Details

analyze2.8s (14.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample4.5s (23.5%)

Results

2.5s	11408×	body	128	invalid
1.9s	8256×	body	128	valid

Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

486×	`fma-neg_binary64`
409×	`sub-neg_binary64`
351×	`unsub-neg_binary64`
284×	`fma-def_binary64`
258×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	43
1	59	41
2	155	41
3	548	39
4	1925	39
5	4453	39

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

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

15.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.3b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))

Compiler

Compiled 137 to 72 computations (47.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 a c) (.f64 y i))
✓	4.7b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))
✓	5.9b	(fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i))))
✓	6.9b	(.f64 j (-.f64 (.f64 a c) (*.f64 y i)))

series216.0ms (1.1%)

Counts

4 → 312

Calls

4 calls:

100.0ms	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))
91.0ms	(fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i))))
17.0ms	(.f64 j (-.f64 (.f64 a c) (*.f64 y i)))
8.0ms	(-.f64 (.f64 a c) (.f64 y i))

rewrite47.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

248×	`add-sqr-sqrt_binary64`
231×	`log1p-expm1-u_binary64`
231×	`expm1-log1p-u_binary64`
230×	`add-cbrt-cube_binary64`
226×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	88
1	482	88

Stop Event

1×	node limit

Counts

4 → 94

Calls

4 calls:

45.0ms	(-.f64 (.f64 a c) (.f64 y i))
45.0ms	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))
45.0ms	(fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i))))
45.0ms	(.f64 j (-.f64 (.f64 a c) (*.f64 y i)))

simplify141.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-neg_binary64`
486×	`associate-+l-_binary64`
379×	`sub-neg_binary64`
359×	`associate--l+_binary64`
328×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	7678
1	575	7597
2	1413	7516
3	2824	7105

Stop Event

1×	node limit

Counts

406 → 181

prune293.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	175	6	181
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	175	7	182

Error

0.0b

Counts

182 → 7

Alt Table

Status	Error	Program
	24.9b	(fma.f64 z (-.f64 (.f64 y x) (.f64 c b)) (.f64 i (-.f64 (.f64 t b) (*.f64 j y))))
▶	13.0b	(+.f64 (.f64 c (fma.f64 j a (.f64 b (neg.f64 z)))) (fma.f64 y (-.f64 (.f64 z x) (.f64 j i)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x))))))
✓	15.3b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))
	17.7b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z)))))
	30.2b	(fma.f64 z (-.f64 (.f64 y x) (.f64 c b)) (.f64 a (fma.f64 j c (neg.f64 (.f64 t x)))))
	28.8b	(fma.f64 j (-.f64 (.f64 c a) (.f64 i y)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x)))))
	35.3b	(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (.f64 y z) (.f64 a t)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 i t)) (.f64 j (fma.f64 a c (*.f64 (neg.f64 y) i)))))) 2)

Compiler

Compiled 5501 to 1056 computations (80.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 j a (*.f64 b (neg.f64 z)))
✓	4.6b	(fma.f64 y (-.f64 (.f64 z x) (.f64 j i)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x)))))
✓	5.3b	(.f64 t (fma.f64 i b (.f64 a (neg.f64 x))))
✓	5.6b	(.f64 c (fma.f64 j a (.f64 b (neg.f64 z))))

series120.0ms (0.6%)

Counts

4 → 264

Calls

4 calls:

61.0ms	(fma.f64 y (-.f64 (.f64 z x) (.f64 j i)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x)))))
27.0ms	(.f64 t (fma.f64 i b (.f64 a (neg.f64 x))))
22.0ms	(.f64 c (fma.f64 j a (.f64 b (neg.f64 z))))
10.0ms	(fma.f64 j a (*.f64 b (neg.f64 z)))

rewrite41.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

239×	`add-sqr-sqrt_binary64`
220×	`log1p-expm1-u_binary64`
220×	`expm1-log1p-u_binary64`
219×	`add-cbrt-cube_binary64`
217×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	62
1	465	54

Stop Event

1×	node limit

Counts

4 → 66

Calls

4 calls:

40.0ms	(fma.f64 j a (*.f64 b (neg.f64 z)))
40.0ms	(fma.f64 y (-.f64 (.f64 z x) (.f64 j i)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x)))))
40.0ms	(.f64 t (fma.f64 i b (.f64 a (neg.f64 x))))
40.0ms	(.f64 c (fma.f64 j a (.f64 b (neg.f64 z))))

simplify295.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1694×	`fma-neg_binary64`
756×	`fma-def_binary64`
272×	`sub-neg_binary64`
260×	`unsub-neg_binary64`
235×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	4332
1	262	4252
2	697	4180
3	1473	4036
4	2915	4036
5	3892	4036
6	4255	4036
7	4406	4036
8	4468	4036
9	4474	4036
10	4474	4036
11	4584	4036
12	4628	4036
13	4628	4036

