Details

analyze3.0ms (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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample80.0ms (0.8%)

Algorithm

1×

intervals

Results

36.0ms	72×	body	1024	valid
12.0ms	119×	body	128	valid
10.0ms	34×	body	512	valid
8.0ms	11×	body	2048	valid
3.0ms	20×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify166.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (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

33.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.5b	(log.f64 (+.f64 N 1))
2.5b	(log.f64 (+.f64 N 1))
3.4b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_404`
11×	`log-prod_binary64_490`
8×	`pow1_binary64_465` `add-sqr-sqrt_binary64_426`
6×	`add-cube-cbrt_binary64_439` `log-pow_binary64_493`
4×	`log-div_binary64_491` `cancel-sign-sub-inv_binary64_370` `associate--l+_binary64_341` `distribute-lft-out--_binary64_356`
3×	`add-exp-log_binary64_442` `associate--r+_binary64_340`
2×	`associate--l-_binary64_342` `add-cbrt-cube_binary64_440` `flip3-+_binary64_407` `add-log-exp_binary64_443` `flip-+_binary64_378` `distribute-lft-out_binary64_355`
1×	`rem-log-exp_binary64_445` `diff-log_binary64_496` `flip3--_binary64_408` `difference-of-squares_binary64_373` `sub-neg_binary64_397` `flip--_binary64_379`

Counts

2 → 44

Calls

4 calls:

15.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
6.0ms	(log.f64 (+.f64 N 1))
0.0ms	(log.f64 (+.f64 N 1))
0.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

series153.0ms (1.5%)

Counts

2 → 18

Calls

2 calls:

108.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
45.0ms	(log.f64 (+.f64 N 1))

Compiler

Compiled 274 to 237 computations (13.5% saved)

simplify139.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4920	794
1	4920	794

prune182.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	3	63

Error

0.0b

Counts

63 → 3

Compiler

Compiled 777 to 493 computations (36.6% saved)

localize29.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 1/4 (pow.f64 N 4))
0.2b	(/.f64 1/3 (pow.f64 N 3))
0.0b	(+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))
0.0b	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
0.2b	(/.f64 1/3 (pow.f64 N 3))
0.2b	(/.f64 1/4 (pow.f64 N 4))
0.5b	(/.f64 1/2 (*.f64 N N))
19.1b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

rewrite158.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_404`
60×	`times-frac_binary64_410`
50×	`add-sqr-sqrt_binary64_426`
48×	`add-cube-cbrt_binary64_439`
24×	`unpow-prod-down_binary64_483`
20×	`associate-/r*_binary64_348`
19×	`add-exp-log_binary64_442`
16×	`add-log-exp_binary64_443`
13×	`add-cbrt-cube_binary64_440`
12×	`cube-prod_binary64_432`
9×	`frac-sub_binary64_413` `associate-/l*_binary64_349`
8×	`div-exp_binary64_455` `sqr-pow_binary64_376` `distribute-lft-out_binary64_355`
6×	`frac-add_binary64_412` `distribute-lft-out--_binary64_356` `flip3-+_binary64_407` `flip-+_binary64_378`
5×	`div-inv_binary64_401`
4×	`pow1_binary64_465` `unpow3_binary64_470` `cancel-sign-sub-inv_binary64_370` `sum-log_binary64_495` `diff-log_binary64_496` `cbrt-undiv_binary64_438` `cube-mult_binary64_434`
3×	`frac-2neg_binary64_415` `clear-num_binary64_403`
2×	`pow-to-exp_binary64_473` `pow-exp_binary64_472`
1×	`associate--l+_binary64_341` `flip3--_binary64_408` `difference-of-squares_binary64_373` `sub-neg_binary64_397` `flip--_binary64_379` `associate--r+_binary64_340` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`

Counts

4 → 167

Calls

8 calls:

96.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
10.0ms	(/.f64 1/3 (pow.f64 N 3))
9.0ms	(/.f64 1/2 (*.f64 N N))
8.0ms	(/.f64 1/4 (pow.f64 N 4))
0.0ms	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))

series238.0ms (2.3%)

Counts

4 → 19

Calls

4 calls:

65.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
59.0ms	(/.f64 1/3 (pow.f64 N 3))
57.0ms	(/.f64 1/4 (pow.f64 N 4))
57.0ms	(/.f64 1/2 (*.f64 N N))

