Details

analyze1.2s (21%)

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)

sample1.1s (19.8%)

Results

979.0ms	8256×	body	128	valid
88.0ms	773×	body	128	invalid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess41.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

878×	`div-sub_binary64`
306×	`fma-def_binary64`
304×	`times-frac_binary64`
248×	`fma-neg_binary64`
219×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
1	158	176
2	306	176
3	640	176
4	1557	176
5	3631	176
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
663×	`div-sub_binary64`
241×	`cancel-sign-sub-inv_binary64`
213×	`distribute-neg-frac_binary64`
210×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	53	16
3	100	16
4	210	16
5	422	16
6	913	16
7	2616	16

Stop Event

1×	node limit

Counts

1 → 2

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

12.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.3b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 34 computations (42.4% 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))
✓	12.0b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series64.0ms (1.2%)

Counts

3 → 78

Calls

33 calls:

7.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	a	-inf
5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	y	inf
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	t	-inf
4.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	a	0
3.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))	x	-inf

rewrite75.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

412×	`fma-def_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
217×	`egg-rr`
195×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	253	30
2	3872	30

Stop Event

1×	node limit

Counts

3 → 217

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Rules

605×	`associate-/r*_binary64`
552×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
174×	`sub-neg_binary64`
149×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	2873
1	413	2732
2	1887	2525

Stop Event

1×	node limit

Counts

295 → 261

prune209.0ms (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	251	10	261
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	252	10	262

Error

2.0b

Counts

262 → 10

Alt Table

Status	Error	Program
	44.4b	(/.f64 (-.f64 x (.f64 y z)) (/.f64 1 (/.f64 (fma.f64 (.f64 z a) (fma.f64 z a t) (.f64 t t)) (-.f64 (pow.f64 t 3) (pow.f64 (.f64 z a) 3)))))
	12.4b	(pow.f64 (/.f64 (-.f64 t (*.f64 z a)) (fma.f64 y (neg.f64 z) x)) -1)
	36.6b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))
▶	8.9b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))
	13.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (fma.f64 y (neg.f64 z) x) (cbrt.f64 (-.f64 t (*.f64 z a)))))
	33.7b	(.f64 (/.f64 (neg.f64 y) (-.f64 t (.f64 z a))) z)
	33.9b	(/.f64 (-.f64 x (*.f64 y z)) t)
	42.9b	(/.f64 y a)
	32.0b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 y (neg.f64 z) x) 2)) (.f64 (cbrt.f64 (fma.f64 y (neg.f64 z) x)) (/.f64 1 (-.f64 t (*.f64 z a)))))
	12.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))

Compiler

Compiled 6487 to 1930 computations (70.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))
✓	3.0b	(/.f64 y (/.f64 (-.f64 t (*.f64 z a)) z))
✓	4.1b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	8.8b	(/.f64 (-.f64 t (*.f64 z a)) z)

series144.0ms (2.6%)

Counts

4 → 192

Calls

48 calls:

7.0ms	(/.f64 x (-.f64 t (*.f64 z a)))	z	-inf
6.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))	x	inf
5.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 z a)) z))	t	0
5.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))	z	-inf
5.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 z a)) z))	y	-inf

rewrite85.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`log1p-udef_binary64`
164×	`egg-rr`
154×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	287	58
2	4842	58

Stop Event

1×	node limit

Counts

4 → 164

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

629×	`associate-/r*_binary64`
623×	`fma-def_binary64`
487×	`cancel-sign-sub-inv_binary64`
201×	`sub-neg_binary64`
169×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	5797
1	469	5521
2	2067	5138

Stop Event

1×	node limit

Counts

356 → 248

prune200.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	244	4	248
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	251	7	258

Error

0.0b

Counts

258 → 7

Alt Table

Status	Error	Program
▶	3.8b	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))
	32.0b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 y (neg.f64 z) x) 2)) (.f64 (cbrt.f64 (fma.f64 y (neg.f64 z) x)) (/.f64 1 (-.f64 t (*.f64 z a)))))
	32.7b	(/.f64 (-.f64 y (/.f64 x z)) a)
	27.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 y t) z))
	12.4b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 1 (-.f64 t (*.f64 z a))) (/.f64 y (/.f64 1 z))))
	36.6b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))
	12.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))

Compiler

Compiled 7318 to 2088 computations (71.5% 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 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))
✓	3.0b	(/.f64 y (-.f64 (/.f64 t z) a))
	4.1b	(/.f64 x (-.f64 t (*.f64 z a)))

series111.0ms (2%)

Counts

3 → 132

Calls

36 calls:

7.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))	x	0
7.0ms	(/.f64 y (-.f64 (/.f64 t z) a))	t	-inf
6.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))	y	inf
5.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))	z	0
5.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))	y	0

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

169×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`
162×	`add-cbrt-cube_binary64`
157×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	314	39

Stop Event

1×	node limit

Counts

3 → 125

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/r*_binary64`
585×	`fma-def_binary64`
479×	`cancel-sign-sub-inv_binary64`
191×	`sub-neg_binary64`
152×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	4200
1	452	3984
2	1983	3661

