Details

analyze1.0s (6.5%)

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%	46.8%	25.1%	7
28.1%	43.7%	28.2%	8
29.7%	34.3%	36%	9
29.7%	31.6%	38.7%	10
31.1%	25.8%	43.1%	11
31.1%	24.6%	44.3%	12
31.5%	21.9%	46.6%	13
31.5%	21%	47.5%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample8.9s (56.6%)

Results

2.4s	2778×	body	1024	valid
2.1s	1723×	body	1024	invalid
1.7s	1791×	body	2048	valid
825.0ms	997×	body	512	invalid
798.0ms	1286×	body	512	valid
355.0ms	1800×	body	128	valid
239.0ms	555×	body	256	invalid
231.0ms	601×	body	256	valid
201.0ms	1129×	body	128	invalid
8.0ms	5×	body	2048	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify50.0ms (0.3%)

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

35.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.0b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 x (/.f64 1 n))
✓	0.2b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
✓	1.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series85.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(pow.f64 x (/.f64 1 n))
34.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
13.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
76×	`unpow-prod-down_binary64`
65×	`add-sqr-sqrt_binary64`
56×	`prod-diff_binary64`
53×	`add-cube-cbrt_binary64`

Counts

3 → 155

Calls

3 calls:

9.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
4.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.0ms	(pow.f64 x (/.f64 1 n))

simplify183.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

580×	`cancel-sign-sub-inv_binary64`
422×	`fma-neg_binary64`
284×	`sub-neg_binary64`
202×	`fma-def_binary64`
194×	`+-commutative_binary64`

Counts

227 → 269

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	395	9164
1	964	7582
2	3311	5432
3	4914	5432
4	4974	5432

prune311.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	264	5	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	5	270

Error

0.8b

Counts

270 → 5

Alt Table

Status	Error	Program
	37.7b	(-.f64 (fma.f64 11/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 n n) (pow.f64 x 4))) (fma.f64 1/3 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 3))) (fma.f64 1/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 4) (pow.f64 n 4))) (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (fma.f64 1/6 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 3) (pow.f64 n 3))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))))) (fma.f64 1/2 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (.f64 n (pow.f64 x 3))))) (.f64 1/4 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 4))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 n 3) (pow.f64 x 4)))))))
	34.2b	(log.f64 (exp.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
	24.7b	(-.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)))
▶	20.7b	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
	34.0b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 9886 to 6683 computations (32.4% 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)
✓	3.2b	(-.f64 (log1p.f64 x) (log.f64 x))

series471.0ms (3%)

Counts

2 → 36

Calls

2 calls:

467.0ms	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
4.0ms	(-.f64 (log1p.f64 x) (log.f64 x))

rewrite13.0ms (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:

5.0ms	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
4.0ms	(-.f64 (log1p.f64 x) (log.f64 x))

simplify126.0ms (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

prune151.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Error

0.1b

Counts

123 → 10

Alt Table

Status	Error	Program
	37.7b	(-.f64 (fma.f64 11/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 n n) (pow.f64 x 4))) (fma.f64 1/3 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 3))) (fma.f64 1/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 4) (pow.f64 n 4))) (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (fma.f64 1/6 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 3) (pow.f64 n 3))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))))) (fma.f64 1/2 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (.f64 n (pow.f64 x 3))))) (.f64 1/4 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 4))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 n 3) (pow.f64 x 4)))))))
▶	20.8b	(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
	20.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (-.f64 (log1p.f64 x) (log.f64 x))) (-.f64 (log1p.f64 x) (log.f64 x)))) n)
	21.0b	(/.f64 (exp.f64 (log.f64 (-.f64 (log1p.f64 x) (log.f64 x)))) n)
	39.1b	(/.f64 (+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))) n)
	34.2b	(log.f64 (exp.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
	21.0b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (.f64 n (fma.f64 (log.f64 x) (log.f64 x) (.f64 (log1p.f64 x) (+.f64 (log.f64 x) (log1p.f64 x))))))
	24.7b	(-.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)))
	20.8b	(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
	34.0b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 2554 to 996 computations (61% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
✓	0.2b	(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))
	3.2b	(-.f64 (log1p.f64 x) (log.f64 x))

series987.0ms (6.3%)

Counts

2 → 48

Calls

2 calls:

503.0ms	(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))
485.0ms	(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64`
126×	`*-un-lft-identity_binary64`
110×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
32×	`distribute-lft-out--_binary64`

Counts

2 → 165

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
4.0ms	(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

395×	`times-frac_binary64`
339×	`associate-/l*_binary64`
331×	`fma-neg_binary64`
326×	`associate-/r*_binary64`
324×	`fma-def_binary64`

