Details

analyze2.4s (16.1%)

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 28 to 19 computations (32.1% saved)

sample4.0s (26.9%)

Symmetry

(sort x y)

(sort z t)

Results

2.2s	7318×	body	128	invalid
1.7s	8256×	body	128	valid

Compiler

Compiled 83 to 56 computations (32.5% saved)

simplify220.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1133×	`distribute-rgt-in_binary64`
1066×	`distribute-lft-in_binary64`
969×	`unsub-neg_binary64`
583×	`fma-def_binary64`
461×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	97	24
3	277	24
4	797	24
5	1809	24
6	2532	24
7	2783	24
8	3128	24
9	3409	24
10	3319	24
11	3327	24
12	3331	24
13	3461	24
14	3620	24
15	3621	24
16	3623	24
17	3623	24
18	5071	24

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

5.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.8b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (.f64 (+.f64 a (.f64 b c)) c) i)))

Compiler

Compiled 98 to 61 computations (37.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (.f64 (+.f64 a (*.f64 b c)) c) i))
✓	0.0b	(+.f64 (.f64 x y) (.f64 z t))
✓	0.1b	(.f64 (+.f64 a (.f64 b c)) c)
✓	7.3b	(.f64 (.f64 (+.f64 a (*.f64 b c)) c) i)

series101.0ms (0.7%)

Counts

4 → 228

Calls

4 calls:

64.0ms	(-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (.f64 (+.f64 a (*.f64 b c)) c) i))
19.0ms	(.f64 (.f64 (+.f64 a (*.f64 b c)) c) i)
10.0ms	(+.f64 (.f64 x y) (.f64 z t))
8.0ms	(.f64 (+.f64 a (.f64 b c)) c)

rewrite60.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

194×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
178×	`associate-r_binary64`
178×	`add-log-exp_binary64`

Counts

4 → 130

Calls

4 calls:

56.0ms	(-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (.f64 (+.f64 a (*.f64 b c)) c) i))
56.0ms	(+.f64 (.f64 x y) (.f64 z t))
56.0ms	(.f64 (+.f64 a (.f64 b c)) c)
56.0ms	(.f64 (.f64 (+.f64 a (*.f64 b c)) c) i)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	54
1	372	48
2	5027	48

simplify390.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
891×	`distribute-rgt-neg-in_binary64`
739×	`cube-prod_binary64`
707×	`distribute-lft-neg-in_binary64`
670×	`fabs-mul_binary64`

Counts

358 → 168

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	47	3604
1	113	2908
2	277	2827
3	574	2827
4	1779	2827
5	2670	2827
6	3267	2827
7	3703	2827
8	4161	2827
9	4249	2827
10	4344	2675
11	3348	2675
12	3490	2675
13	4121	2675
14	4413	2675
15	4569	2675
16	4846	2675
17	4912	2675

prune194.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	8	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	8	169

Error

0.0b

Counts

169 → 8

Alt Table

Status	Error	Program
	27.4b	(.f64 2 (-.f64 (/.f64 (-.f64 (pow.f64 (.f64 x y) 2) (pow.f64 (.f64 z t) 2)) (-.f64 (.f64 x y) (.f64 z t))) (.f64 (.f64 (+.f64 a (.f64 b c)) c) i)))
	11.8b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (+.f64 (.f64 c (.f64 a i)) (.f64 (pow.f64 c 2) (*.f64 i b)))))
	8.7b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (.f64 c a)) i)))
	4.9b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a)))))
	34.2b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) 2))
	22.0b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 (*.f64 c (fma.f64 b c a)) i) 3))))
	29.1b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (pow.f64 (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)) 2)))
▶	1.5b	(.f64 2 (+.f64 (fma.f64 1 (fma.f64 x y (.f64 z t)) (neg.f64 (.f64 (.f64 c i) (fma.f64 b c a)))) (fma.f64 (neg.f64 (.f64 c i)) (fma.f64 b c a) (.f64 (*.f64 c i) (fma.f64 b c a)))))

