Details

analyze1.5s (7.2%)

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%	87.4%	12.6%	5
0%	81.2%	18.8%	6
0%	74.9%	25.1%	7
0%	71.8%	28.2%	8
3.1%	60.9%	36%	9
3.1%	58.1%	38.7%	10
4.7%	52.2%	43.1%	11
4.7%	51%	44.3%	12
5.8%	47.6%	46.6%	13
5.8%	47%	47.1%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample12.0s (58.8%)

Results

4.0s	807×	body	8192	exit
2.3s	2784×	body	1024	valid
1.8s	1526×	body	1024	invalid
1.7s	1758×	body	2048	valid
742.0ms	1278×	body	512	valid
557.0ms	758×	body	512	invalid
354.0ms	1849×	body	128	valid
239.0ms	587×	body	256	valid
201.0ms	1073×	body	128	invalid
159.0ms	378×	body	256	invalid
12.0ms	4×	body	2048	invalid

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

436×	`unswap-sqr_binary64`
377×	`fma-def_binary64`
359×	`sub-neg_binary64`
289×	`unsub-neg_binary64`
253×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	41	19
3	102	19
4	248	19
5	790	19
6	2110	19
7	4405	19
8	5048	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

33.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	33.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 x (/.f64 1 n))
✓	1.9b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series81.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

41.0ms	(pow.f64 x (/.f64 1 n))
40.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`unpow-prod-down_binary64`
67×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
56×	`prod-diff_binary64`
44×	`add-cube-cbrt_binary64`

Counts

2 → 125

Calls

2 calls:

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

simplify160.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

492×	`cancel-sign-sub-inv_binary64`
340×	`fma-neg_binary64`
253×	`sub-neg_binary64`
187×	`fma-def_binary64`
175×	`unswap-sqr_binary64`

Counts

173 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	359	7938
1	867	6269
2	2999	4427
3	4591	4427
4	4862	4427

prune264.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	191	4	195
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	4	196

Error

1.2b

Counts

196 → 4

Alt Table

Status	Error	Program
	36.5b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))) (.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (*.f64 x n)))))
	27.5b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
▶	20.5b	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
	33.2b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 7599 to 5230 computations (31.2% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
✓	2.4b	(-.f64 (log1p.f64 x) (log.f64 x))

series575.0ms (2.8%)

Counts

2 → 36

Calls

2 calls:

570.0ms	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
4.0ms	(-.f64 (log1p.f64 x) (log.f64 x))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
12×	`prod-diff_binary64`

Counts

2 → 83

Calls

2 calls:

6.0ms	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
4.0ms	(-.f64 (log1p.f64 x) (log.f64 x))

simplify161.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-neg_binary64`
399×	`fma-def_binary64`
386×	`associate-l_binary64`
296×	`associate-r_binary64`
171×	`associate-/l*_binary64`

Counts

119 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	2225
1	426	1862
2	1217	1802
3	4071	1801
4	4962	1801
5	4971	1801
6	4934	1801

prune108.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Error

0.0b

Counts

122 → 8

Alt Table

Status	Error	Program
	36.5b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))) (.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (*.f64 x n)))))
	20.7b	(/.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 n (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))))
▶	20.7b	(/.f64 (-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
	40.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))) n)
	27.5b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
	21.4b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (.f64 n (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log.f64 x) (log.f64 x)) (.f64 (log1p.f64 x) (log.f64 x))))))
	33.2b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
	32.9b	(/.f64 (-.f64 (-.f64 (log1p.f64 x) (*.f64 2 (log.f64 (cbrt.f64 x)))) (log.f64 (cbrt.f64 x))) n)

Compiler

Compiled 2334 to 824 computations (64.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (log1p.f64 x) (log1p.f64 x))
✓	0.4b	(/.f64 (-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
✓	0.5b	(*.f64 (log.f64 x) (log.f64 x))
✓	2.4b	(-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x)))

series1.1s (5.4%)

Counts

4 → 60

Calls

4 calls:

1.1s	(/.f64 (-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
27.0ms	(*.f64 (log.f64 x) (log.f64 x))
9.0ms	(-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x)))
7.0ms	(*.f64 (log1p.f64 x) (log1p.f64 x))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`pow1_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 118

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
4.0ms	(-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x)))
4.0ms	(*.f64 (log.f64 x) (log.f64 x))
3.0ms	(*.f64 (log1p.f64 x) (log1p.f64 x))

simplify130.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

321×	`fma-def_binary64`
311×	`associate-/r*_binary64`
240×	`associate-r_binary64`
232×	`fma-neg_binary64`
215×	`associate-l_binary64`

