Details

analyze1.1s (4.6%)

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
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)

sample225.0ms (1%)

Algorithm

1×

intervals

Results

53.0ms	86×	body	1024	valid
51.0ms	64×	body	1024	nan
45.0ms	70×	body	2048	valid
16.0ms	83×	body	128	overflowed
13.0ms	34×	body	512	valid
7.0ms	15×	body	512	nan
5.0ms	10×	body	512	invalid
5.0ms	6×	body	1024	invalid
4.0ms	20×	body	256	valid
4.0ms	46×	body	128	valid
2.0ms	10×	body	256	nan
1.0ms	23×	body	128	nan
1.0ms	4×	body	256	invalid
1.0ms	5×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify137.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

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

30.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
0.0b	(pow.f64 x (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
0.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_100`
19×	`*-un-lft-identity_binary64_78`
16×	`unpow-prod-down_binary64_157`
13×	`pow-unpow_binary64_155`
12×	`add-cube-cbrt_binary64_113`
9×	`times-frac_binary64_84` `difference-of-squares_binary64_47`
8×	`sqr-pow_binary64_50`
7×	`cancel-sign-sub-inv_binary64_44`
4×	`add-log-exp_binary64_117`
3×	`distribute-lft-out--_binary64_30` `add-exp-log_binary64_116` `pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip3--_binary64_82` `diff-log_binary64_170` `div-inv_binary64_75` `pow-pow_binary64_150` `flip--_binary64_53` `distribute-lft-out_binary64_29` `sub-neg_binary64_71`

Counts

2 → 57

Calls

4 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
6.0ms	(pow.f64 x (/.f64 1 n))
0.0ms	(pow.f64 x (/.f64 1 n))
0.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series390.0ms (1.7%)

Counts

2 → 27

Calls

2 calls:

266.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
124.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 1165 to 949 computations (18.5% saved)

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4957	2031
1	4957	2031

prune162.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	6	85

Error

0.7b

Counts

85 → 6

Compiler

Compiled 2074 to 1406 computations (32.2% saved)

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

2.2b	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
1.3b	(log.f64 (+.f64 x 1))
0.1b	(/.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) n)
0.1b	(/.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) n)
1.3b	(log.f64 (+.f64 x 1))
2.2b	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64_78`
30×	`add-sqr-sqrt_binary64_100`
25×	`pow1_binary64_139`
24×	`times-frac_binary64_84`
22×	`log-pow_binary64_167`
20×	`add-cube-cbrt_binary64_113` `distribute-lft-out--_binary64_30`
11×	`log-prod_binary64_164`
8×	`associate-/l*_binary64_23`
6×	`add-exp-log_binary64_116`
5×	`add-cbrt-cube_binary64_114` `difference-of-squares_binary64_47`
4×	`associate--l+_binary64_15` `log-div_binary64_165` `cancel-sign-sub-inv_binary64_44`
3×	`add-log-exp_binary64_117` `associate--r+_binary64_14` `associate-/r*_binary64_22`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `distribute-lft-out_binary64_29` `associate-/l/_binary64_25` `associate--l-_binary64_16` `flip3-+_binary64_81`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `rem-log-exp_binary64_119` `clear-num_binary64_77` `div-sub_binary64_83` `sub-neg_binary64_71`

Counts

3 → 94

Calls

6 calls:

10.0ms	(/.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) n)
8.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
5.0ms	(log.f64 (+.f64 x 1))
0.0ms	(/.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) n)
0.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))

series308.0ms (1.3%)

Counts

3 → 31

Calls

3 calls:

222.0ms	(/.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) n)
56.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
30.0ms	(log.f64 (+.f64 x 1))

Compiler

Compiled 612 to 529 computations (13.6% saved)

simplify99.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4896	2123
1	4896	2123

prune161.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Error

0.1b

Counts

131 → 11

Compiler

Compiled 2132 to 1275 computations (40.2% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

