Details

analyze808.0ms (3.9%)

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

Compiler

Compiled 16 to 12 computations (25% saved)

sample170.0ms (0.8%)

Algorithm

1×

intervals

Results

78.0ms	52×	body	2048	valid
51.0ms	86×	body	1024	valid
12.0ms	38×	body	512	valid
4.0ms	62×	body	128	valid
4.0ms	7×	body	1024	invalid
3.0ms	18×	body	256	valid
3.0ms	7×	body	512	invalid
2.0ms	20×	body	128	invalid
1.0ms	4×	body	256	invalid
1.0ms	14×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify221.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	22
1	4939	22

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

Merged error: 47.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.8b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.8b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
7.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite181.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_3869`
486×	`add-sqr-sqrt_binary64_3885`
367×	`*-un-lft-identity_binary64_3863`
225×	`add-cube-cbrt_binary64_3898`
174×	`associate-r_binary64_3803`
168×	`difference-of-squares_binary64_3832`
88×	`unpow-prod-down_binary64_3942`
85×	`sqr-pow_binary64_3835`
84×	`difference-of-sqr-1_binary64_3833`
29×	`div-inv_binary64_3860`
28×	`distribute-lft-out--_binary64_3815`
19×	`add-exp-log_binary64_3901`
18×	`add-cbrt-cube_binary64_3899`
13×	`associate-/r_binary64_3807` `associate-/l_binary64_3808`
7×	`pow1_binary64_3924`
6×	`add-log-exp_binary64_3902` `div-exp_binary64_3914` `cbrt-undiv_binary64_3897`
3×	`prod-exp_binary64_3912` `cancel-sign-sub-inv_binary64_3829` `cbrt-unprod_binary64_3896` `unswap-sqr_binary64_3831` `pow-unpow_binary64_3940` `associate-l_binary64_3804`
2×	`flip--_binary64_3838` `associate-/l/_binary64_3810` `flip3--_binary64_3867` `associate-/r/_binary64_3809`
1×	`frac-2neg_binary64_3874` `pow-exp_binary64_3931` `distribute-lft-out_binary64_3814` `div-sub_binary64_3868` `-commutative_binary64_3794` `associate-r/_binary64_3805` `pow-to-exp_binary64_3932` `pow-prod-down_binary64_3934` `sub-neg_binary64_3856` `clear-num_binary64_3862` `pow-pow_binary64_3935` `diff-log_binary64_3955`

Counts

4 → 451

Calls

4 calls:

63.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
21.0ms	(/.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)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series1.8s (9%)

Counts

4 → 12

Calls

4 calls:

608.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
581.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
349.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
296.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify148.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5117	14771

prune1.5s (7.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	454	9	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	455	9	464

Merged error: 16.3b

Counts

464 → 9

Compiler

Compiled 25529 to 15271 computations (40.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.3b	(*.f64 1/6 i)
15.0b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_3869`
97×	`add-sqr-sqrt_binary64_3885`
85×	`add-cube-cbrt_binary64_3898` `*-un-lft-identity_binary64_3863`
50×	`associate-r_binary64_3803`
25×	`add-cbrt-cube_binary64_3899` `add-exp-log_binary64_3901`
13×	`associate-/r*_binary64_3807` `pow1_binary64_3924`
9×	`div-inv_binary64_3860`
7×	`prod-exp_binary64_3912` `cbrt-unprod_binary64_3896` `associate-l_binary64_3804`
6×	`div-exp_binary64_3914` `cbrt-undiv_binary64_3897`
5×	`unswap-sqr_binary64_3831` `pow-prod-down_binary64_3934`
4×	`add-log-exp_binary64_3902`
3×	`associate-/l_binary64_3808` `-commutative_binary64_3794` `associate-*r/_binary64_3805`
2×	`associate-/l/_binary64_3810` `flip3-+_binary64_3866` `associate-/r/_binary64_3809` `flip-+_binary64_3837`
1×	`frac-2neg_binary64_3874` `distribute-rgt-in_binary64_3813` `distribute-lft-in_binary64_3812` `clear-num_binary64_3862`

Counts

4 → 179

Calls

4 calls:

19.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
9.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
8.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series310.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
96.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
95.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
21.0ms	(*.f64 1/6 i)

simplify106.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4928	5462
1	4928	5462

prune1.6s (7.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	178	13	191
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	179	21	200

Merged error: 8.5b

Counts

200 → 21

Compiler

Compiled 33105 to 22063 computations (33.4% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 50 (*.f64 50/3 i))
0.1b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.5b	(*.f64 50/3 i)
3.1b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3885`
10×	`add-cube-cbrt_binary64_3898` `pow1_binary64_3924` `add-cbrt-cube_binary64_3899` `*-un-lft-identity_binary64_3863` `add-exp-log_binary64_3901`
9×	`associate-r_binary64_3803` `associate-l_binary64_3804`
6×	`add-log-exp_binary64_3902`
4×	`associate-*r/_binary64_3805`
3×	`prod-exp_binary64_3912` `cbrt-unprod_binary64_3896` `unswap-sqr_binary64_3831` `flip3-+_binary64_3866` `*-commutative_binary64_3794` `pow-prod-down_binary64_3934` `flip-+_binary64_3837`
2×	`distribute-rgt-in_binary64_3813` `distribute-lft-in_binary64_3812`
1×	`sum-log_binary64_3954` `+-commutative_binary64_3793`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
6.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
4.0ms	(*.f64 50/3 i)
3.0ms	(+.f64 50 (*.f64 50/3 i))

series223.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
76.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
38.0ms	(+.f64 50 (*.f64 50/3 i))
22.0ms	(*.f64 50/3 i)

simplify49.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5829	1060

prune285.0ms (1.4%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	20	20
Picked	0	1	1
Done	0	0	0
Total	84	22	106

