Details

analyze1.5s (10.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5242	38
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
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample215.0ms (1.5%)

Algorithm

1×

intervals

Results

42.0ms	70×	body	1024	valid
39.0ms	52×	body	1024	nan
37.0ms	68×	body	2048	valid
19.0ms	108×	body	128	overflowed
16.0ms	43×	body	512	valid
9.0ms	21×	body	512	nan
8.0ms	9×	body	1024	invalid
7.0ms	6×	body	512	invalid
5.0ms	54×	body	128	valid
5.0ms	21×	body	256	valid
2.0ms	34×	body	128	nan
2.0ms	9×	body	256	nan
1.0ms	5×	body	256	invalid
1.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4831	19
1	4831	19

prune2.0ms (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

30.4b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
1.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite130.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

30.4b

Rules

33×	`add-sqr-sqrt_binary64_441`
30×	`*-un-lft-identity_binary64_419`
26×	`pow-unpow_binary64_496`
21×	`add-cube-cbrt_binary64_454`
20×	`unpow-prod-down_binary64_498`
18×	`times-frac_binary64_425`
9×	`difference-of-squares_binary64_388` `sqr-pow_binary64_391`
7×	`cancel-sign-sub-inv_binary64_385`
5×	`add-log-exp_binary64_458` `pow1_binary64_480` `add-exp-log_binary64_457`
3×	`add-cbrt-cube_binary64_455` `distribute-lft-out--_binary64_371`
2×	`distribute-lft-out_binary64_370` `div-inv_binary64_416` `pow-pow_binary64_491` `pow-to-exp_binary64_488` `pow-exp_binary64_487`
1×	`diff-log_binary64_511` `flip3--_binary64_423` `sub-neg_binary64_412` `flip--_binary64_394`

Counts

3 → 85

Calls

3 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
3.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 1914 to 1374 computations (28.2% saved)

series439.0ms (3.1%)

Error

0.6b

Counts

3 → 32

Calls

3 calls:

208.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
107.0ms	(pow.f64 x (/.f64 1 n))
79.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

Compiler

Compiled 2161 to 1686 computations (22% saved)

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4968	2196
1	4968	2196

prune134.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	4	118

Error

0.6b

Counts

118 → 4

Compiler

Compiled 2476 to 1698 computations (31.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)
2.6b	(log.f64 (+.f64 1 x))
3.2b	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))

rewrite119.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

44×	`*-un-lft-identity_binary64_419`
30×	`add-sqr-sqrt_binary64_441`
25×	`pow1_binary64_480`
24×	`times-frac_binary64_425`
22×	`log-pow_binary64_508`
20×	`add-cube-cbrt_binary64_454` `distribute-lft-out--_binary64_371`
11×	`log-prod_binary64_505`
8×	`associate-/l*_binary64_364`
6×	`add-exp-log_binary64_457`
5×	`add-cbrt-cube_binary64_455` `difference-of-squares_binary64_388`
4×	`cancel-sign-sub-inv_binary64_385` `log-div_binary64_506` `associate--l+_binary64_356`
3×	`add-log-exp_binary64_458` `associate--r+_binary64_355` `associate-/r*_binary64_363`
2×	`flip3--_binary64_423` `flip--_binary64_394` `flip3-+_binary64_422` `associate--l-_binary64_357` `flip-+_binary64_393` `distribute-lft-out_binary64_370` `associate-/l/_binary64_366`
1×	`diff-log_binary64_511` `sub-neg_binary64_412` `rem-log-exp_binary64_460` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `frac-2neg_binary64_430` `div-sub_binary64_424` `clear-num_binary64_418` `div-inv_binary64_416`

Counts

3 → 94

Calls

3 calls:

10.0ms	(/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)
8.0ms	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
3.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 1606 to 980 computations (39% saved)

series325.0ms (2.3%)

Error

0.3b

Counts

3 → 32

Calls

3 calls:

211.0ms	(/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)
59.0ms	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
25.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 1071 to 841 computations (21.5% saved)

simplify112.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4915	2200
1	4915	2200

prune121.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Error

0.3b

Counts

130 → 10

Compiler

Compiled 2145 to 1288 computations (40% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)))
0.1b	(/.f64 1 (/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))))
2.6b	(log.f64 (+.f64 x 1))
3.2b	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))

rewrite353.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

210×	`times-frac_binary64_425`
172×	`*-un-lft-identity_binary64_419`
134×	`add-sqr-sqrt_binary64_441`
100×	`add-cube-cbrt_binary64_454`
75×	`pow1_binary64_480`
70×	`log-pow_binary64_508`
68×	`distribute-lft-out--_binary64_371`
38×	`associate-/r*_binary64_363`
18×	`add-exp-log_binary64_457`
17×	`difference-of-squares_binary64_388`
11×	`add-cbrt-cube_binary64_455` `log-prod_binary64_505` `associate-/r/_binary64_365`
8×	`div-exp_binary64_470`
6×	`flip3--_binary64_423` `flip--_binary64_394` `div-inv_binary64_416` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458` `cancel-sign-sub-inv_binary64_385` `log-div_binary64_506` `associate--l+_binary64_356` `cbrt-undiv_binary64_453`
3×	`associate--r+_binary64_355`
2×	`flip3-+_binary64_422` `associate--l-_binary64_357` `flip-+_binary64_393` `distribute-lft-out_binary64_370` `1-exp_binary64_463` `rec-exp_binary64_469` `frac-2neg_binary64_430` `clear-num_binary64_418`
1×	`diff-log_binary64_511` `sub-neg_binary64_412` `rem-log-exp_binary64_460` `inv-pow_binary64_504` `pow-flip_binary64_493`

