Details

analyze1.2s (19.3%)

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)

sample1.4s (21.1%)

Results

1.2s	8256×	body	128	valid
91.0ms	772×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify124.0ms (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

prune3.0ms (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)

localize7.0ms (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:

64.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
7.0ms	(-.f64 t (*.f64 a z))
5.0ms	(-.f64 x (*.f64 y z))

rewrite226.0ms (3.5%)

Algorithm

3×	egg-rewrite

Rules

98×	`egg`
98×	`egg`
72×	`egg`

Counts

3 → 268

Calls

3 calls:

102.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
60.0ms	(-.f64 t (*.f64 a z))
57.0ms	(-.f64 x (*.f64 y z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	253	16
2	3617	16
3	4990	16
4	5001	16
0	6	7
1	132	7
2	1712	7
3	5386	7
0	6	7
1	132	7
2	1712	7
3	5386	7

simplify100.0ms (1.5%)

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

346 → 310

Iterations

Useful iterations: 2 (0.0ms)

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

prune207.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	304	6	310
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	304	7	311

Error

1.9b

Counts

311 → 7

Alt Table

Status	Error	Program
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (cbrt.f64 (-.f64 t (.f64 a z))) 3))
	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	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
	42.9b	(/.f64 y a)
	35.9b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 a z))) 2))
▶	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 8782 to 2007 computations (77.1% saved)

localize10.0ms (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))
✓	0.4b	(/.f64 1 (-.f64 t (*.f64 z a)))
✓	10.3b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

series97.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

72.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
20.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
5.0ms	(-.f64 t (*.f64 z a))

rewrite185.0ms (2.9%)

Algorithm

3×	egg-rewrite

Rules

98×	`egg`
70×	`egg`
29×	`egg`

Counts

3 → 197

Calls

3 calls:

69.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
58.0ms	(-.f64 t (*.f64 z a))
54.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	286	16
2	3693	16
3	5019	16
0	8	10
1	171	10
2	2095	10
3	6246	10
0	6	7
1	132	7
2	1712	7
3	5386	7

simplify99.0ms (1.5%)

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

329 → 253

Iterations

Useful iterations: 2 (0.0ms)

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

prune227.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	353	1	354
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	353	8	361

Error

1.9b

Counts

361 → 8

Alt Table

Status	Error	Program
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (cbrt.f64 (-.f64 t (.f64 a z))) 3))
	35.9b	(.f64 (pow.f64 (-.f64 t (.f64 z a)) -1/2) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 z a)))))
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	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	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
	42.9b	(/.f64 y a)
	35.9b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 a z))) 2))

Compiler

Compiled 10000 to 2825 computations (71.8% 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	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
✓	10.3b	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))

series134.0ms (2.1%)

Counts

2 → 120

Calls

2 calls:

71.0ms	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))
62.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))

rewrite193.0ms (3%)

Algorithm

2×	egg-rewrite

Rules

72×	`egg`
63×	`egg`

Counts

2 → 135

Calls

2 calls:

115.0ms	(/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z)))
75.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	253	16
2	3617	16
3	4990	16
4	5001	16
0	13	19
1	294	16
2	4040	16
3	5041	16

simplify121.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

930×	`cancel-sign-sub-inv_binary64`
369×	`sub-neg_binary64`
306×	`times-frac_binary64`
261×	`unswap-sqr_binary64`
258×	`fma-neg_binary64`

Counts

255 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	5610
1	786	5360
2	3138	5288
3	5276	5288

prune281.0ms (4.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	414	1	415
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	415	8	423

Error

1.9b

Counts

423 → 8

Alt Table

Status	Error	Program
▶	11.2b	(/.f64 1 (.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y)))))
	35.9b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 a z))) 2))
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (cbrt.f64 (-.f64 t (.f64 a z))) 3))
	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	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
	42.9b	(/.f64 y a)
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 12333 to 3579 computations (71% saved)

localize12.0ms (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)))
✓	0.8b	(/.f64 1 (.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y)))))
✓	10.3b	(.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y))))

series168.0ms (2.6%)

Counts

4 → 192

Calls

4 calls:

72.0ms	(.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y))))
67.0ms	(/.f64 1 (.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y)))))
21.0ms	(/.f64 1 (-.f64 x (*.f64 z y)))
7.0ms	(-.f64 x (*.f64 z y))

rewrite262.0ms (4.1%)

Algorithm

4×	egg-rewrite

Rules

98×	`egg`
70×	`egg`
40×	`egg`
29×	`egg`

Counts

4 → 237

Calls

4 calls:

71.0ms	(.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y))))
68.0ms	(/.f64 1 (.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y)))))
60.0ms	(-.f64 x (*.f64 z y))
55.0ms	(/.f64 1 (-.f64 x (*.f64 z y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	285	16
2	3663	16
3	4982	16
0	14	19
1	311	16
2	4022	16
3	5019	16
0	8	10
1	171	10
2	2095	10
3	6246	10
0	6	7
1	132	7
2	1712	7
3	5386	7

simplify146.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

936×	`cancel-sign-sub-inv_binary64`
378×	`sub-neg_binary64`
336×	`times-frac_binary64`
265×	`fma-neg_binary64`
261×	`unswap-sqr_binary64`

Counts

429 → 333

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	6922
1	862	6652
2	3414	6570
3	5587	6570

prune220.0ms (3.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	333	0	333
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	333	8	341

Error

1.9b

Counts

341 → 8

Alt Table

Status	Error	Program
✓	11.2b	(/.f64 1 (.f64 (-.f64 t (.f64 z a)) (/.f64 1 (-.f64 x (*.f64 z y)))))
	35.9b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (sqrt.f64 (-.f64 t (.f64 a z))) 2))
✓	10.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	11.6b	(/.f64 (-.f64 x (.f64 y z)) (pow.f64 (cbrt.f64 (-.f64 t (.f64 a z))) 3))
	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	(/.f64 1 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))))
	42.9b	(/.f64 y a)
✓	10.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

Compiler

Compiled 9790 to 3445 computations (64.8% saved)

regimes820.0ms (12.7%)

Accuracy

Total 3.3b remaining (62.7%)

Threshold costs 0b (0%)

Counts

80 → 5

Compiler

Compiled 11366 to 6988 computations (38.5% saved)

bsearch3.0ms (0%)

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	25	128
1	37	128
2	53	128
3	63	128
4	69	128
5	70	128
6	70	128

end108.0ms (1.7%)

Compiler: Compiled 332 to 143 computations (56.9% saved)

Details

analyze1.2s (19.3%)

sample1.4s (21.1%)

simplify124.0ms (1.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series76.0ms (1.2%)

rewrite226.0ms (3.5%)

simplify100.0ms (1.5%)

prune207.0ms (3.2%)

localize10.0ms (0.1%)

series97.0ms (1.5%)

rewrite185.0ms (2.9%)

simplify99.0ms (1.5%)

prune227.0ms (3.5%)

localize9.0ms (0.1%)

series134.0ms (2.1%)

rewrite193.0ms (3%)

simplify121.0ms (1.9%)

prune281.0ms (4.4%)

localize12.0ms (0.2%)

series168.0ms (2.6%)

rewrite262.0ms (4.1%)

simplify146.0ms (2.3%)

prune220.0ms (3.4%)

regimes820.0ms (12.7%)

bsearch3.0ms (0%)

simplify6.0ms (0.1%)

end108.0ms (1.7%)

Profiling