Compiler

Compiled 4810 to 1454 computations (69.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 (fma.f64 x y (.f64 z t)) (neg.f64 (.f64 (*.f64 c i) (fma.f64 b c a))))
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	4.9b	(.f64 (.f64 c i) (fma.f64 b c a))
✓	50.7b	(fma.f64 (neg.f64 (.f64 c i)) (fma.f64 b c a) (.f64 (*.f64 c i) (fma.f64 b c a)))

series126.0ms (0.9%)

Counts

4 → 240

Calls

4 calls:

57.0ms	(fma.f64 1 (fma.f64 x y (.f64 z t)) (neg.f64 (.f64 (*.f64 c i) (fma.f64 b c a))))
41.0ms	(fma.f64 (neg.f64 (.f64 c i)) (fma.f64 b c a) (.f64 (*.f64 c i) (fma.f64 b c a)))
18.0ms	(.f64 (.f64 c i) (fma.f64 b c a))
9.0ms	(fma.f64 x y (*.f64 z t))

rewrite111.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

333×	`fma-neg_binary64`
311×	`expm1-udef_binary64`
311×	`log1p-udef_binary64`
191×	`add-sqr-sqrt_binary64`
173×	`associate-r_binary64`

Counts

4 → 99

Calls

4 calls:

108.0ms	(fma.f64 1 (fma.f64 x y (.f64 z t)) (neg.f64 (.f64 (*.f64 c i) (fma.f64 b c a))))
108.0ms	(fma.f64 x y (*.f64 z t))
108.0ms	(.f64 (.f64 c i) (fma.f64 b c a))
108.0ms	(fma.f64 (neg.f64 (.f64 c i)) (fma.f64 b c a) (.f64 (*.f64 c i) (fma.f64 b c a)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	66
1	379	54
2	4064	54
3	4976	54
4	5260	54

simplify347.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

953×	`distribute-rgt-in_binary64`
691×	`unswap-sqr_binary64`
566×	`unsub-neg_binary64`
547×	`distribute-lft-in_binary64`
526×	`distribute-rgt-neg-in_binary64`

Counts

339 → 137

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	55	3880
1	137	2608
2	336	2608
3	692	2608
4	2019	2608
5	2644	2608
6	3089	2608
7	3756	2608
8	3825	2608
9	4000	2456
10	3114	2456
11	3953	2456
12	3583	2456
13	4727	2456
14	4756	2456
15	5000	2456
16	4549	2456

prune217.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	170	8	178

Error

0.0b

Counts

178 → 8

Alt Table

Status	Error	Program
	27.4b	(.f64 2 (-.f64 (/.f64 (-.f64 (pow.f64 (.f64 x y) 2) (pow.f64 (.f64 z t) 2)) (-.f64 (.f64 x y) (.f64 z t))) (.f64 (.f64 (+.f64 a (.f64 b c)) c) i)))
	11.8b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (+.f64 (.f64 c (.f64 a i)) (.f64 (pow.f64 c 2) (*.f64 i b)))))
	8.7b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (.f64 c a)) i)))
▶	4.9b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 c (*.f64 i (fma.f64 c b a)))))
	34.2b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 (.f64 c (fma.f64 b c a)) i))) 2))
	22.0b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 (*.f64 c (fma.f64 b c a)) i) 3))))
	29.1b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (pow.f64 (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)) 2)))
✓	1.5b	(.f64 2 (+.f64 (fma.f64 1 (fma.f64 x y (.f64 z t)) (neg.f64 (.f64 (.f64 c i) (fma.f64 b c a)))) (fma.f64 (neg.f64 (.f64 c i)) (fma.f64 b c a) (.f64 (*.f64 c i) (fma.f64 b c a)))))