Stop Event

1×	node limit

Counts

257 → 194

prune180.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	244	7	251

Error

0.0b

Counts

251 → 7

Alt Table

Status	Error	Program
✓	3.8b	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))
	32.0b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 y (neg.f64 z) x) 2)) (.f64 (cbrt.f64 (fma.f64 y (neg.f64 z) x)) (/.f64 1 (-.f64 t (*.f64 z a)))))
	27.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 y t) z))
▶	12.4b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 1 (-.f64 t (*.f64 z a))) (/.f64 y (/.f64 1 z))))
	36.6b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))
	12.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))
	36.7b	(-.f64 (+.f64 (/.f64 y a) (*.f64 (/.f64 (/.f64 t a) a) (-.f64 (/.f64 y z) (/.f64 (/.f64 x z) z)))) (/.f64 (/.f64 x z) a))

Compiler

Compiled 7037 to 2125 computations (69.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 y (/.f64 1 z))
✓	0.5b	(/.f64 1 (-.f64 t (*.f64 z a)))
	4.1b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	11.2b	(.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 y (/.f64 1 z)))

series57.0ms (1%)

Counts

3 → 108

Calls

27 calls:

8.0ms	(.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 y (/.f64 1 z)))	y	0
4.0ms	(.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 y (/.f64 1 z)))	y	inf
4.0ms	(.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 y (/.f64 1 z)))	y	-inf
2.0ms	(.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 y (/.f64 1 z)))	t	-inf
2.0ms	(.f64 (/.f64 1 (-.f64 t (.f64 z a))) (/.f64 y (/.f64 1 z)))	z	-inf

rewrite66.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

657×	`prod-diff_binary64`
134×	`add-sqr-sqrt_binary64`
126×	`log1p-expm1-u_binary64`
126×	`expm1-log1p-u_binary64`
125×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	267	27
2	3815	27

Stop Event

1×	node limit

Counts

3 → 110

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Rules

809×	`associate-/l*_binary64`
524×	`associate-/r*_binary64`
371×	`associate-l_binary64`
346×	`fma-def_binary64`
198×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	2581
1	295	2501
2	1220	2324

Stop Event

1×	node limit

Counts

218 → 148

prune164.0ms (3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	198	7	205

Error

0.0b

Counts

205 → 7

Alt Table

Status	Error	Program
✓	3.8b	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))
	32.0b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 y (neg.f64 z) x) 2)) (.f64 (cbrt.f64 (fma.f64 y (neg.f64 z) x)) (/.f64 1 (-.f64 t (*.f64 z a)))))
	36.7b	(-.f64 (+.f64 (/.f64 y a) (*.f64 (/.f64 (/.f64 t a) a) (-.f64 (/.f64 y z) (/.f64 (/.f64 x z) z)))) (/.f64 (/.f64 x z) a))
	9.6b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (/.f64 y (-.f64 t (.f64 z a))) (/.f64 1 z)))
✓	12.4b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 1 (-.f64 t (*.f64 z a))) (/.f64 y (/.f64 1 z))))
	36.6b	(.f64 (/.f64 (fma.f64 y (neg.f64 z) x) (-.f64 (.f64 t t) (pow.f64 (*.f64 z a) 2))) (fma.f64 z a t))
	12.4b	(.f64 (fma.f64 y (neg.f64 z) x) (/.f64 1 (-.f64 t (.f64 z a))))

Compiler

Compiled 5462 to 2058 computations (62.3% saved)

regimes1.3s (23.9%)

Accuracy

Total 1.7b remaining (98.1%)

Threshold costs 0b (0%)

Counts

172 → 3

Compiler

Compiled 21152 to 12952 computations (38.8% saved)

bsearch39.0ms (0.7%)

Algorithm

2×	binary-search

Calls

2 calls:

18.0ms	z
16.0ms	z

Steps

Iters	Point		Range
4.4228944462314166e-44	∈ [	3.512299962295259e-45	,	6.516117539692511e-42	]
-1.965510614121794e+42	∈ [	-2.5353738529778784e+43	,	-1.9246107374003606e+42	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	75
1	55	75
2	87	75
3	98	75
4	103	75

Stop Event

1×

saturated

end114.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 283 to 154 computations (45.6% saved)

Details

analyze1.2s (21%)

sample1.1s (19.8%)

preprocess41.0ms (0.7%)

simplify25.0ms (0.5%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series64.0ms (1.2%)

rewrite75.0ms (1.4%)

simplify55.0ms (1%)

prune209.0ms (3.8%)

localize8.0ms (0.2%)

series144.0ms (2.6%)

rewrite85.0ms (1.5%)

simplify89.0ms (1.6%)

prune200.0ms (3.6%)

localize10.0ms (0.2%)

series111.0ms (2%)

rewrite44.0ms (0.8%)

simplify70.0ms (1.3%)

prune180.0ms (3.3%)

localize13.0ms (0.2%)

series57.0ms (1%)

rewrite66.0ms (1.2%)

simplify53.0ms (1%)

prune164.0ms (3%)

regimes1.3s (23.9%)

bsearch39.0ms (0.7%)

simplify8.0ms (0.1%)

end114.0ms (2.1%)

Profiling