Counts

4 → 237

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))))
8.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
6.0ms	(/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)))
3.0ms	(log.f64 (+.f64 x 1))

Compiler

Compiled 5274 to 3464 computations (34.3% saved)

series560.0ms (3.9%)

Error

0.3b

Counts

4 → 47

Calls

4 calls:

240.0ms	(/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)))
199.0ms	(/.f64 1 (/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))))
55.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
25.0ms	(log.f64 (+.f64 x 1))

Compiler

Compiled 1730 to 1321 computations (23.6% saved)

simplify113.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4991	6304
1	4991	6304

prune324.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	281	3	284
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	284	10	294

Error

0.3b

Counts

294 → 10

Compiler

Compiled 5509 to 3431 computations (37.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(*.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) (/.f64 1 n))
2.6b	(log.f64 (+.f64 1 x))
3.2b	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))

rewrite115.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

28×	`*-un-lft-identity_binary64_419`
26×	`add-sqr-sqrt_binary64_441`
15×	`pow1_binary64_480` `add-cube-cbrt_binary64_454`
13×	`add-exp-log_binary64_457` `associate-r_binary64_359`
11×	`log-prod_binary64_505` `times-frac_binary64_425`
10×	`log-pow_binary64_508`
8×	`add-cbrt-cube_binary64_455` `distribute-lft-out--_binary64_371` `associate-l_binary64_360`
4×	`cancel-sign-sub-inv_binary64_385` `log-div_binary64_506` `associate--l+_binary64_356` `prod-exp_binary64_468`
3×	`add-log-exp_binary64_458` `flip3--_binary64_423` `flip--_binary64_394` `associate--r+_binary64_355` `unswap-sqr_binary64_387`
2×	`difference-of-squares_binary64_388` `flip3-+_binary64_422` `associate--l-_binary64_357` `flip-+_binary64_393` `distribute-lft-out_binary64_370` `div-exp_binary64_470` `cbrt-unprod_binary64_452` `frac-times_binary64_429` `associate-*l/_binary64_362`
1×	`diff-log_binary64_511` `sub-neg_binary64_412` `rem-log-exp_binary64_460` `pow-prod-down_binary64_490` `1-exp_binary64_463` `rec-exp_binary64_469` `cbrt-undiv_binary64_453` `un-div-inv_binary64_417` `associate-r/_binary64_361` `div-inv_binary64_416` `-commutative_binary64_350`

Counts

3 → 89

Calls

3 calls:

12.0ms	(*.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) (/.f64 1 n))
7.0ms	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
3.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 1702 to 1147 computations (32.6% saved)

series308.0ms (2.1%)

Error

0.3b

Counts

3 → 32

Calls

3 calls:

201.0ms	(*.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) (/.f64 1 n))
56.0ms	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
25.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 1149 to 920 computations (19.9% saved)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5271	1941

prune99.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	121	10	131

Error

0.3b

Counts

131 → 10

Compiler

Compiled 1912 to 1204 computations (37% saved)

regimes952.0ms (6.6%)

Accuracy

Total 6.7b remaining (96.4%)

Threshold costs 0b (0%)

Compiler

Compiled 8246 to 6523 computations (20.9% saved)

bsearch55.0ms (0.4%)

Steps

Iters	Range		Point
9	18717.624495767242	1277234282.1790814	96823.49085771796

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	19	31

end0.0ms (0%)

sample8.2s (57%)

Algorithm

1×

intervals

Results

1.5s	2670×	body	1024	valid
1.1s	1476×	body	1024	nan
1.0s	1728×	body	2048	valid
526.0ms	2731×	body	128	overflowed
483.0ms	1258×	body	512	valid
333.0ms	737×	body	512	nan
167.0ms	1796×	body	128	valid
166.0ms	186×	body	1024	invalid
124.0ms	548×	body	256	valid
118.0ms	239×	body	512	invalid
80.0ms	333×	body	256	nan
51.0ms	838×	body	128	nan
44.0ms	156×	body	256	invalid
34.0ms	268×	body	128	invalid
8.0ms	6×	body	2048	nan

Compiler

Compiled 1965 to 1550 computations (21.1% saved)

Details

analyze1.5s (10.2%)

sample215.0ms (1.5%)

simplify51.0ms (0.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite130.0ms (0.9%)

series439.0ms (3.1%)

simplify87.0ms (0.6%)

prune134.0ms (0.9%)

localize8.0ms (0.1%)

rewrite119.0ms (0.8%)

series325.0ms (2.3%)

simplify112.0ms (0.8%)

prune121.0ms (0.8%)

localize12.0ms (0.1%)

rewrite353.0ms (2.5%)

series560.0ms (3.9%)

simplify113.0ms (0.8%)

prune324.0ms (2.3%)

localize9.0ms (0.1%)

rewrite115.0ms (0.8%)

series308.0ms (2.1%)

simplify68.0ms (0.5%)

prune99.0ms (0.7%)

regimes952.0ms (6.6%)

bsearch55.0ms (0.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.2s (57%)

Profiling