Stop Event

1×	node limit

Counts

330 → 116

prune113.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	116	7	123

Error

0.0b

Counts

123 → 7

Alt Table

Status	Error	Program
	24.9b	(fma.f64 z (-.f64 (.f64 y x) (.f64 c b)) (.f64 i (-.f64 (.f64 t b) (*.f64 j y))))
✓	13.0b	(+.f64 (.f64 c (fma.f64 j a (.f64 b (neg.f64 z)))) (fma.f64 y (-.f64 (.f64 z x) (.f64 j i)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x))))))
✓	15.3b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))
▶	17.7b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z)))))
	30.2b	(fma.f64 z (-.f64 (.f64 y x) (.f64 c b)) (.f64 a (fma.f64 j c (neg.f64 (.f64 t x)))))
	28.8b	(fma.f64 j (-.f64 (.f64 c a) (.f64 i y)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x)))))
	35.3b	(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (.f64 y z) (.f64 a t)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 i t)) (.f64 j (fma.f64 a c (*.f64 (neg.f64 y) i)))))) 2)

Compiler

Compiled 3699 to 728 computations (80.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 t b) (.f64 j y))
✓	4.2b	(fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z))))
✓	4.6b	(.f64 c (.f64 b (neg.f64 z)))
✓	4.7b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z)))))

series164.0ms (0.9%)

Counts

4 → 276

Calls

4 calls:

88.0ms	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z)))))
59.0ms	(fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z))))
8.0ms	(.f64 c (.f64 b (neg.f64 z)))
8.0ms	(-.f64 (.f64 t b) (.f64 j y))

rewrite45.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

239×	`add-sqr-sqrt_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
222×	`add-cbrt-cube_binary64`
218×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	76
1	465	70

Stop Event

1×	node limit

Counts

4 → 101

Calls

4 calls:

43.0ms	(-.f64 (.f64 t b) (.f64 j y))
43.0ms	(fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z))))
43.0ms	(.f64 c (.f64 b (neg.f64 z)))
43.0ms	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z)))))

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-neg_binary64`
588×	`sub-neg_binary64`
532×	`fma-def_binary64`
376×	`cancel-sign-sub-inv_binary64`
265×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	5852
1	404	5699
2	1049	5696
3	2333	5609
4	4543	5609

Stop Event

1×	node limit

Counts

377 → 165

prune162.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	163	9	172

Error

0.0b

Counts

172 → 9

Alt Table

Status	Error	Program
	35.0b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (cbrt.f64 (pow.f64 (-.f64 (.f64 t b) (.f64 y j)) 3)) (.f64 c (.f64 b (neg.f64 z)))))
▶	16.7b	(-.f64 (fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (.f64 x a)))) (.f64 i (*.f64 y j)))
✓	13.0b	(+.f64 (.f64 c (fma.f64 j a (.f64 b (neg.f64 z)))) (fma.f64 y (-.f64 (.f64 z x) (.f64 j i)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x))))))
✓	15.3b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))
✓	17.7b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z)))))
	30.2b	(fma.f64 z (-.f64 (.f64 y x) (.f64 c b)) (.f64 a (fma.f64 j c (neg.f64 (.f64 t x)))))
	28.8b	(fma.f64 j (-.f64 (.f64 c a) (.f64 i y)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x)))))
	25.7b	(fma.f64 y (-.f64 (.f64 z x) (.f64 i j)) (.f64 b (-.f64 (.f64 i t) (*.f64 c z))))
	35.3b	(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (.f64 y z) (.f64 a t)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 i t)) (.f64 j (fma.f64 a c (*.f64 (neg.f64 y) i)))))) 2)

Compiler

Compiled 4888 to 1069 computations (78.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (.f64 x a)))) (.f64 i (*.f64 y j)))
✓	4.8b	(fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (*.f64 x a))))
✓	5.3b	(.f64 t (-.f64 (.f64 i b) (*.f64 x a)))
✓	5.8b	(.f64 i (.f64 y j))

series184.0ms (1%)

Counts

4 → 280

Calls

4 calls:

81.0ms	(-.f64 (fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (.f64 x a)))) (.f64 i (*.f64 y j)))
74.0ms	(fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (*.f64 x a))))
17.0ms	(.f64 t (-.f64 (.f64 i b) (*.f64 x a)))
11.0ms	(.f64 i (.f64 y j))

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

244×	`add-sqr-sqrt_binary64`
230×	`log1p-expm1-u_binary64`
230×	`expm1-log1p-u_binary64`
229×	`add-cbrt-cube_binary64`
224×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	81
1	473	81

