Details

analyze173.0ms (5.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample882.0ms (25.9%)

Results

828.0ms	8256×	body	128	valid
41.0ms	257×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

preprocess58.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

1036×	`fma-def_binary64`
369×	`distribute-rgt-in_binary64`
349×	`times-frac_binary64`
322×	`distribute-lft-in_binary64`
310×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	38	28
2	66	28
3	170	28
4	365	28
5	820	28
6	1235	28
7	1544	28
8	2721	28
9	3468	28
10	4344	28
11	4895	28
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify42.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

971×	`fma-def_binary64`
587×	`distribute-rgt-in_binary64`
569×	`distribute-lft-in_binary64`
406×	`unswap-sqr_binary64`
398×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	14
2	36	14
3	81	14
4	143	14
5	287	14
6	742	14
7	1081	14
8	1605	14
9	1832	14
10	2262	14
11	2926	14
12	3255	14
13	3794	14

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

9.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.1b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 47 to 27 computations (42.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 x y) x)
✓	8.4b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series20.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))	y	-inf
3.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))	y	0
2.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))	x	0
2.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))	y	inf
2.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))	x	-inf

rewrite54.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

447×	`log-prod_binary64`
199×	`prod-diff_binary64`
164×	`pow1/3_binary64`
158×	`log1p-udef_binary64`
157×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	175	22
2	2446	22

Stop Event

1×	node limit

Counts

2 → 69

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
530×	`associate-+l-_binary64`
372×	`cancel-sign-sub-inv_binary64`
348×	`associate--r+_binary64`
317×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	711
1	131	707
2	420	649
3	1743	585

Stop Event

1×	node limit

Counts

117 → 93

prune57.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	5	94

Error

0.0b

Counts

94 → 5

Alt Table

Status	Error	Program
	30.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))
✓	9.1b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
	35.4b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
▶	9.2b	(pow.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)) -1)
	35.3b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))

Compiler

Compiled 1610 to 743 computations (53.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (/.f64 x y) x)
✓	0.2b	(pow.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)) -1)
✓	8.4b	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))

series43.0ms (1.3%)

Counts

2 → 48

Calls

12 calls:

8.0ms	(pow.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)) -1)	y	-inf
8.0ms	(pow.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)) -1)	y	0
6.0ms	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))	y	0
4.0ms	(pow.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)) -1)	y	inf
2.0ms	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))	y	-inf

rewrite60.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

511×	`log-prod_binary64`
199×	`prod-diff_binary64`
185×	`log1p-udef_binary64`
184×	`expm1-udef_binary64`
164×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	217	28
2	2912	28

Stop Event

1×	node limit

Counts

2 → 83

simplify85.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

722×	`times-frac_binary64`
713×	`fma-def_binary64`
287×	`sub-neg_binary64`
213×	`cancel-sign-sub-inv_binary64`
171×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	2087
1	538	2079
2	2190	1915

Stop Event

1×	node limit

Counts

131 → 141

prune132.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	174	5	179

Error

Counts

179 → 5

Alt Table

Status	Error	Program
▶	10.1b	(pow.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)) -1)
	35.3b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
	30.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))
	35.4b	(pow.f64 (+.f64 (/.f64 y x) (-.f64 (/.f64 (/.f64 y x) x) (*.f64 (/.f64 y x) (/.f64 y x)))) -1)
✓	9.1b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 4220 to 2263 computations (46.4% saved)

localize31.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)
✓	0.5b	(cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))
	8.4b	(/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))

series266.0ms (7.8%)

Counts

3 → 40

Calls

18 calls:

39.0ms	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)	x	-inf
35.0ms	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)	x	inf
34.0ms	(cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x)))	x	inf
29.0ms	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)	y	0
25.0ms	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)	x	0

rewrite66.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`log-prod_binary64`
199×	`prod-diff_binary64`
194×	`log1p-udef_binary64`
193×	`expm1-udef_binary64`
172×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	258	49
2	3078	49

Stop Event

1×	node limit

Counts

3 → 96

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

623×	`times-frac_binary64`
288×	`cancel-sign-sub-inv_binary64`
223×	`sub-neg_binary64`
155×	`fma-def_binary64`
152×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	3009
1	665	2843
2	2559	2756

