Details

analyze1.1s (7.6%)

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%	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)

sample8.4s (58.6%)

Results

2.2s	2786×	body	1024	valid
2.1s	1842×	body	1024	invalid
1.6s	1817×	body	2048	valid
735.0ms	978×	body	512	invalid
701.0ms	1253×	body	512	valid
347.0ms	1819×	body	128	valid
242.0ms	569×	body	256	invalid
207.0ms	1207×	body	128	invalid
202.0ms	581×	body	256	valid
14.0ms	9×	body	2048	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

436×	`unswap-sqr_binary64`
377×	`fma-def_binary64`
235×	`distribute-rgt-in_binary64`
219×	`distribute-lft-in_binary64`
212×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	42	19
3	104	19
4	340	19
5	1111	19
6	3393	19

Stop Event

1×	node limit

Counts

1 → 1

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

33.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	33.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
✓	0.0b	(pow.f64 x (/.f64 1 n))
✓	1.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series90.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

40.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
39.0ms	(pow.f64 x (/.f64 1 n))
10.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

rewrite73.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

547×	`prod-diff_binary64`
294×	`fma-def_binary64`
178×	`log1p-udef_binary64`
177×	`expm1-udef_binary64`
155×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	207	32
2	2829	32

Stop Event

1×	node limit

Counts

3 → 145

Calls

3 calls:

69.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
69.0ms	(pow.f64 x (/.f64 1 n))
69.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-def_binary64`
569×	`associate-/l*_binary64`
379×	`cancel-sign-sub-inv_binary64`
229×	`sub-neg_binary64`
156×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	2805
1	684	2796
2	2550	2288

Stop Event

1×	node limit

Counts

217 → 206

prune225.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	202	5	207

Error

1.2b

Counts

207 → 5

Alt Table

Status	Error	Program
▶	18.8b	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
	29.6b	(/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n))
	54.5b	(+.f64 (/.f64 x n) (-.f64 1 (exp.f64 (/.f64 (log.f64 x) n))))
	24.1b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n))))
✓	33.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 6779 to 4061 computations (40.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
✓	2.2b	(-.f64 (log1p.f64 x) (log.f64 x))

series390.0ms (2.7%)

Counts

2 → 36

Calls

2 calls:

388.0ms	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
3.0ms	(-.f64 (log1p.f64 x) (log.f64 x))

rewrite86.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`expm1-log1p-u_binary64`
576×	`prod-diff_binary64`
228×	`egg-rr`
80×	`add-sqr-sqrt_binary64`
77×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	154	19
2	2268	19

Stop Event

1×	node limit

Counts

2 → 228

Calls

2 calls:

77.0ms	(/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)
77.0ms	(-.f64 (log1p.f64 x) (log.f64 x))

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

446×	`associate-/r*_binary64`
433×	`fma-def_binary64`
243×	`cancel-sign-sub-inv_binary64`
207×	`associate-l_binary64`
206×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	598
1	192	590
2	505	590
3	1463	563

Stop Event

1×	node limit

Counts

264 → 260

prune202.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	252	8	260
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	253	12	265

Error

0.0b

Counts

265 → 12

Alt Table

Status	Error	Program
▶	18.8b	(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
	38.9b	(/.f64 (/.f64 1 x) n)
	31.2b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) n)) 2)
	29.6b	(/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n))
	39.1b	(+.f64 (fma.f64 (log1p.f64 x) (/.f64 1 n) (neg.f64 (.f64 (/.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 n)) (/.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (pow.f64 (cbrt.f64 n) 2))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 n))) (/.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (pow.f64 (cbrt.f64 n) 2)) (.f64 (/.f64 (cbrt.f64 (log.f64 x)) (cbrt.f64 n)) (/.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (pow.f64 (cbrt.f64 n) 2)))))
	54.5b	(+.f64 (/.f64 x n) (-.f64 1 (exp.f64 (/.f64 (log.f64 x) n))))
	18.9b	(/.f64 (/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (+.f64 (pow.f64 (log1p.f64 x) 2) (*.f64 (log.f64 x) (+.f64 (log1p.f64 x) (log.f64 x))))) n)
	18.9b	(.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) (/.f64 1 n)))
	61.3b	(/.f64 (+.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)) (log.f64 x))) n)
	18.8b	(pow.f64 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))) -1)
	24.1b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n))))
✓	33.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 9283 to 3038 computations (67.3% 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))
	2.2b	(-.f64 (log1p.f64 x) (log.f64 x))

series371.0ms (2.6%)

Counts

1 → 24

Calls

1 calls:

371.0ms

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

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

895×	`expm1-log1p-u_binary64`
894×	`log1p-expm1-u_binary64`
403×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
86×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	187	11
2	2461	11

Stop Event

1×	node limit

Counts

1 → 41

Calls

1 calls:

41.0ms

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

simplify32.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-neg_binary64`
380×	`associate-/r*_binary64`
226×	`sub-neg_binary64`
213×	`fma-def_binary64`
175×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	408
1	138	406
2	344	406
3	960	382
4	3761	378

