907

prune437.0ms (4.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	114	17	131

Merged error: 7.5b

Counts

131 → 17

regimes276.0ms (2.6%)

Accuracy

Total 7.0b remaining (44.5%)

Threshold costs 0b (0%)

bsearch189.0ms (1.8%)

Steps

Iters	Range		Point
10	2.8200312415126368e+287	6.5744174042505425e+299	7.413989741085994e+291
10	1.699801443634594e-08	2797559013.103562	0.051881246670273766
8	-1.1042507866546514e+31	-4.269651298532529e+28	-4.331633902717184e+28

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	162	98
1	162	98

end0.0ms (0%)

sample6.0s (56.6%)

Algorithm

1×

intervals

Results

2.4s	2785×	body	1280	valid
2.0s	929×	body	2560	valid
620.0ms	1526×	body	640	valid
173.0ms	743×	body	320	valid
112.0ms	1663×	body	80	valid
109.0ms	222×	body	640	invalid
97.0ms	118×	body	1280	invalid
51.0ms	166×	body	320	invalid
50.0ms	345×	body	160	valid
40.0ms	424×	body	80	invalid
40.0ms	9×	body	5120	valid
20.0ms	11×	body	2560	invalid
17.0ms	93×	body	160	invalid
14.0ms	318×	body	80	nan

Details

analyze810.0ms (7.7%)

sample203.0ms (1.9%)

simplify36.0ms (0.3%)

prune10.0ms (0.1%)

localize9.0ms (0.1%)

rewrite87.0ms (0.8%)

series184.0ms (1.7%)

simplify100.0ms (0.9%)

prune680.0ms (6.4%)

localize16.0ms (0.2%)

rewrite61.0ms (0.6%)

series62.0ms (0.6%)

simplify61.0ms (0.6%)

prune694.0ms (6.6%)

localize18.0ms (0.2%)

rewrite32.0ms (0.3%)

series50.0ms (0.5%)

simplify35.0ms (0.3%)

prune369.0ms (3.5%)

localize21.0ms (0.2%)

rewrite44.0ms (0.4%)

series36.0ms (0.3%)

simplify59.0ms (0.6%)

prune437.0ms (4.1%)

regimes276.0ms (2.6%)

bsearch189.0ms (1.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.0s (56.6%)

Profiling