Compiler

Compiled 541 to 460 computations (15% saved)

simplify147.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5309	3761

prune566.0ms (5.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	185	4	189

Error

0.0b

Counts

189 → 4

Compiler

Compiled 5262 to 3822 computations (27.4% saved)

localize45.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))
0.0b	(+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))
0.0b	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
0.0b	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
9.1b	(sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))))
9.3b	(-.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
22.8b	(sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
22.8b	(sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

rewrite246.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_404`
34×	`sqrt-prod_binary64_420`
27×	`sqrt-div_binary64_421`
20×	`add-sqr-sqrt_binary64_426`
13×	`distribute-lft-out_binary64_355`
9×	`frac-add_binary64_412` `flip3-+_binary64_407` `flip-+_binary64_378` `frac-sub_binary64_413` `add-cube-cbrt_binary64_439`
7×	`pow1_binary64_465` `cancel-sign-sub-inv_binary64_370` `distribute-lft-out--_binary64_356`
6×	`add-log-exp_binary64_443`
4×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442` `difference-of-squares_binary64_373`
3×	`pow1/2_binary64_484` `sqrt-pow1_binary64_422` `div-inv_binary64_401` `rem-sqrt-square_binary64_417`
2×	`times-frac_binary64_410`
1×	`diff-log_binary64_496` `flip3--_binary64_408` `sub-neg_binary64_397` `flip--_binary64_379`

Counts

4 → 91

Calls

8 calls:

101.0ms	(-.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
53.0ms	(sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))))
30.0ms	(sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
30.0ms	(sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
0.0ms	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))

series279.0ms (2.7%)

Counts

4 → 16

Calls

4 calls:

109.0ms	(sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
74.0ms	(sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))
56.0ms	(-.f64 (sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))) (sqrt.f64 (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
39.0ms	(sqrt.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))))

Compiler

Compiled 1263 to 1042 computations (17.5% saved)

simplify141.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4877	3546
1	4877	3546

prune589.0ms (5.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	107	4	111

Error

0.0b

Counts

111 → 4

Compiler

Compiled 6098 to 4615 computations (24.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(log.f64 (/.f64 (+.f64 N 1) N))
0.0b	(/.f64 (+.f64 N 1) N)
0.0b	(/.f64 (+.f64 N 1) N)
3.5b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_404`
24×	`times-frac_binary64_410`
19×	`add-cube-cbrt_binary64_439` `add-sqr-sqrt_binary64_426`
16×	`log-prod_binary64_490`
7×	`add-exp-log_binary64_442` `distribute-lft-out_binary64_355`
4×	`add-cbrt-cube_binary64_440` `associate-/l*_binary64_349`
3×	`pow1_binary64_465` `associate-/r*_binary64_348`
2×	`associate-/l/_binary64_351` `div-exp_binary64_455` `rem-log-exp_binary64_445` `div-inv_binary64_401` `add-log-exp_binary64_443`
1×	`log-div_binary64_491` `frac-2neg_binary64_415` `flip3-+_binary64_407` `clear-num_binary64_403` `flip-+_binary64_378` `cbrt-undiv_binary64_438` `log-pow_binary64_493`

Counts

2 → 60

Calls

4 calls:

10.0ms	(/.f64 (+.f64 N 1) N)
8.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
0.0ms	(/.f64 (+.f64 N 1) N)
0.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series150.0ms (1.4%)

Counts

2 → 17

Calls

2 calls:

88.0ms	(log.f64 (/.f64 (+.f64 N 1) N))
62.0ms	(/.f64 (+.f64 N 1) N)

Compiler

Compiled 198 to 182 computations (8.1% saved)

simplify167.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4918	1053
1	4918	1053

prune104.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	76	5	81

Error

0.0b

Counts

81 → 5

Compiler

Compiled 866 to 579 computations (33.1% saved)

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	398	901
1	398	901

regimes157.0ms (1.5%)

Accuracy

Total 0.0b remaining (56.9%)

Threshold costs 0.0b (56.9%)

Compiler

Compiled 587 to 463 computations (21.1% saved)

bsearch43.0ms (0.4%)

Steps

Iters	Range		Point
8	167.72365186291802	106152.99019898237	978.1423904054542

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	70	61
1	70	61

end0.0ms (0%)

sample6.6s (62.8%)

Algorithm

1×

intervals

Results

899.0ms	2041×	body	1024	valid
436.0ms	4244×	body	128	valid
268.0ms	961×	body	512	valid
187.0ms	264×	body	2048	valid
83.0ms	490×	body	256	valid

Compiler

Compiled 1843 to 1453 computations (21.2% saved)

Pareto

-0.20294762165185615

Details

analyze3.0ms (0%)

sample80.0ms (0.8%)

simplify166.0ms (1.6%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite27.0ms (0.3%)

series153.0ms (1.5%)

simplify139.0ms (1.3%)

prune182.0ms (1.7%)

localize29.0ms (0.3%)

rewrite158.0ms (1.5%)

series238.0ms (2.3%)

simplify147.0ms (1.4%)

prune566.0ms (5.4%)

localize45.0ms (0.4%)

rewrite246.0ms (2.4%)

series279.0ms (2.7%)

simplify141.0ms (1.3%)

prune589.0ms (5.6%)

localize9.0ms (0.1%)

rewrite27.0ms (0.3%)

series150.0ms (1.4%)

simplify167.0ms (1.6%)

prune104.0ms (1%)

simplify31.0ms (0.3%)

regimes157.0ms (1.5%)

bsearch43.0ms (0.4%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.6s (62.8%)

Profiling