Counts

213 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4582
1	488	4291
2	1445	4175
3	4353	4175
4	4992	4175

prune240.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	262	11	273

Error

0.1b

Counts

273 → 11

Alt Table

Status	Error	Program
	34.2b	(log.f64 (exp.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
	21.0b	(/.f64 1 (/.f64 n (exp.f64 (log.f64 (-.f64 (log1p.f64 x) (log.f64 x))))))
	37.7b	(-.f64 (fma.f64 11/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 n n) (pow.f64 x 4))) (fma.f64 1/3 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 3))) (fma.f64 1/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 4) (pow.f64 n 4))) (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (fma.f64 1/6 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 3) (pow.f64 n 3))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))))) (fma.f64 1/2 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (.f64 n (pow.f64 x 3))))) (.f64 1/4 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 4))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 n 3) (pow.f64 x 4)))))))
✓	20.8b	(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
	20.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (-.f64 (log1p.f64 x) (log.f64 x))) (-.f64 (log1p.f64 x) (log.f64 x)))) n)
	38.9b	(/.f64 1 (fma.f64 (/.f64 n x) -1/12 (*.f64 n (+.f64 x 1/2))))
	39.1b	(/.f64 (+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))) n)
	21.0b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (.f64 n (fma.f64 (log.f64 x) (log.f64 x) (.f64 (log1p.f64 x) (+.f64 (log.f64 x) (log1p.f64 x))))))
	24.7b	(-.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)))
▶	20.8b	(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
	34.0b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 5832 to 2146 computations (63.2% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
	3.2b	(-.f64 (log1p.f64 x) (log.f64 x))

series472.0ms (3%)

Counts

1 → 24

Calls

1 calls:

472.0ms

(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 45

Calls

1 calls:

8.0ms

(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

763×	`fma-def_binary64`
436×	`times-frac_binary64`
422×	`fma-neg_binary64`
209×	`distribute-rgt-neg-out_binary64`
208×	`associate-l_binary64`

Counts

69 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	125	1178
1	302	1086
2	838	1086
3	2198	1086
4	4900	1086
5	5110	1086

prune124.0ms (0.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	138	12	150

Error

0.1b

Counts

150 → 12

Alt Table

Status	Error	Program
	34.2b	(log.f64 (exp.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
	21.0b	(/.f64 1 (/.f64 n (exp.f64 (log.f64 (-.f64 (log1p.f64 x) (log.f64 x))))))
	21.0b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (.f64 n (fma.f64 (log.f64 x) (log.f64 x) (.f64 (log1p.f64 x) (+.f64 (log.f64 x) (log1p.f64 x))))))
	39.2b	(.f64 (-.f64 (/.f64 1 x) (/.f64 1/2 (.f64 x x))) (/.f64 1 n))
	37.7b	(-.f64 (fma.f64 11/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 n n) (pow.f64 x 4))) (fma.f64 1/3 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 3))) (fma.f64 1/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 4) (pow.f64 n 4))) (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x x) (.f64 n n))) (fma.f64 1/6 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 3) (pow.f64 n 3))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))))) (fma.f64 1/2 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (.f64 n (pow.f64 x 3))))) (.f64 1/4 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 4))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 n 3) (pow.f64 x 4)))))))
✓	20.8b	(/.f64 1 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))))
	20.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (-.f64 (log1p.f64 x) (log.f64 x))) (-.f64 (log1p.f64 x) (log.f64 x)))) n)
	38.9b	(/.f64 1 (fma.f64 (/.f64 n x) -1/12 (*.f64 n (+.f64 x 1/2))))
	39.1b	(/.f64 (+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 1/2 (*.f64 x x)))) n)
	24.7b	(-.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)))
✓	20.8b	(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
	34.0b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 2770 to 1167 computations (57.9% saved)

regimes2.0s (12.6%)

Accuracy

Total 6.9b remaining (98%)

Threshold costs 0b (0%)

Counts

217 → 2

Compiler

Compiled 19052 to 11969 computations (37.2% saved)

bsearch85.0ms (0.5%)

Steps

Iters	Range		Point
9	1.6672574015366395	878182.1653203844	502.9330801505896

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	50
1	29	50
2	35	50
3	39	50
4	41	50
5	40	50

end209.0ms (1.3%)

Compiler: Compiled 404 to 260 computations (35.6% saved)

Details

analyze1.0s (6.5%)

sample8.9s (56.6%)

simplify50.0ms (0.3%)

prune2.0ms (0%)

localize7.0ms (0%)

series85.0ms (0.5%)

rewrite29.0ms (0.2%)

simplify183.0ms (1.2%)

prune311.0ms (2%)

localize6.0ms (0%)

series471.0ms (3%)

rewrite13.0ms (0.1%)

simplify126.0ms (0.8%)

prune151.0ms (1%)

localize7.0ms (0%)

series987.0ms (6.3%)

rewrite32.0ms (0.2%)

simplify138.0ms (0.9%)

prune240.0ms (1.5%)

localize7.0ms (0%)

series472.0ms (3%)

rewrite15.0ms (0.1%)

simplify76.0ms (0.5%)

prune124.0ms (0.8%)

regimes2.0s (12.6%)

bsearch85.0ms (0.5%)

simplify3.0ms (0%)

end209.0ms (1.3%)

Profiling