Details

analyze1.3s (14.9%)

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
12.5%	87.4%	0.1%	6
15.6%	84.3%	0.1%	7
18.7%	81.1%	0.1%	8
25.7%	73.3%	0.9%	9
28.5%	60.8%	10.7%	10
30.2%	58.7%	11.1%	11
32.7%	52.2%	15.2%	12
33.5%	39.2%	27.4%	13
34.3%	37.8%	27.9%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.8s (20.5%)

Results

1.2s	8256×	body	128	valid
543.0ms	3835×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

preprocess50.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

549×	`associate-l_binary64`
388×	`associate-r_binary64`
288×	`unswap-sqr_binary64`
269×	`associate-/l*_binary64`
260×	`sqr-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	88
1	71	72
2	171	68
3	369	68
4	1018	68
5	3458	68
6	4263	68
7	4441	68
8	4731	68
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-l_binary64`
401×	`*-commutative_binary64`
393×	`associate-*r/_binary64`
357×	`unswap-sqr_binary64`
261×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	56	17
3	111	17
4	279	17
5	877	17
6	2831	17
7	4305	17
8	4397	17
9	4562	17
10	4781	17

Stop Event

1×	node limit

Counts

1 → 2

prune14.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

2.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.9b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 60 to 37 computations (38.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	2.8b	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))

series488.0ms (5.7%)

Counts

3 → 84

Calls

21 calls:

102.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	a	0
71.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	a	inf
70.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (fma.f64 k (+.f64 k 10) 1))	a	-inf
67.0ms	(*.f64 a (pow.f64 k m))	a	0
50.0ms	(*.f64 a (pow.f64 k m))	a	inf

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
211×	`expm1-udef_binary64`
211×	`log1p-udef_binary64`
189×	`log-pow_binary64`
157×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	236	32
2	3128	32

Stop Event

1×	node limit

Counts

3 → 90

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-r_binary64`
489×	`associate-l_binary64`
474×	`fma-def_binary64`
279×	`associate-/l*_binary64`
240×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	1645
1	373	1542
2	1191	1286

Stop Event

1×	node limit

Counts

174 → 139

prune144.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	6	140

Error

0.0b

Counts

140 → 6

Alt Table

Status	Error	Program
	3.0b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) 2)))
	3.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 a (pow.f64 k m))) 2) (.f64 (cbrt.f64 (.f64 a (pow.f64 k m))) (/.f64 1 (fma.f64 k (+.f64 k 10) 1))))
	16.4b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k m))) 2)
	23.2b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))
▶	2.8b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
	2.9b	(/.f64 (*.f64 a (pow.f64 k m)) (pow.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) 2))

Compiler

Compiled 3158 to 1814 computations (42.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k (+.f64 k 10) 1)
✓	0.0b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))
✓	0.5b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))
✓	2.7b	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))

series309.0ms (3.6%)

Counts

3 → 84

Calls

21 calls:

72.0ms	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	0
67.0ms	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	-inf
65.0ms	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	inf
17.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))	m	inf
14.0ms	(*.f64 a (/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	m	inf

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
212×	`log-pow_binary64`
154×	`fma-def_binary64`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	265	45
2	3518	45

Stop Event

1×	node limit

Counts

3 → 99

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

618×	`cancel-sign-sub-inv_binary64`
289×	`times-frac_binary64`
217×	`distribute-rgt-neg-in_binary64`
202×	`distribute-lft-neg-in_binary64`
173×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2832
1	660	2542
2	2323	2148

Stop Event

1×	node limit

Counts

183 → 184

prune248.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	220	5	225

Error

0.0b

Counts

225 → 5

Alt Table

Status	Error	Program
	3.0b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) 2)))
	16.4b	(pow.f64 (sqrt.f64 (*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) 2)
	23.2b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))
▶	2.9b	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))
	2.9b	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))

Compiler

Compiled 5342 to 3273 computations (38.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))
✓	0.5b	(/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m)))))
✓	2.7b	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))
✓	11.6b	(sqrt.f64 (fma.f64 k (+.f64 k 10) 1))

series473.0ms (5.5%)

Counts

4 → 96

Calls

24 calls:

114.0ms	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))	a	inf
98.0ms	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))	a	-inf
65.0ms	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))	a	0
42.0ms	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))	m	0
33.0ms	(/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m)))))	m	0