Merged error: 8.5b

Counts

106 → 22

Compiler

Compiled 5520 to 3970 computations (28.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 i)
0.6b	(cbrt.f64 i)
1.8b	(/.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) (/.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 (cbrt.f64 n) (cbrt.f64 n)))) (/.f64 (cbrt.f64 i) (cbrt.f64 n)))
6.6b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) (/.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 (cbrt.f64 n) (cbrt.f64 n))))

rewrite323.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

2313×	`times-frac_binary64_3869`
910×	`add-sqr-sqrt_binary64_3885` `add-cube-cbrt_binary64_3898` `*-un-lft-identity_binary64_3863`
762×	`cbrt-prod_binary64_3894`
191×	`div-inv_binary64_3860`
78×	`add-exp-log_binary64_3901`
45×	`associate-/r*_binary64_3807` `div-exp_binary64_3914` `cbrt-undiv_binary64_3897`
43×	`associate-/r/_binary64_3809`
42×	`add-cbrt-cube_binary64_3899`
23×	`associate-/l*_binary64_3808`
12×	`prod-exp_binary64_3912` `cbrt-unprod_binary64_3896`
4×	`add-log-exp_binary64_3902` `pow1_binary64_3924`
3×	`associate-/l/_binary64_3810`
2×	`frac-2neg_binary64_3874` `pow1/3_binary64_3945` `clear-num_binary64_3862`
1×	`flip3-+_binary64_3866` `flip-+_binary64_3837`

Counts

4 → 964

Calls

4 calls:

49.0ms	(/.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) (/.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 (cbrt.f64 n) (cbrt.f64 n)))) (/.f64 (cbrt.f64 i) (cbrt.f64 n)))
15.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) (/.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 (cbrt.f64 n) (cbrt.f64 n))))
1.0ms	(cbrt.f64 i)
1.0ms	(cbrt.f64 i)

series589.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) (/.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 (cbrt.f64 n) (cbrt.f64 n))))
150.0ms	(cbrt.f64 i)
150.0ms	(cbrt.f64 i)
95.0ms	(/.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) (/.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 (cbrt.f64 n) (cbrt.f64 n)))) (/.f64 (cbrt.f64 i) (cbrt.f64 n)))

simplify664.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

976 → 976

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4969	74485
1	4969	74485

prune4.8s (23.2%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	965	11	976
Fresh	4	16	20
Picked	1	0	1
Done	0	1	1
Total	970	28	998

Merged error: 8.5b

Counts

998 → 28

Compiler

Compiled 84724 to 45067 computations (46.8% saved)

regimes311.0ms (1.5%)

Compiler: Compiled 2832 to 1882 computations (33.5% saved)

bsearch181.0ms (0.9%)

Steps

Iters	Range		Point
10	2.7375921188498964	68698724998597.086	3.042363773132192
8	-2.115097477919029e-06	-2.2729728429401622e-10	-2.0660858770764103e-06

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	34	48
1	34	48

end0.0ms (0%)

sample6.1s (29.9%)

Algorithm

1×

intervals

Results

2.7s	1767×	body	2048	valid
1.6s	2712×	body	1024	valid
329.0ms	1149×	body	512	valid
125.0ms	1823×	body	128	valid
101.0ms	169×	body	1024	invalid
84.0ms	521×	body	256	valid
80.0ms	28×	body	4096	valid
78.0ms	220×	body	512	invalid
47.0ms	497×	body	128	invalid
33.0ms	158×	body	256	invalid
23.0ms	17×	body	2048	invalid
15.0ms	304×	body	128	nan

Compiler

Compiled 1008 to 670 computations (33.5% saved)

Details

analyze808.0ms (3.9%)

sample170.0ms (0.8%)

simplify221.0ms (1.1%)

prune2.0ms (0%)

localize9.0ms (0%)

rewrite181.0ms (0.9%)

series1.8s (9%)

simplify148.0ms (0.7%)

prune1.5s (7.1%)

localize11.0ms (0.1%)

rewrite61.0ms (0.3%)

series310.0ms (1.5%)

simplify106.0ms (0.5%)

prune1.6s (7.8%)

localize8.0ms (0%)

rewrite25.0ms (0.1%)

series223.0ms (1.1%)

simplify49.0ms (0.2%)

prune285.0ms (1.4%)

localize22.0ms (0.1%)

rewrite323.0ms (1.6%)

series589.0ms (2.9%)

simplify664.0ms (3.2%)

prune4.8s (23.2%)

regimes311.0ms (1.5%)

bsearch181.0ms (0.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.1s (29.9%)

Profiling