2.2b	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
1.3b	(log.f64 (+.f64 x 1))
0.1b	(/.f64 1 (/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))))
0.1b	(/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)))
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))))
1.3b	(log.f64 (+.f64 x 1))
2.2b	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64_84`
172×	`*-un-lft-identity_binary64_78`
134×	`add-sqr-sqrt_binary64_100`
100×	`add-cube-cbrt_binary64_113`
75×	`pow1_binary64_139`
70×	`log-pow_binary64_167`
68×	`distribute-lft-out--_binary64_30`
38×	`associate-/r*_binary64_22`
18×	`add-exp-log_binary64_116`
17×	`difference-of-squares_binary64_47`
11×	`add-cbrt-cube_binary64_114` `log-prod_binary64_164` `associate-/r/_binary64_24`
8×	`div-exp_binary64_129`
6×	`flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `associate-/l*_binary64_23`
4×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `associate--l+_binary64_15` `log-div_binary64_165` `cancel-sign-sub-inv_binary64_44`
3×	`associate--r+_binary64_14`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `1-exp_binary64_122` `rec-exp_binary64_128` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `associate--l-_binary64_16` `flip3-+_binary64_81`
1×	`inv-pow_binary64_163` `diff-log_binary64_170` `pow-flip_binary64_152` `rem-log-exp_binary64_119` `sub-neg_binary64_71`

Counts

4 → 237

Calls

8 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))
0.0ms	(/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)))

series565.0ms (2.4%)

Counts

4 → 44

Calls

4 calls:

246.0ms	(/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)))
229.0ms	(/.f64 1 (/.f64 n (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))))
60.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
30.0ms	(log.f64 (+.f64 x 1))

Compiler

Compiled 963 to 816 computations (15.3% saved)

simplify113.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4970	6183
1	4970	6183

prune321.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	281	11	292

Error

0.1b

Counts

292 → 11

Compiler

Compiled 5450 to 3383 computations (37.9% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

2.2b	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
1.3b	(log.f64 (+.f64 x 1))
0.2b	(*.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) (/.f64 1 n))
0.2b	(*.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) (/.f64 1 n))
1.3b	(log.f64 (+.f64 x 1))
2.2b	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_78`
26×	`add-sqr-sqrt_binary64_100`
15×	`add-cube-cbrt_binary64_113` `pow1_binary64_139`
13×	`associate-r_binary64_18` `add-exp-log_binary64_116`
11×	`times-frac_binary64_84` `log-prod_binary64_164`
10×	`log-pow_binary64_167`
8×	`add-cbrt-cube_binary64_114` `associate-l_binary64_19` `distribute-lft-out--_binary64_30`
4×	`prod-exp_binary64_127` `associate--l+_binary64_15` `log-div_binary64_165` `cancel-sign-sub-inv_binary64_44`
3×	`add-log-exp_binary64_117` `flip3--_binary64_82` `associate--r+_binary64_14` `flip--_binary64_53` `unswap-sqr_binary64_46`
2×	`cbrt-unprod_binary64_111` `div-exp_binary64_129` `flip-+_binary64_52` `frac-times_binary64_88` `associate-*l/_binary64_21` `difference-of-squares_binary64_47` `distribute-lft-out_binary64_29` `associate--l-_binary64_16` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `cbrt-undiv_binary64_112` `diff-log_binary64_170` `un-div-inv_binary64_76` `1-exp_binary64_122` `div-inv_binary64_75` `rec-exp_binary64_128` `rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `sub-neg_binary64_71`

Counts

3 → 89

Calls

6 calls:

12.0ms	(*.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) (/.f64 1 n))
8.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
3.0ms	(log.f64 (+.f64 x 1))
0.0ms	(*.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) (/.f64 1 n))
0.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))

series308.0ms (1.3%)

Counts

3 → 31

Calls

3 calls:

218.0ms	(*.f64 (-.f64 (log.f64 (+.f64 x 1)) (log.f64 x)) (/.f64 1 n))
56.0ms	(-.f64 (log.f64 (+.f64 x 1)) (log.f64 x))
34.0ms	(log.f64 (+.f64 x 1))

Compiler

Compiled 656 to 573 computations (12.7% saved)

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5297	1864

prune101.0ms (0.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	119	12	131

Error

0.1b

Counts

131 → 12

Compiler

Compiled 1863 to 1164 computations (37.5% saved)

simplify28.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	527	1537
1	527	1537

regimes764.0ms (3.3%)

Compiler: Compiled 4230 to 3381 computations (20.1% saved)

bsearch49.0ms (0.2%)

Steps

Iters	Range		Point
8	0.6400884701246073	6264.291086638127	3749.2329152300117

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes195.0ms (0.8%)

Compiler: Compiled 270 to 284 computations (-5.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

regimes186.0ms (0.8%)

Compiler: Compiled 246 to 263 computations (-6.9% saved)

bsearch95.0ms (0.4%)

Steps

Iters	Range		Point
5	8.007015952066224e+154	2.3380919094028116e+155	1.144349130405594e+155
8	0.6400884701246073	6264.291086638127	0.9894323734666607