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	323	58
2	4242	58

Stop Event

1×	node limit

Counts

4 → 105

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

421×	`times-frac_binary64`
350×	`associate-r_binary64`
348×	`fma-def_binary64`
308×	`associate-/l*_binary64`
266×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	401	5829
1	1363	5233

Stop Event

1×	node limit

Counts

201 → 225

prune364.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	270	5	275

Error

0.0b

Counts

275 → 5

Alt Table

Status	Error	Program
	3.0b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) 2)))
	16.4b	(pow.f64 (sqrt.f64 (*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) 2)
	23.2b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))
✓	2.9b	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))
▶	2.9b	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))

Compiler

Compiled 10817 to 7130 computations (34.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))
✓	0.0b	(/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
✓	0.0b	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
✓	6.5b	(sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))

series565.0ms (6.6%)

Counts

3 → 96

Calls

24 calls:

79.0ms	(/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	0
79.0ms	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	0
70.0ms	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	inf
68.0ms	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	-inf
66.0ms	(/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))	a	inf

rewrite70.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
177×	`prod-diff_binary64`
142×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	286	52
2	3947	52

Stop Event

1×	node limit

Counts

3 → 117

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

527×	`associate-r_binary64`
385×	`fma-def_binary64`
367×	`associate-l_binary64`
351×	`fma-neg_binary64`
303×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	4874
1	1158	4047
2	4629	4009

Stop Event

1×	node limit

Counts

213 → 220

prune585.0ms (6.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	398	1	399
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	398	6	404

Error

0.0b

Counts

404 → 6

Alt Table

Status	Error	Program
	5.2b	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (pow.f64 (pow.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)) 3/2) 1/3))
✓	2.9b	(/.f64 (/.f64 a (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m)))) (sqrt.f64 (/.f64 (fma.f64 k (+.f64 k 10) 1) (pow.f64 k m))))
	3.0b	(/.f64 (.f64 a (pow.f64 k m)) (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) 2)))
	16.4b	(pow.f64 (sqrt.f64 (*.f64 a (/.f64 (pow.f64 k m) (fma.f64 k (+.f64 k 10) 1)))) 2)
	23.2b	(*.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k))
✓	2.9b	(.f64 a (/.f64 1 (.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (*.f64 (sqrt.f64 (fma.f64 k (+.f64 k 10) 1)) (pow.f64 k (neg.f64 m))))))

Compiler

Compiled 17516 to 11025 computations (37.1% saved)

regimes1.6s (18.4%)

Accuracy

Total 0.0b remaining (46.2%)

Threshold costs 0.0b (46.2%)

Counts

306 → 2

Compiler

Compiled 23712 to 16826 computations (29% saved)

bsearch12.0ms (0.1%)

Algorithm

1×	binary-search

Calls

1 calls:

3.0ms

Steps

Iters	Point		Range
9.708206840295397e+40	∈ [	7.405379405568222e+34	,	1.320936909582695e+47	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	32	40
2	42	40
3	51	40
4	56	40
5	59	40
6	60	40

Stop Event

1×

saturated

end117.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 202 to 134 computations (33.7% saved)

Details

analyze1.3s (14.9%)

sample1.8s (20.5%)

preprocess50.0ms (0.6%)

simplify41.0ms (0.5%)

prune14.0ms (0.2%)

localize7.0ms (0.1%)

series488.0ms (5.7%)

rewrite59.0ms (0.7%)

simplify40.0ms (0.5%)

prune144.0ms (1.7%)

localize8.0ms (0.1%)

series309.0ms (3.6%)

rewrite63.0ms (0.7%)

simplify57.0ms (0.7%)

prune248.0ms (2.9%)

localize11.0ms (0.1%)

series473.0ms (5.5%)

rewrite60.0ms (0.7%)

simplify83.0ms (1%)

prune364.0ms (4.2%)

localize9.0ms (0.1%)

series565.0ms (6.6%)

rewrite70.0ms (0.8%)

simplify101.0ms (1.2%)

prune585.0ms (6.8%)

regimes1.6s (18.4%)

bsearch12.0ms (0.1%)

simplify3.0ms (0%)

end117.0ms (1.4%)

Profiling