Compiler

Compiled 7105 to 1689 computations (76.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a))))
	0.0b	(+.f64 (.f64 x y) (.f64 z t))
✓	1.1b	(*.f64 i (fma.f64 c b a))
✓	3.9b	(.f64 c (.f64 i (fma.f64 c b a)))

series82.0ms (0.6%)

Counts

3 → 192

Calls

3 calls:

52.0ms	(-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a))))
19.0ms	(.f64 c (.f64 i (fma.f64 c b a)))
10.0ms	(*.f64 i (fma.f64 c b a))

rewrite81.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

324×	`log1p-udef_binary64`
179×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
165×	`associate-r_binary64`

Counts

3 → 87

Calls

3 calls:

78.0ms	(-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a))))
78.0ms	(*.f64 i (fma.f64 c b a))
78.0ms	(.f64 c (.f64 i (fma.f64 c b a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	343	40
2	4486	40
3	5024	40

simplify384.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-neg_binary64`
891×	`distribute-rgt-neg-in_binary64`
739×	`cube-prod_binary64`
707×	`distribute-lft-neg-in_binary64`
670×	`fabs-mul_binary64`

Counts

279 → 124

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	51	3283
1	121	2587
2	279	2587
3	568	2587
4	1776	2587
5	2670	2587
6	3267	2587
7	3703	2587
8	4161	2587
9	4249	2587
10	4344	2435
11	3348	2435
12	3490	2435
13	4121	2435
14	4413	2435
15	4569	2435
16	4846	2435
17	4912	2435

prune197.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	166	8	174

Error

0.0b

Counts

174 → 8

Alt Table

Status	Error	Program
	8.7b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (.f64 c a)) i)))
	33.7b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 x y (.f64 z t)) (.f64 c (.f64 i (fma.f64 c b a))))) 2))
	27.4b	(.f64 2 (-.f64 (/.f64 (-.f64 (pow.f64 (.f64 x y) 2) (pow.f64 (.f64 z t) 2)) (-.f64 (.f64 x y) (.f64 z t))) (.f64 (.f64 (+.f64 a (.f64 b c)) c) i)))
	11.8b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (+.f64 (.f64 c (.f64 a i)) (.f64 (pow.f64 c 2) (*.f64 i b)))))
▶	8.4b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (*.f64 a i)))))
	22.0b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (cbrt.f64 (pow.f64 (.f64 (*.f64 c (fma.f64 b c a)) i) 3))))
	29.1b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (pow.f64 (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)) 2)))
✓	1.5b	(.f64 2 (+.f64 (fma.f64 1 (fma.f64 x y (.f64 z t)) (neg.f64 (.f64 (.f64 c i) (fma.f64 b c a)))) (fma.f64 (neg.f64 (.f64 c i)) (fma.f64 b c a) (.f64 (*.f64 c i) (fma.f64 b c a)))))

Compiler

Compiled 4440 to 1328 computations (70.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
	0.0b	(+.f64 (.f64 x y) (.f64 z t))
✓	3.9b	(.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))
✓	6.8b	(.f64 c (.f64 i b))

series41.0ms (0.3%)

Counts

3 → 84

Calls

3 calls:

20.0ms	(.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))
13.0ms	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
8.0ms	(.f64 c (.f64 i b))

rewrite73.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

630×	`log-prod_binary64`
451×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
195×	`fma-neg_binary64`

Counts

3 → 157

Calls

3 calls:

69.0ms	(+.f64 (.f64 c (.f64 i b)) (*.f64 a i))
69.0ms	(.f64 c (+.f64 (.f64 c (.f64 i b)) (.f64 a i)))
69.0ms	(.f64 c (.f64 i b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	216	32
2	2840	32
3	5483	32

simplify193.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
630×	`fabs-mul_binary64`
585×	`cube-prod_binary64`
420×	`associate-l_binary64`
381×	`pow-sqr_binary64`

