Details

analyze1.2s (8.3%)

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%	35.7%	19.8%	13
45.5%	34.4%	20.1%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample250.0ms (1.7%)

Algorithm

1×

intervals

Results

119.0ms	59×	body	2048	valid
69.0ms	83×	body	1024	valid
12.0ms	26×	body	512	valid
10.0ms	24×	body	256	valid
7.0ms	7×	body	1024	invalid
6.0ms	63×	body	128	valid
5.0ms	9×	body	512	invalid
3.0ms	1×	body	4096	valid
2.0ms	13×	body	128	invalid
1.0ms	2×	body	256	invalid
1.0ms	8×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify240.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	5036	22

prune3.0ms (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

Error

46.5b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.3b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.7b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.7b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite254.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_1448`
486×	`add-sqr-sqrt_binary64_1464`
367×	`*-un-lft-identity_binary64_1442`
225×	`add-cube-cbrt_binary64_1477`
174×	`associate-r_binary64_1382`
168×	`difference-of-squares_binary64_1411`
88×	`unpow-prod-down_binary64_1521`
85×	`sqr-pow_binary64_1414`
84×	`difference-of-sqr-1_binary64_1412`
29×	`div-inv_binary64_1439`
28×	`distribute-lft-out--_binary64_1394`
19×	`add-exp-log_binary64_1480`
18×	`add-cbrt-cube_binary64_1478`
13×	`associate-/r_binary64_1386` `associate-/l_binary64_1387`
7×	`pow1_binary64_1503`
6×	`cbrt-undiv_binary64_1476` `add-log-exp_binary64_1481` `div-exp_binary64_1493`
3×	`cancel-sign-sub-inv_binary64_1408` `cbrt-unprod_binary64_1475` `associate-l_binary64_1383` `pow-unpow_binary64_1519` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
2×	`associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417`
1×	`associate-r/_binary64_1384` `pow-exp_binary64_1510` `sub-neg_binary64_1435` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `div-sub_binary64_1447` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 451

Calls

4 calls:

68.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
28.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
21.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
21.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series1.4s (9.3%)

Counts

4 → 12

Calls

4 calls:

483.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
441.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
244.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
224.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify273.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4954	14743
1	4954	14743

prune1.2s (7.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	452	11	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	453	11	464

Error

18.2b

Counts

464 → 11

Compiler

Compiled 14099 to 7414 computations (47.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.3b	(*.f64 1/6 i)
17.1b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_1448`
97×	`add-sqr-sqrt_binary64_1464`
85×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
50×	`associate-r_binary64_1382`
25×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
13×	`associate-/r*_binary64_1386` `pow1_binary64_1503`
9×	`div-inv_binary64_1439`
7×	`cbrt-unprod_binary64_1475` `associate-l_binary64_1383` `prod-exp_binary64_1491`
6×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
5×	`pow-prod-down_binary64_1513` `unswap-sqr_binary64_1410`
4×	`add-log-exp_binary64_1481`
3×	`associate-r/_binary64_1384` `associate-/l_binary64_1387` `*-commutative_binary64_1373`
2×	`associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`clear-num_binary64_1441` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`

Counts

4 → 179

Calls

4 calls:

17.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
11.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
7.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series150.0ms (1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
45.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
45.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
10.0ms	(*.f64 1/6 i)

simplify101.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4971	5462
1	4971	5462

prune292.0ms (1.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	183	8	191
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	184	18	202

Error

8.2b

Counts

202 → 18

Compiler

Compiled 5947 to 3272 computations (45% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.1b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.3b	(*.f64 i 1/6)
2.1b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1464`
15×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
12×	`associate-l_binary64_1383`
11×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
10×	`associate-r_binary64_1382`
8×	`associate-*r/_binary64_1384`
6×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `prod-exp_binary64_1491`
4×	`*-commutative_binary64_1373` `add-log-exp_binary64_1481`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`

Counts

4 → 86

Calls

4 calls:

8.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
7.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
6.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
4.0ms	(*.f64 i 1/6)

series138.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
44.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
34.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
11.0ms	(*.f64 i 1/6)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4993	1381
1	4993	1381

prune112.0ms (0.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	98	18	116

Error

8.2b

Counts

116 → 18

Compiler

Compiled 2190 to 1570 computations (28.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
10.9b	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
10.9b	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
10.9b	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`associate-*r/_binary64_1384`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
6×	`cbrt-div_binary64_1474`
5×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416`
3×	`cbrt-unprod_binary64_1475` `cbrt-prod_binary64_1473` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `pow1/3_binary64_1524` `prod-exp_binary64_1491`
1×	`associate-r_binary64_1382` `*-commutative_binary64_1373`

Counts

4 → 57

Calls

4 calls:

7.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
5.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
4.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
4.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))

series466.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
140.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
139.0ms	(cbrt.f64 (.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))))))
42.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

simplify57.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5065	1795

prune162.0ms (1.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	70	17	87

Error

8.2b

Counts

87 → 17

Compiler

Compiled 3645 to 2678 computations (26.5% saved)

regimes1.3s (8.4%)

Accuracy

Total 6.2b remaining (43.1%)

Threshold costs 0b (0%)

Compiler

Compiled 14001 to 9615 computations (31.3% saved)

bsearch149.0ms (1%)

Steps

Iters	Range		Point
9	1.1839100579809183e-15	7.583982537435853e-08	7.432995259070106e-08
10	-165315705439.7733	-5.3424819284647654e-05	-0.009077757186457397

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	96
1	54	96

end0.0ms (0%)

sample7.1s (47.2%)

Algorithm

1×

intervals

Results

2.2s	1765×	body	2048	valid
1.4s	2679×	body	1024	valid
297.0ms	1180×	body	512	valid
123.0ms	1805×	body	128	valid
111.0ms	174×	body	1024	invalid
85.0ms	40×	body	4096	valid
76.0ms	207×	body	512	invalid
75.0ms	531×	body	256	valid
46.0ms	489×	body	128	invalid
34.0ms	148×	body	256	invalid
13.0ms	299×	body	128	nan
11.0ms	12×	body	2048	invalid

Compiler

Compiled 3558 to 2436 computations (31.5% saved)

Details

analyze1.2s (8.3%)

sample250.0ms (1.7%)

simplify240.0ms (1.6%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite254.0ms (1.7%)

series1.4s (9.3%)

simplify273.0ms (1.8%)

prune1.2s (7.8%)

localize10.0ms (0.1%)

rewrite59.0ms (0.4%)

series150.0ms (1%)

simplify101.0ms (0.7%)

prune292.0ms (1.9%)

localize8.0ms (0.1%)

rewrite31.0ms (0.2%)

series138.0ms (0.9%)

simplify58.0ms (0.4%)

prune112.0ms (0.7%)

localize14.0ms (0.1%)

rewrite27.0ms (0.2%)

series466.0ms (3.1%)

simplify57.0ms (0.4%)

prune162.0ms (1.1%)

regimes1.3s (8.4%)

bsearch149.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.1s (47.2%)

Profiling