Details

analyze1.3s (23.9%)

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
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.3s (25.5%)

Results

1.0s	8256×	body	128	valid
304.0ms	2601×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

preprocess31.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

355×	`fma-neg_binary64`
312×	`sub-neg_binary64`
245×	`associate-/l*_binary64`
235×	`div-sub_binary64`
223×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	143
1	112	143
2	283	143
3	920	133
4	2971	121
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
245×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	107	13
4	326	11
5	814	11
6	1834	11
7	3225	11
8	3920	11
9	3976	11
10	4006	11
11	4011	11
12	4011	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.3b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	4.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	5.3b	(/.f64 (*.f64 y (-.f64 z t)) a)

series62.0ms (1.2%)

Counts

3 → 144

Calls

36 calls:

8.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))	a	inf
6.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))	x	-inf
5.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)	y	0
2.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))	x	0
2.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))	x	inf

rewrite126.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`prod-diff_binary64`
214×	`egg-rr`
120×	`add-sqr-sqrt_binary64`
115×	`log1p-expm1-u_binary64`
115×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	226	30
2	3408	30

Stop Event

1×	node limit

Counts

3 → 214

simplify104.0ms (2%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
364×	`fma-def_binary64`
242×	`cancel-sign-sub-inv_binary64`
119×	`distribute-rgt-in_binary64`
112×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	1390
1	91	1390
2	206	1388
3	500	1298
4	1160	1298
5	2345	1298
6	3081	1298
7	3293	1298
8	3347	1298
9	3361	1298
10	3365	1298

Stop Event

1×

saturated

Counts

358 → 246

prune194.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	241	5	246
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	242	6	248

Error

Counts

248 → 6

Alt Table

Status	Error	Program
	38.3b	(/.f64 (-.f64 t z) (/.f64 a y))
	2.9b	(-.f64 x (pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1))
	3.2b	(-.f64 x (pow.f64 (cbrt.f64 (*.f64 (/.f64 y a) (-.f64 z t))) 3))
▶	2.8b	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))
	8.4b	(-.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 a))))
✓	4.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 7373 to 2193 computations (70.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))
✓	9.1b	(*.f64 (-.f64 z t) (/.f64 y a))

series44.0ms (0.8%)

Counts

2 → 108

Calls

27 calls:

3.0ms	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))	x	inf
3.0ms	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))	a	inf
2.0ms	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))	x	0
2.0ms	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))	x	-inf
2.0ms	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))	z	0

rewrite63.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

370×	`fma-def_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
192×	`log-pow_binary64`
164×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	229	23
2	3455	23

Stop Event

1×	node limit

Counts

2 → 136

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
361×	`fma-def_binary64`
241×	`cancel-sign-sub-inv_binary64`
119×	`distribute-rgt-in_binary64`
113×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	1150
1	88	1150
2	203	1148
3	506	1058
4	1169	1058
5	2347	1058
6	3087	1058
7	3299	1058
8	3353	1058
9	3367	1058
10	3371	1058

Stop Event

1×

saturated

Counts

244 → 161

prune127.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	162	5	167

Error

Counts

167 → 5

Alt Table

Status	Error	Program
	2.9b	(-.f64 x (pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1))
	3.2b	(-.f64 x (pow.f64 (cbrt.f64 (*.f64 (/.f64 y a) (-.f64 z t))) 3))
✓	2.8b	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))
▶	2.9b	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))
✓	4.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 3168 to 720 computations (77.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))
✓	9.1b	(/.f64 (-.f64 z t) (/.f64 a y))

series56.0ms (1.1%)

Counts

2 → 108

Calls

27 calls:

15.0ms	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))	t	0
3.0ms	(/.f64 (-.f64 z t) (/.f64 a y))	y	0
2.0ms	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))	x	0
2.0ms	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))	x	-inf
2.0ms	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))	x	inf

rewrite72.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

403×	`fma-def_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
204×	`fma-neg_binary64`
161×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	235	23
2	3785	23

