Details

analyze1.2s (4.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4977	44
1	4977	44
0	2	2
1	2	2

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)

sample168.0ms (0.7%)

Algorithm

1×

intervals

Results

81.0ms	62×	body	2048	valid
45.0ms	84×	body	1024	valid
10.0ms	40×	body	512	valid
5.0ms	8×	body	1024	invalid
3.0ms	50×	body	128	valid
2.0ms	1×	body	4096	valid
2.0ms	19×	body	256	valid
1.0ms	4×	body	512	invalid
1.0ms	12×	body	128	invalid
1.0ms	5×	body	256	invalid
1.0ms	1×	body	2048	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5036	22

prune6.0ms (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

47.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0%)

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)))
1.0b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
4.7b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
11.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite1.5s (5.7%)

Algorithm

1×	rewrite-expression-head

Error

47.6b

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-/l_binary64_1387` `associate-/r_binary64_1386`
7×	`pow1_binary64_1503`
6×	`div-exp_binary64_1493` `add-log-exp_binary64_1481` `cbrt-undiv_binary64_1476`
3×	`pow-unpow_binary64_1519` `cancel-sign-sub-inv_binary64_1408` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `associate-l_binary64_1383`
2×	`flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `distribute-lft-out_binary64_1393` `pow-pow_binary64_1514` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `diff-log_binary64_1534` `sub-neg_binary64_1435` `pow-prod-down_binary64_1513` `associate-r/_binary64_1384` `-commutative_binary64_1373`

Counts

4 → 451

Calls

4 calls:

63.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
19.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
12.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 14661 to 7953 computations (45.8% saved)

series1.5s (5.8%)

Error

3.0b

Counts

4 → 59

Calls

4 calls:

440.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
393.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
361.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
192.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 5282 to 3710 computations (29.8% saved)

simplify176.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

510 → 510

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4948	16700
1	4948	16700

prune1.1s (4.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	497	13	510
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	498	13	511

Error

0.2b

Counts

511 → 13

Compiler

Compiled 15789 to 8309 computations (47.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/6 (.f64 i i))
2.2b	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
2.4b	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
5.1b	(/.f64 (*.f64 i i) n)

rewrite229.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

22×	`associate-*r/_binary64_1384`
20×	`frac-add_binary64_1450`
18×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
16×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
13×	`add-log-exp_binary64_1481`
12×	`add-sqr-sqrt_binary64_1464`
11×	`pow1_binary64_1503`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-l_binary64_1383` `sum-log_binary64_1533`
5×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
4×	`pow-prod-down_binary64_1513` `associate-r_binary64_1382`
3×	`times-frac_binary64_1448` `associate-/r*_binary64_1386`
2×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `unswap-sqr_binary64_1410` `distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `*-commutative_binary64_1373` `associate-+r+_binary64_1374`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/l*_binary64_1387` `associate-+l+_binary64_1375` `+-commutative_binary64_1372`

Counts

4 → 90

Calls

4 calls:

13.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
7.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
6.0ms	(.f64 1/6 (.f64 i i))
5.0ms	(/.f64 (*.f64 i i) n)

Compiler

Compiled 5383 to 2602 computations (51.7% saved)

series860.0ms (3.4%)

Error

0.2b

Counts

4 → 36

Calls

4 calls:

512.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
191.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
75.0ms	(/.f64 (*.f64 i i) n)
31.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 2657 to 1882 computations (29.2% saved)

simplify88.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5436	4694

prune302.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	124	15	139

Error

0.2b

Counts

139 → 15

Compiler

Compiled 6025 to 3281 computations (45.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(/.f64 (*.f64 i i) n)
15.6b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
15.6b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
15.6b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))

rewrite778.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

96×	`associate-*r/_binary64_1384`
60×	`frac-add_binary64_1450`
51×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
42×	`cbrt-div_binary64_1474`
9×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-cube-cbrt_binary64_1477` `cbrt-prod_binary64_1473` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`pow1_binary64_1503` `add-log-exp_binary64_1481`
3×	`pow1/3_binary64_1524` `times-frac_binary64_1448` `associate-/r*_binary64_1386`
2×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
1×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/l*_binary64_1387`

Counts

4 → 96

Calls

4 calls:

16.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
14.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
13.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
5.0ms	(/.f64 (*.f64 i i) n)

Compiler

Compiled 14425 to 7220 computations (49.9% saved)

series2.9s (11.2%)

Error

0.2b

Counts

4 → 45

Calls

4 calls:

874.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
864.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
732.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 -1/2 (+.f64 i (*.f64 i i))))))
112.0ms	(/.f64 (*.f64 i i) n)