Stop Event

1×	node limit

Counts

4 → 78

Calls

4 calls:

46.0ms	(-.f64 (fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (.f64 x a)))) (.f64 i (*.f64 y j)))
46.0ms	(fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (*.f64 x a))))
46.0ms	(.f64 t (-.f64 (.f64 i b) (*.f64 x a)))
45.0ms	(.f64 i (.f64 y j))

simplify159.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

634×	`sub-neg_binary64`
597×	`fma-def_binary64`
569×	`fma-neg_binary64`
383×	`cancel-sign-sub-inv_binary64`
296×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	6754
1	383	6569
2	1035	6494
3	2393	6263
4	4547	6263

Stop Event

1×	node limit

Counts

358 → 141

prune228.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	2	3	5
Picked	1	0	1
Done	0	3	3
Total	142	8	150

Error

0.0b

Counts

150 → 8

Alt Table

Status	Error	Program
	34.7b	(-.f64 (fma.f64 z (-.f64 (.f64 y x) (.f64 b c)) (.f64 t (-.f64 (.f64 i b) (.f64 x a)))) (pow.f64 (sqrt.f64 (.f64 i (*.f64 y j))) 2))
✓	13.0b	(+.f64 (.f64 c (fma.f64 j a (.f64 b (neg.f64 z)))) (fma.f64 y (-.f64 (.f64 z x) (.f64 j i)) (.f64 t (fma.f64 i b (.f64 a (neg.f64 x))))))
✓	15.3b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 t i)) (.f64 j (-.f64 (.f64 a c) (.f64 y i)))))
✓	17.7b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (-.f64 (.f64 t b) (.f64 j y)) (.f64 c (.f64 b (neg.f64 z)))))
	30.2b	(fma.f64 z (-.f64 (.f64 y x) (.f64 c b)) (.f64 a (fma.f64 j c (neg.f64 (.f64 t x)))))
	35.0b	(fma.f64 x (-.f64 (.f64 y z) (.f64 t a)) (fma.f64 i (cbrt.f64 (pow.f64 (-.f64 (.f64 t b) (.f64 y j)) 3)) (.f64 c (.f64 b (neg.f64 z)))))
	17.8b	(fma.f64 y (fma.f64 i (neg.f64 j) (.f64 x z)) (-.f64 (.f64 b (-.f64 (.f64 i t) (.f64 z c))) (.f64 t (.f64 a x))))
	35.3b	(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (.f64 y z) (.f64 a t)) (fma.f64 b (fma.f64 z (neg.f64 c) (.f64 i t)) (.f64 j (fma.f64 a c (*.f64 (neg.f64 y) i)))))) 2)

Compiler

Compiled 4151 to 715 computations (82.8% saved)

regimes9.0s (47.5%)

Accuracy

Total 3.0b remaining (94.8%)

Threshold costs 0b (0%)

Counts

222 → 3

Compiler

Compiled 64486 to 41138 computations (36.2% saved)

bsearch9.0ms (0%)

Compiler: Compiled 38 to 23 computations (39.5% saved)

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

216×	`distribute-rgt-neg-in_binary64`
179×	`cancel-sign-sub-inv_binary64`
145×	`distribute-lft-neg-in_binary64`
142×	`neg-sub0_binary64`
142×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	224
1	136	224
2	207	222
3	268	222
4	338	222
5	388	222
6	441	222
7	560	222
8	686	222
9	803	222
10	987	222
11	1192	222
12	1398	222
13	1555	222
14	1625	222
15	1658	222
16	1672	222
17	1676	222

Stop Event

1×

saturated

end190.0ms (1%)

Compiler: Compiled 595 to 288 computations (51.6% saved)

Details

analyze2.8s (14.5%)

sample4.5s (23.5%)

simplify33.0ms (0.2%)

prune4.0ms (0%)

localize22.0ms (0.1%)

series216.0ms (1.1%)

rewrite47.0ms (0.2%)

simplify141.0ms (0.7%)

prune293.0ms (1.5%)

localize21.0ms (0.1%)

series120.0ms (0.6%)

rewrite41.0ms (0.2%)

simplify295.0ms (1.6%)

prune113.0ms (0.6%)

localize18.0ms (0.1%)

series164.0ms (0.9%)

rewrite45.0ms (0.2%)

simplify139.0ms (0.7%)

prune162.0ms (0.9%)

localize20.0ms (0.1%)

series184.0ms (1%)

rewrite48.0ms (0.3%)

simplify159.0ms (0.8%)

prune228.0ms (1.2%)

regimes9.0s (47.5%)

bsearch9.0ms (0%)

simplify34.0ms (0.2%)

end190.0ms (1%)

Profiling