Stop Event

1×	node limit

Counts

2 → 161

simplify93.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
361×	`fma-def_binary64`
241×	`cancel-sign-sub-inv_binary64`
119×	`distribute-rgt-in_binary64`
113×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	1150
1	88	1150
2	203	1148
3	506	1058
4	1169	1058
5	2347	1058
6	3087	1058
7	3299	1058
8	3353	1058
9	3367	1058
10	3371	1058

Stop Event

1×

saturated

Counts

269 → 186

prune118.0ms (2.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	186	5	191

Error

Counts

191 → 5

Alt Table

Status	Error	Program
▶	2.9b	(-.f64 x (pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1))
	3.2b	(-.f64 x (pow.f64 (cbrt.f64 (*.f64 (/.f64 y a) (-.f64 z t))) 3))
✓	2.8b	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))
✓	2.9b	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))
✓	4.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 3954 to 786 computations (80.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1))
✓	0.4b	(pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1)
✓	8.9b	(/.f64 (/.f64 a y) (-.f64 z t))

series305.0ms (5.8%)

Counts

3 → 156

Calls

39 calls:

35.0ms	(pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1)	y	inf
26.0ms	(pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1)	a	0
19.0ms	(pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1)	t	0
16.0ms	(pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1)	t	inf
16.0ms	(-.f64 x (pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1))	z	-inf

rewrite99.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

874×	`prod-diff_binary64`
242×	`egg-rr`
143×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	274	33
2	4056	33

Stop Event

1×	node limit

Counts

3 → 242

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary64`
406×	`times-frac_binary64`
332×	`associate-/l*_binary64`
281×	`distribute-neg-frac_binary64`
263×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	2176
1	235	2080
2	777	1997
3	3670	1997

Stop Event

1×	node limit

Counts

398 → 286

prune189.0ms (3.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	286	5	291

Error

Counts

291 → 5

Alt Table

Status	Error	Program
✓	2.9b	(-.f64 x (pow.f64 (/.f64 (/.f64 a y) (-.f64 z t)) -1))
	3.2b	(-.f64 x (pow.f64 (cbrt.f64 (*.f64 (/.f64 y a) (-.f64 z t))) 3))
✓	2.8b	(-.f64 x (*.f64 (-.f64 z t) (/.f64 y a)))
✓	2.9b	(-.f64 x (/.f64 (-.f64 z t) (/.f64 a y)))
✓	4.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 8278 to 2541 computations (69.3% saved)

regimes650.0ms (12.4%)

Accuracy

Total 0.5b remaining (96.4%)

Threshold costs 0.5b (96.4%)

Counts

47 → 3

Compiler

Compiled 5906 to 3972 computations (32.7% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(*.f64 y (-.f64 z t))
0.0ms	(*.f64 y (-.f64 z t))

Steps

Iters	Point		Range
5.196317462097143e+225	∈ [	5.196317462097143e+225	,	2.113998938217442e+227	]
-8.432815853165983e+146	∈ [	-8.432815853165983e+146	,	-6.244005907367754e+146	]

Compiler

Compiled 10 to 7 computations (30% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`+-commutative_binary64`
12×	`*-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	66
1	38	66
2	65	66
3	98	66
4	127	66
5	138	66
6	139	66

Stop Event

1×

saturated

end71.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 175 to 100 computations (42.9% saved)

Details

analyze1.3s (23.9%)

sample1.3s (25.5%)

preprocess31.0ms (0.6%)

simplify49.0ms (0.9%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series62.0ms (1.2%)

rewrite126.0ms (2.4%)

simplify104.0ms (2%)

prune194.0ms (3.7%)

localize7.0ms (0.1%)

series44.0ms (0.8%)

rewrite63.0ms (1.2%)

simplify88.0ms (1.7%)

prune127.0ms (2.4%)

localize6.0ms (0.1%)

series56.0ms (1.1%)

rewrite72.0ms (1.4%)

simplify93.0ms (1.8%)

prune118.0ms (2.2%)

localize8.0ms (0.1%)

series305.0ms (5.8%)

rewrite99.0ms (1.9%)

simplify69.0ms (1.3%)

prune189.0ms (3.6%)

regimes650.0ms (12.4%)

bsearch1.0ms (0%)

simplify6.0ms (0.1%)

end71.0ms (1.4%)

Profiling