Counts

178 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	439	5412
1	1316	5007
2	4912	5005
3	5049	5005

prune257.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	241	9	250

Error

0.0b

Counts

250 → 9

Alt Table

Status	Error	Program
	40.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))) n)
	40.5b	(/.f64 (+.f64 (/.f64 1 (.f64 x x)) (fma.f64 (/.f64 -1 x) (/.f64 (log.f64 x) x) (/.f64 (.f64 2 (log.f64 x)) x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
	36.5b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))) (.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (*.f64 x n)))))
▶	20.7b	(/.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 n (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))))
✓	20.7b	(/.f64 (-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
	27.5b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
	21.4b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (.f64 n (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log.f64 x) (log.f64 x)) (.f64 (log1p.f64 x) (log.f64 x))))))
	33.2b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
	32.9b	(/.f64 (-.f64 (-.f64 (log1p.f64 x) (*.f64 2 (log.f64 (cbrt.f64 x)))) (log.f64 (cbrt.f64 x))) n)

Compiler

Compiled 9297 to 4263 computations (54.1% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 n (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))))
✓	0.2b	(cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))
✓	0.3b	(*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))))
	2.4b	(-.f64 (log1p.f64 x) (log.f64 x))

series544.0ms (2.7%)

Counts

3 → 48

Calls

3 calls:

517.0ms

(/.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 n (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))))

15.0ms

(*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))))

11.0ms

(cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`*-un-lft-identity_binary64`
87×	`times-frac_binary64`
82×	`cbrt-prod_binary64`
74×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`

Counts

3 → 179

Calls

3 calls:

18.0ms

(/.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 n (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))))

12.0ms

(*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))))

3.0ms

(cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))

simplify242.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-def_binary64`
282×	`associate-/l*_binary64`
226×	`fma-neg_binary64`
195×	`associate-r_binary64`
178×	`sub-neg_binary64`

Counts

227 → 299

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	402	8079
1	982	7032
2	3495	6268
3	4772	6141
4	4990	6141
5	4948	6141

prune515.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	557	0	557
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	557	9	566

Error

0.0b

Counts

566 → 9

Alt Table

Status	Error	Program
	40.5b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x))) n)
	40.5b	(/.f64 (+.f64 (/.f64 1 (.f64 x x)) (fma.f64 (/.f64 -1 x) (/.f64 (log.f64 x) x) (/.f64 (.f64 2 (log.f64 x)) x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
	36.5b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))) (.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (*.f64 x n)))))
✓	20.7b	(/.f64 (*.f64 (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) (/.f64 n (cbrt.f64 (-.f64 (log1p.f64 x) (log.f64 x)))))
✓	20.7b	(/.f64 (-.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (.f64 (log.f64 x) (log.f64 x))) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
	27.5b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (/.f64 (log.f64 (+.f64 1 x)) n)) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n)))
	21.4b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (.f64 n (+.f64 (.f64 (log1p.f64 x) (log1p.f64 x)) (+.f64 (.f64 (log.f64 x) (log.f64 x)) (.f64 (log1p.f64 x) (log.f64 x))))))
	33.2b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
	32.9b	(/.f64 (-.f64 (-.f64 (log1p.f64 x) (*.f64 2 (log.f64 (cbrt.f64 x)))) (log.f64 (cbrt.f64 x))) n)

Compiler

Compiled 18781 to 4739 computations (74.8% saved)

regimes2.3s (11.4%)

Accuracy

Total 6.9b remaining (97.3%)

Threshold costs 0b (0%)

Counts

213 → 2

Compiler

Compiled 19573 to 10526 computations (46.2% saved)

bsearch101.0ms (0.5%)

Steps

Iters	Range		Point
9	0.03365737498385137	1019306.2919526637	105986.23398746474

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	20	31
2	19	31

end162.0ms (0.8%)

Compiler: Compiled 271 to 163 computations (39.9% saved)

Details

analyze1.5s (7.2%)

sample12.0s (58.8%)

simplify51.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0%)

series81.0ms (0.4%)

rewrite26.0ms (0.1%)

simplify160.0ms (0.8%)

prune264.0ms (1.3%)

localize6.0ms (0%)

series575.0ms (2.8%)

rewrite16.0ms (0.1%)

simplify161.0ms (0.8%)

prune108.0ms (0.5%)

localize12.0ms (0.1%)

series1.1s (5.4%)

rewrite29.0ms (0.1%)

simplify130.0ms (0.6%)

prune257.0ms (1.3%)

localize10.0ms (0%)

series544.0ms (2.7%)

rewrite58.0ms (0.3%)

simplify242.0ms (1.2%)

prune515.0ms (2.5%)

regimes2.3s (11.4%)

bsearch101.0ms (0.5%)

simplify2.0ms (0%)

end162.0ms (0.8%)

Profiling