Counts

241 → 171

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	1089
1	58	774
2	102	774
3	158	774
4	326	774
5	856	774
6	1159	774
7	1428	774
8	1453	774
9	1563	774
10	1681	774
11	1848	774
12	2012	774
13	2240	774
14	2574	774
15	2969	774
16	3527	774
17	4211	774
18	4436	774
19	4701	774
20	4988	774
21	4799	774

prune244.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	215	6	221

Error

0.0b

Counts

221 → 6

Alt Table

Status	Error	Program
✓	8.4b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 c (+.f64 (.f64 c (.f64 i b)) (*.f64 a i)))))
	27.4b	(.f64 2 (-.f64 (/.f64 (-.f64 (pow.f64 (.f64 x y) 2) (pow.f64 (.f64 z t) 2)) (-.f64 (.f64 x y) (.f64 z t))) (.f64 (.f64 (+.f64 a (.f64 b c)) c) i)))
	8.5b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (fma.f64 (.f64 c a) i (.f64 c (.f64 c (*.f64 i b))))))
	6.6b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (fma.f64 (.f64 c (.f64 c i)) b (.f64 c (*.f64 i a)))))
	29.1b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (pow.f64 (sqrt.f64 (.f64 (*.f64 c (fma.f64 b c a)) i)) 2)))
✓	1.5b	(.f64 2 (+.f64 (fma.f64 1 (fma.f64 x y (.f64 z t)) (neg.f64 (.f64 (.f64 c i) (fma.f64 b c a)))) (fma.f64 (neg.f64 (.f64 c i)) (fma.f64 b c a) (.f64 (*.f64 c i) (fma.f64 b c a)))))

Compiler

Compiled 5937 to 1595 computations (73.1% saved)

regimes5.0s (34.2%)

Accuracy

Total 0.6b remaining (94.4%)

Threshold costs 0.6b (94.4%)

Counts

220 → 3

Compiler

Compiled 102387 to 64945 computations (36.6% saved)

bsearch71.0ms (0.5%)

Steps

Iters	Range		Point
4	784785841338991700.0	9.627634839416162e+33	9.250348944498564e+30
4	-1.6565745236325962e+64	-9.719884273545077e+63	-1.052379155071738e+64

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`*-commutative_binary64`
18×	`+-commutative_binary64`
16×	`distribute-rgt-neg-in_binary64`
16×	`sub-neg_binary64`
14×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	102
1	73	102
2	101	102
3	133	102
4	165	102
5	176	102
6	181	102
7	182	102
8	180	102

end147.0ms (1%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 670 to 362 computations (46% saved)

Iter	Nodes	Cost
0	41	102
1	73	102
2	101	102
3	133	102
4	165	102
5	176	102
6	181	102
7	182	102
8	180	102

Iter	Nodes	Cost
0	41	102
1	73	102
2	101	102
3	133	102
4	165	102
5	176	102
6	181	102
7	182	102
8	180	102

Details

analyze2.4s (16.1%)

sample4.0s (26.9%)

simplify220.0ms (1.5%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series101.0ms (0.7%)

rewrite60.0ms (0.4%)

simplify390.0ms (2.6%)

prune194.0ms (1.3%)

localize21.0ms (0.1%)

series126.0ms (0.9%)

rewrite111.0ms (0.8%)

simplify347.0ms (2.4%)

prune217.0ms (1.5%)

localize14.0ms (0.1%)

series82.0ms (0.6%)

rewrite81.0ms (0.5%)

simplify384.0ms (2.6%)

prune197.0ms (1.3%)

localize15.0ms (0.1%)

series41.0ms (0.3%)

rewrite73.0ms (0.5%)

simplify193.0ms (1.3%)

prune244.0ms (1.7%)

regimes5.0s (34.2%)

bsearch71.0ms (0.5%)

simplify8.0ms (0.1%)

end147.0ms (1%)

Profiling

Iter	Nodes	Cost
0	41	102
1	73	102
2	101	102
3	133	102
4	165	102
5	176	102
6	181	102
7	182	102
8	180	102