Compiler

Compiled 16500 to 11952 computations (27.6% saved)

simplify177.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4955	12691
1	4955	12691

prune1.2s (4.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	141	15	156

Error

0.2b

Counts

156 → 15

Compiler

Compiled 18263 to 9977 computations (45.4% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3))))))
6.5b	(-.f64 (+.f64 (.f64 (.f64 n i) 50) (+.f64 (.f64 (/.f64 (.f64 i i) n) 100/3) (+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3)))))))) (+.f64 (.f64 25 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 50 (+.f64 i (.f64 i i)))))
7.7b	(.f64 n (.f64 i i))
12.4b	(/.f64 (pow.f64 i 3) (*.f64 n n))

rewrite714.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

54×	`add-log-exp_binary64_1481`
28×	`sum-log_binary64_1533`
22×	`add-exp-log_binary64_1480`
17×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
16×	`associate-*r/_binary64_1384`
15×	`add-sqr-sqrt_binary64_1464`
14×	`add-cbrt-cube_binary64_1478` `*-un-lft-identity_binary64_1442`
12×	`add-cube-cbrt_binary64_1477` `times-frac_binary64_1448` `associate-/l*_binary64_1387` `frac-sub_binary64_1451`
10×	`diff-log_binary64_1534`
9×	`pow1_binary64_1503`
8×	`frac-add_binary64_1450`
6×	`prod-exp_binary64_1491` `div-exp_binary64_1493` `unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
4×	`cbrt-unprod_binary64_1475`
3×	`pow-prod-down_binary64_1513` `associate-l_binary64_1383` `cancel-sign-sub-inv_binary64_1408`
2×	`pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `cbrt-undiv_binary64_1476` `unpow3_binary64_1508` `cube-mult_binary64_1472` `sqr-pow_binary64_1414`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `associate-/r_binary64_1386` `unswap-sqr_binary64_1410` `associate-r_binary64_1382` `-commutative_binary64_1373` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `associate--l+_binary64_1379` `associate--r+_binary64_1378` `associate-+r+_binary64_1374` `+-commutative_binary64_1372`

Counts

4 → 114

Calls

4 calls:

53.0ms	(-.f64 (+.f64 (.f64 (.f64 n i) 50) (+.f64 (.f64 (/.f64 (.f64 i i) n) 100/3) (+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3)))))))) (+.f64 (.f64 25 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 50 (+.f64 i (.f64 i i)))))
16.0ms	(+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3))))))
7.0ms	(/.f64 (pow.f64 i 3) (*.f64 n n))
6.0ms	(.f64 n (.f64 i i))

Compiler

Compiled 11984 to 6721 computations (43.9% saved)

series902.0ms (3.5%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

371.0ms	(-.f64 (+.f64 (.f64 (.f64 n i) 50) (+.f64 (.f64 (/.f64 (.f64 i i) n) 100/3) (+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3)))))))) (+.f64 (.f64 25 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 50 (+.f64 i (.f64 i i)))))
201.0ms	(+.f64 (.f64 (.f64 n (.f64 i i)) 50/3) (+.f64 (.f64 (/.f64 (pow.f64 i 3) n) 275/6) (.f64 n (+.f64 100 (.f64 25/6 (pow.f64 i 3))))))
134.0ms	(/.f64 (pow.f64 i 3) (*.f64 n n))
96.0ms	(.f64 n (.f64 i i))

Compiler

Compiled 5426 to 3868 computations (28.7% saved)

simplify110.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5221	10849

prune871.0ms (3.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	1	11	12
Picked	1	0	1
Done	0	2	2
Total	157	15	172

Error

0.2b

Counts

172 → 15

Compiler

Compiled 12701 to 7276 computations (42.7% saved)

regimes1.6s (6.4%)

Accuracy

Total 11.1b remaining (95.6%)

Threshold costs 0b (0%)

Compiler

Compiled 20230 to 13579 computations (32.9% saved)

bsearch317.0ms (1.2%)

Steps

Iters	Range		Point
7	2.6566475429446913e+226	1.4882007215757351e+228	2.018574178061804e+227
10	8.141101411665496e+178	9.029104174423418e+191	5.375287223785503e+191
12	5.782475113295913e-26	1.143256642332046e+33	0.0006241617893643045
9	-751.4873023446623	-0.00018481786151330014	-0.00018743494896283588

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	540	326
1	540	326

end0.0ms (0%)

sample8.7s (34.2%)

Algorithm

1×

intervals

Results

2.3s	1807×	body	2048	valid
1.5s	2621×	body	1024	valid
321.0ms	1200×	body	512	valid
133.0ms	1809×	body	128	valid
117.0ms	179×	body	1024	invalid
83.0ms	212×	body	512	invalid
79.0ms	536×	body	256	valid
65.0ms	27×	body	4096	valid
44.0ms	443×	body	128	invalid
30.0ms	125×	body	256	invalid
23.0ms	22×	body	2048	invalid
15.0ms	310×	body	128	nan

Compiler

Compiled 5262 to 3531 computations (32.9% saved)

Details

analyze1.2s (4.7%)

sample168.0ms (0.7%)

simplify78.0ms (0.3%)

prune6.0ms (0%)

localize9.0ms (0%)

rewrite1.5s (5.7%)

series1.5s (5.8%)

simplify176.0ms (0.7%)

prune1.1s (4.2%)

localize17.0ms (0.1%)

rewrite229.0ms (0.9%)

series860.0ms (3.4%)

simplify88.0ms (0.3%)

prune302.0ms (1.2%)

localize26.0ms (0.1%)

rewrite778.0ms (3.1%)

series2.9s (11.2%)

simplify177.0ms (0.7%)

prune1.2s (4.7%)

localize33.0ms (0.1%)

rewrite714.0ms (2.8%)

series902.0ms (3.5%)

simplify110.0ms (0.4%)

prune871.0ms (3.4%)

regimes1.6s (6.4%)

bsearch317.0ms (1.2%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample8.7s (34.2%)

Profiling