Stop Event

1×	node limit

Counts

65 → 58

prune119.0ms (0.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	121	12	133

Error

0.0b

Counts

133 → 12

Alt Table

Status	Error	Program
	18.9b	(*.f64 (pow.f64 (sqrt.f64 (-.f64 (log1p.f64 x) (log.f64 x))) 2) (/.f64 1 n))
	19.1b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 2) (pow.f64 (log.f64 x) 2)) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
	18.9b	(/.f64 (/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (+.f64 (pow.f64 (log1p.f64 x) 2) (*.f64 (log.f64 x) (+.f64 (log1p.f64 x) (log.f64 x))))) n)
✓	18.8b	(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
	38.9b	(/.f64 (/.f64 1 x) n)
	61.3b	(/.f64 (+.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)) (log.f64 x))) n)
▶	18.8b	(pow.f64 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))) -1)
	29.6b	(/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n))
	54.5b	(+.f64 (/.f64 x n) (-.f64 1 (exp.f64 (/.f64 (log.f64 x) n))))
	19.2b	(/.f64 (/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
	24.1b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n))))
✓	33.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 2392 to 1208 computations (49.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))
✓	0.2b	(pow.f64 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))) -1)
	2.2b	(-.f64 (log1p.f64 x) (log.f64 x))

series765.0ms (5.3%)

Counts

2 → 48

Calls

2 calls:

391.0ms	(pow.f64 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))) -1)
373.0ms	(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))

rewrite47.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

459×	`log-prod_binary64`
412×	`prod-diff_binary64`
182×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	193	22
2	2598	22

Stop Event

1×	node limit

Counts

2 → 86

Calls

2 calls:

45.0ms	(/.f64 n (-.f64 (log1p.f64 x) (log.f64 x)))
45.0ms	(pow.f64 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))) -1)

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

356×	`sub-neg_binary64`
234×	`times-frac_binary64`
232×	`fma-def_binary64`
210×	`associate-/r*_binary64`
210×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	848
1	254	838
2	776	802
3	3283	767

Stop Event

1×	node limit

Counts

134 → 120

prune155.0ms (1.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	183	12	195

Error

0.0b

Counts

195 → 12

Alt Table

Status	Error	Program
	19.1b	(/.f64 (-.f64 (pow.f64 (log1p.f64 x) 2) (pow.f64 (log.f64 x) 2)) (*.f64 n (+.f64 (log1p.f64 x) (log.f64 x))))
	18.9b	(/.f64 (/.f64 (-.f64 (pow.f64 (log1p.f64 x) 3) (pow.f64 (log.f64 x) 3)) (+.f64 (pow.f64 (log1p.f64 x) 2) (*.f64 (log.f64 x) (+.f64 (log1p.f64 x) (log.f64 x))))) n)
✓	18.8b	(*.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (/.f64 1 n))
	38.9b	(/.f64 (/.f64 1 x) n)
	18.9b	(pow.f64 (*.f64 n (/.f64 1 (-.f64 (log1p.f64 x) (log.f64 x)))) -1)
✓	33.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
	61.3b	(/.f64 (+.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (log.f64 x))) (sqrt.f64 (log.f64 x)) (log.f64 x))) n)
✓	18.8b	(pow.f64 (/.f64 n (-.f64 (log1p.f64 x) (log.f64 x))) -1)
	29.6b	(/.f64 (exp.f64 (/.f64 (log.f64 x) n)) (*.f64 x n))
	54.5b	(+.f64 (/.f64 x n) (-.f64 1 (exp.f64 (/.f64 (log.f64 x) n))))
	19.2b	(/.f64 (/.f64 (-.f64 (log1p.f64 x) (log.f64 x)) (pow.f64 (cbrt.f64 n) 2)) (cbrt.f64 n))
	24.1b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (pow.f64 n 2))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 (+.f64 1 x)) n))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 (log.f64 x) 3) (pow.f64 n 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 2))) (/.f64 (log.f64 x) n))))

Compiler

Compiled 3226 to 1434 computations (55.5% saved)

regimes1.5s (10.5%)

Accuracy

Total 7.0b remaining (93.4%)

Threshold costs 0b (0%)

Counts

167 → 4

Compiler

Compiled 13957 to 9241 computations (33.8% saved)

bsearch377.0ms (2.6%)

Steps

Iters	Range		Point
8	322.39857272076483	821964.8675784155	9705.140304668308
9	3.5877296784984715e-265	3.8181448191002346e-260	1.2988131937612738e-262
8	4.426187162211178e-290	8.384146739215936e-286	1.3156010340719408e-288

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	129
1	54	129
2	60	129
3	64	129
4	66	129

Stop Event

1×

saturated

end185.0ms (1.3%)

Compiler: Compiled 397 to 245 computations (38.3% saved)

Details

analyze1.1s (7.6%)

sample8.4s (58.6%)

simplify22.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0%)

series90.0ms (0.6%)

rewrite73.0ms (0.5%)

simplify58.0ms (0.4%)

prune225.0ms (1.6%)

localize7.0ms (0%)

series390.0ms (2.7%)

rewrite86.0ms (0.6%)

simplify31.0ms (0.2%)

prune202.0ms (1.4%)

localize7.0ms (0%)

series371.0ms (2.6%)

rewrite42.0ms (0.3%)

simplify32.0ms (0.2%)

prune119.0ms (0.8%)

localize8.0ms (0.1%)

series765.0ms (5.3%)

rewrite47.0ms (0.3%)

simplify38.0ms (0.3%)

prune155.0ms (1.1%)

regimes1.5s (10.5%)

bsearch377.0ms (2.6%)

simplify7.0ms (0%)

end185.0ms (1.3%)

Profiling