Stop Event

1×	node limit

Counts

136 → 142

prune250.0ms (7.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	314	5	319

Error

Counts

319 → 5

Alt Table

Status	Error	Program
✓	10.1b	(pow.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)) -1)
	35.3b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
▶	30.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))
	35.4b	(pow.f64 (+.f64 (/.f64 y x) (-.f64 (/.f64 (/.f64 y x) x) (*.f64 (/.f64 y x) (/.f64 y x)))) -1)
✓	9.1b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 12111 to 6924 computations (42.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (pow.f64 x 2) y) x)
✓	3.4b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))
✓	9.4b	(/.f64 (pow.f64 x 2) y)

series31.0ms (0.9%)

Counts

3 → 12

Calls

18 calls:

4.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))	y	0
2.0ms	(/.f64 (pow.f64 x 2) y)	x	0
2.0ms	(/.f64 (pow.f64 x 2) y)	y	-inf
2.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))	y	-inf
2.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))	y	inf

rewrite78.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

561×	`fma-def_binary64`
446×	`log-prod_binary64`
295×	`fma-neg_binary64`
244×	`egg-rr`
171×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	33
1	190	33
2	2827	31

Stop Event

1×	node limit

Counts

3 → 244

simplify36.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

352×	`fma-neg_binary64`
294×	`distribute-rgt-in_binary64`
263×	`distribute-lft-in_binary64`
226×	`associate-l_binary64`
200×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	72
1	23	72
2	47	72
3	119	72
4	400	66
5	1660	66
6	4487	66

Stop Event

1×	node limit

Counts

256 → 251

prune143.0ms (4.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	251	5	256

Error

Counts

256 → 5

Alt Table

Status	Error	Program
✓	10.1b	(pow.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (fma.f64 x (/.f64 x y) x))) 2)) -1)
	35.3b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
✓	30.9b	(-.f64 (+.f64 (/.f64 (pow.f64 x 2) y) x) (pow.f64 x 2))
	35.4b	(pow.f64 (+.f64 (/.f64 y x) (-.f64 (/.f64 (/.f64 y x) x) (*.f64 (/.f64 y x) (/.f64 y x)))) -1)
✓	9.1b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 4863 to 1746 computations (64.1% saved)

regimes654.0ms (19.2%)

Accuracy

Total 0.1b remaining (79.7%)

Threshold costs 0.1b (79.7%)

Counts

111 → 3

Compiler

Compiled 5195 to 3392 computations (34.7% saved)

bsearch23.0ms (0.7%)

Algorithm

2×	binary-search

Calls

2 calls:

18.0ms	x
3.0ms	x

Steps

Iters	Point		Range
7848370427169039.0	∈ [	2163696582.8970065	,	21903218700442948.0	]
-1.236259081343894e+24	∈ [	-8.54293593786347e+25	,	-1.833289251571289e+22	]

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	24	52
2	30	52
3	32	52
4	33	52

Stop Event

1×

saturated

end93.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 162 to 96 computations (40.7% saved)

Details

analyze173.0ms (5.1%)

sample882.0ms (25.9%)

preprocess58.0ms (1.7%)

simplify42.0ms (1.2%)

prune7.0ms (0.2%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite54.0ms (1.6%)

simplify31.0ms (0.9%)

prune57.0ms (1.7%)

localize7.0ms (0.2%)

series43.0ms (1.3%)

rewrite60.0ms (1.8%)

simplify85.0ms (2.5%)

prune132.0ms (3.9%)

localize31.0ms (0.9%)

series266.0ms (7.8%)

rewrite66.0ms (1.9%)

simplify64.0ms (1.9%)

prune250.0ms (7.3%)

localize6.0ms (0.2%)

series31.0ms (0.9%)

rewrite78.0ms (2.3%)

simplify36.0ms (1.1%)

prune143.0ms (4.2%)

regimes654.0ms (19.2%)

bsearch23.0ms (0.7%)

simplify6.0ms (0.2%)

end93.0ms (2.7%)

Profiling