Details

analyze1.3s (20.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (19.9%)

Results

1.0s	8256×	body	128	valid
96.0ms	772×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1539×	`fma-neg_binary64`
1346×	`fma-def_binary64`
1046×	`div-sub_binary64`
750×	`associate-/r/_binary64`
420×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	96	16
4	183	16
5	339	16
6	657	16
7	1726	16
8	2830	16
9	2687	16
10	2951	16
11	3172	16
12	3258	16
13	4297	16
14	5213	16

prune2.0ms (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

10.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 a z))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	10.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series76.0ms (1.2%)

Counts

3 → 78

Calls

3 calls:

66.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
5.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 a z))

rewrite117.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

217× egg-rr

Counts

3 → 217

Calls

2 calls:

111.0ms	((/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z))) (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	253	30
2	3617	30
3	4990	30
4	5001	30
0	0	0
1	0	0

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/r*_binary64`
552×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
212×	`associate-*l/_binary64`

Counts

295 → 260

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	2873
1	410	2732
2	1600	2525
3	4690	2525
4	4985	2525

prune184.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	254	6	260
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	254	7	261

Error

1.9b

Counts

261 → 7

Alt Table

Status	Error	Program
	33.7b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	11.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	35.9b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 z a))) 2))
	42.9b	(/.f64 y a)
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)))
▶	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 6308 to 1780 computations (71.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z a))
	0.0b	(-.f64 x (*.f64 y z))
✓	0.4b	(/.f64 1 (-.f64 t (*.f64 z a)))
✓	10.3b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

series97.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

64.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
20.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
14.0ms	(-.f64 t (*.f64 z a))

rewrite82.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

156× egg-rr

Counts

3 → 156

Calls

2 calls:

79.0ms	((.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (.f64 z a)))) (/.f64 1 (-.f64 t (.f64 z a))) (-.f64 t (*.f64 z a)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	286	33
2	3693	33
3	5019	33
0	0	0
1	0	0

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/r*_binary64`
670×	`fma-def_binary64`
460×	`cancel-sign-sub-inv_binary64`
196×	`associate-/l/_binary64`
182×	`sub-neg_binary64`

Counts

288 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	4117
1	478	3956
2	1853	3688
3	5005	3688

prune195.0ms (3.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	298	8	306

Error

1.9b

Counts

306 → 8

Alt Table

Status	Error	Program
	35.1b	(.f64 (-.f64 x (.f64 y z)) (pow.f64 (pow.f64 (-.f64 t (*.f64 z a)) -1/2) 2))
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	33.7b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
▶	11.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
	35.9b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 z a))) 2))
	42.9b	(/.f64 y a)
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)))
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 7377 to 2528 computations (65.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 t (*.f64 z a))
	0.0b	(-.f64 x (*.f64 y z))
✓	0.8b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
✓	10.3b	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))

series319.0ms (5.2%)

Counts

2 → 120

Calls

2 calls:

247.0ms	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
71.0ms	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))

rewrite87.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

99× egg-rr

Counts

2 → 99

Calls

2 calls:

84.0ms	((/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) (pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	295	32
2	4005	32
3	4990	32
0	0	0
1	0	0

simplify132.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-/l*_binary64`
570×	`associate-/r*_binary64`
397×	`associate-l_binary64`
218×	`fma-def_binary64`
159×	`+-commutative_binary64`

Counts

219 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	472	10169
1	1805	9817
2	5033	9817

prune313.0ms (5.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	374	2	376
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	377	7	384

Error

1.9b

Counts

384 → 7

Alt Table

Status	Error	Program
	33.7b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	33.4b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 y z))) (sqrt.f64 (*.f64 y z)) x)) -1)
▶	10.9b	(/.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 1 (-.f64 x (.f64 z y))))
✓	11.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	42.9b	(/.f64 y a)
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 14720 to 5630 computations (61.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 z y))
✓	0.2b	(/.f64 1 (-.f64 x (*.f64 z y)))
	0.4b	(/.f64 1 (-.f64 t (*.f64 z a)))
✓	10.2b	(/.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 1 (-.f64 x (.f64 z y))))

series102.0ms (1.7%)

Counts

3 → 132

Calls

3 calls:

75.0ms	(/.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 1 (-.f64 x (.f64 z y))))
19.0ms	(/.f64 1 (-.f64 x (*.f64 z y)))
7.0ms	(-.f64 x (*.f64 z y))

rewrite103.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

112× egg-rr

Counts

3 → 112

Calls

2 calls:

101.0ms	((/.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 1 (-.f64 x (.f64 z y)))) (/.f64 1 (-.f64 x (.f64 z y))) (-.f64 x (.f64 z y)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	316	33
2	4119	33
3	4991	33
4	4933	33
0	0	0
1	0	0

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

843×	`associate-/r*_binary64`
661×	`fma-def_binary64`
465×	`cancel-sign-sub-inv_binary64`
184×	`associate-/l/_binary64`
183×	`sub-neg_binary64`

Counts

244 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	4117
1	507	3956
2	2010	3686
3	5614	3686

prune137.0ms (2.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	208	7	215

Error

1.9b

Counts

215 → 7

Alt Table

Status	Error	Program
	33.7b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))
	33.4b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 y z))) (sqrt.f64 (*.f64 y z)) x)) -1)
✓	10.9b	(/.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 1 (-.f64 x (.f64 z y))))
✓	11.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	42.9b	(/.f64 y a)
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 5295 to 2199 computations (58.5% saved)

regimes1.2s (19.3%)

Accuracy

Total 3.2b remaining (62.6%)

Threshold costs 0b (0%)

Counts

126 → 5

Compiler

Compiled 16934 to 10678 computations (36.9% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	128
1	42	128
2	57	128
3	66	128
4	71	128
5	72	128
6	72	128

end109.0ms (1.8%)

Compiler: Compiled 318 to 137 computations (56.9% saved)

Details

analyze1.3s (20.4%)

sample1.2s (19.9%)

simplify116.0ms (1.9%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series76.0ms (1.2%)

rewrite117.0ms (1.9%)

simplify87.0ms (1.4%)

prune184.0ms (3%)

localize10.0ms (0.2%)

series97.0ms (1.6%)

rewrite82.0ms (1.3%)

simplify86.0ms (1.4%)

prune195.0ms (3.2%)

localize9.0ms (0.1%)

series319.0ms (5.2%)

rewrite87.0ms (1.4%)

simplify132.0ms (2.1%)

prune313.0ms (5.1%)

localize10.0ms (0.2%)

series102.0ms (1.7%)

rewrite103.0ms (1.7%)

simplify87.0ms (1.4%)

prune137.0ms (2.2%)

regimes1.2s (19.3%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end109.0ms (1.8%)

Profiling