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes154.0ms (0.7%)

Compiler: Compiled 161 to 181 computations (-12.4% saved)

bsearch99.0ms (0.4%)

Steps

Iters	Range		Point
5	8.007015952066224e+154	2.3380919094028116e+155	1.304932758506748e+155
7	0.039368410821231006	0.6400884701246073	0.5537129511135368

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes112.0ms (0.5%)

Compiler: Compiled 146 to 166 computations (-13.7% saved)

bsearch2.4s (10.4%)

Steps

Iters	Range		Point
7	1.2169884079186046	29.422695430196452	29.133824801667156
13	-4.735421662104085e-304	3.3569820985883246e-229	4.412972815379056e-285
10	-8929.771112879866	-1.212300905914543e-06	-4.4521808829022955

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes104.0ms (0.4%)

Compiler: Compiled 86 to 118 computations (-37.2% saved)

bsearch2.6s (11.3%)

Steps

Iters	Range		Point
7	1.2169884079186046	29.422695430196452	29.133824801667156
13	-4.735421662104085e-304	3.3569820985883246e-229	3.965136627028028e-281
10	-8929.771112879866	-1.212300905914543e-06	-3.2646001001743175

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes262.0ms (1.1%)

Compiler: Compiled 20 to 36 computations (-80% saved)

bsearch2.4s (10.2%)

Steps

Iters	Range		Point
7	1.2169884079186046	29.422695430196452	29.133824801667156
13	-4.735421662104085e-304	3.3569820985883246e-229	3.924502705116223e-280
10	-8929.771112879866	-1.212300905914543e-06	-3.5850968805999273

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes31.0ms (0.1%)

Accuracy

Total 6.7b remaining (95.1%)

Threshold costs 0b (0%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch2.1s (8.8%)

Steps

Iters	Range		Point
7	9.109519876480436e+43	2.1289546758283374e+45	9.888380016423709e+43
13	-4.735421662104085e-304	3.3569820985883246e-229	4.602593217058747e-282

Compiler

Compiled 222 to 178 computations (19.8% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	110	319
1	110	319

end0.0ms (0%)

sample7.5s (32.1%)

Algorithm

1×

intervals

Results

1.5s	2677×	body	1024	valid
1.2s	1483×	body	1024	nan
1.1s	1789×	body	2048	valid
500.0ms	2584×	body	128	overflowed
453.0ms	1196×	body	512	valid
318.0ms	678×	body	512	nan
178.0ms	1754×	body	128	valid
142.0ms	158×	body	1024	invalid
138.0ms	584×	body	256	valid
132.0ms	249×	body	512	invalid
88.0ms	359×	body	256	nan
54.0ms	815×	body	128	nan
41.0ms	147×	body	256	invalid
37.0ms	256×	body	128	invalid
6.0ms	5×	body	2048	nan

Compiler

Compiled 1225 to 972 computations (20.7% saved)

Pareto

0.5040319134859071

Details

analyze1.1s (4.6%)

sample225.0ms (1%)

simplify137.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite23.0ms (0.1%)

series390.0ms (1.7%)

simplify85.0ms (0.4%)

prune162.0ms (0.7%)

localize8.0ms (0%)

rewrite30.0ms (0.1%)

series308.0ms (1.3%)

simplify99.0ms (0.4%)

prune161.0ms (0.7%)

localize9.0ms (0%)

rewrite61.0ms (0.3%)

series565.0ms (2.4%)

simplify113.0ms (0.5%)

prune321.0ms (1.4%)

localize9.0ms (0%)

rewrite30.0ms (0.1%)

series308.0ms (1.3%)

simplify66.0ms (0.3%)

prune101.0ms (0.4%)

simplify28.0ms (0.1%)

regimes764.0ms (3.3%)

bsearch49.0ms (0.2%)

regimes195.0ms (0.8%)

bsearch1.0ms (0%)

regimes186.0ms (0.8%)

bsearch95.0ms (0.4%)

regimes154.0ms (0.7%)

bsearch99.0ms (0.4%)

regimes112.0ms (0.5%)

bsearch2.4s (10.4%)

regimes104.0ms (0.4%)

bsearch2.6s (11.3%)

regimes262.0ms (1.1%)

bsearch2.4s (10.2%)

regimes31.0ms (0.1%)

bsearch2.1s (8.8%)

simplify7.0ms (0%)

end0.0ms (0%)

sample7.5s (32.1%)

Profiling