Details

analyze89.0ms (4.5%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample735.0ms (37.4%)

Results

706.0ms	8256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	51	11
4	69	11
5	75	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
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series7.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

rewrite31.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`log1p-expm1-u_binary64`
571×	`expm1-log1p-u_binary64`
303×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	140	11
2	1600	11

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

30.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

simplify69.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
591×	`associate-l_binary64`
372×	`cube-prod_binary64`
330×	`associate-r_binary64`
284×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	231
1	20	231
2	36	231
3	67	231
4	152	231
5	441	231
6	1734	231
7	2049	231
8	2327	231
9	2578	231
10	2919	231
11	3416	231
12	4073	231
13	4861	231

Stop Event

1×	node limit

Counts

53 → 35

prune26.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	31	4	35
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Error

0.0b

Counts

37 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	1.2b	(.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))) 2))
▶	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	36.2b	(/.f64 (-.f64 (.f64 (.f64 y (.f64 y 3)) (.f64 y (.f64 y 3))) (pow.f64 x 4)) (-.f64 (.f64 y (.f64 y 3)) (.f64 x x)))

Compiler

Compiled 608 to 357 computations (41.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 y y))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(*.f64 3 (*.f64 y y))

rewrite28.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

400×	`log1p-expm1-u_binary64`
400×	`expm1-log1p-u_binary64`
347×	`pow1_binary64`
278×	`unpow-prod-down_binary64`
221×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1149	7

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

28.0ms

(*.f64 3 (*.f64 y y))

simplify58.0ms (3%)

Algorithm

1×	egg-herbie

Rules

609×	`sqr-pow_binary64`
451×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
271×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	106	84
5	315	84
6	1235	84
7	2116	84
8	2280	84
9	2464	84
10	2672	84
11	2963	84
12	3356	84
13	3834	84
14	4395	84

Stop Event

1×	node limit

Counts

35 → 25

prune18.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	26	4	30

Error

0.0b

Counts

30 → 4

Alt Table

Status	Error	Program
	13.9b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
▶	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 362 to 222 computations (38.7% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3))))
✓	0.2b	(.f64 y (.f64 y 3))
✓	0.2b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
✓	18.5b	(sqrt.f64 (.f64 y (.f64 y 3)))

series91.0ms (4.6%)

Counts

4 → 72

Calls

4 calls:

70.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
16.0ms	(hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3))))
3.0ms	(sqrt.f64 (.f64 y (.f64 y 3)))
2.0ms	(.f64 y (.f64 y 3))

rewrite46.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

768×	`log1p-expm1-u_binary64`
768×	`expm1-log1p-u_binary64`
191×	`prod-diff_binary64`
94×	`add-sqr-sqrt_binary64`
89×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	206	33
2	2230	33

Stop Event

1×	node limit

Counts

4 → 87

Calls

4 calls:

45.0ms	(hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3))))
45.0ms	(.f64 y (.f64 y 3))
45.0ms	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
45.0ms	(sqrt.f64 (.f64 y (.f64 y 3)))

simplify31.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

714×	`times-frac_binary64`
328×	`associate-/l*_binary64`
300×	`associate-r_binary64`
291×	`associate-/r*_binary64`
262×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	1351
1	214	1062
2	791	1038

Stop Event

1×	node limit

Counts

159 → 123

prune84.0ms (4.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	121	6	127

Error

0.0b

Counts

127 → 6

Alt Table

Status	Error	Program
	13.9b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
▶	0.7b	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3)))))
	28.5b	(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
✓	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 2034 to 1522 computations (25.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x (*.f64 y (sqrt.f64 3))))
✓	0.3b	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3))))
✓	0.3b	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3)))))
✓	0.4b	(*.f64 y (sqrt.f64 3))

series127.0ms (6.4%)

Counts

4 → 40

Calls

4 calls:

76.0ms	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3)))))
28.0ms	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3))))
20.0ms	(sqrt.f64 (hypot.f64 x (*.f64 y (sqrt.f64 3))))
3.0ms	(*.f64 y (sqrt.f64 3))

rewrite45.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

730×	`log1p-expm1-u_binary64`
730×	`expm1-log1p-u_binary64`
153×	`log1p-udef_binary64`
93×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	59
1	200	40
2	2130	40

Stop Event

1×	node limit

Counts

4 → 72

Calls

4 calls:

44.0ms	(sqrt.f64 (hypot.f64 x (*.f64 y (sqrt.f64 3))))
44.0ms	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3))))
44.0ms	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (*.f64 y (sqrt.f64 3)))))
44.0ms	(*.f64 y (sqrt.f64 3))

simplify47.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-r_binary64`
679×	`associate-l_binary64`
574×	`fma-neg_binary64`
354×	`fma-def_binary64`
221×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1077
1	341	872
2	1064	839
3	4739	839

Stop Event

1×	node limit

Counts

112 → 108

prune138.0ms (7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	175	7	182

Error

Counts

182 → 7

Alt Table

Status	Error	Program
	13.9b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	0.9b	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3))))) (cbrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3))))) (hypot.f64 x (*.f64 y (sqrt.f64 3)))))
	28.5b	(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
✓	0.3b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 y 3)))) 2)
	0.6b	(.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (.f64 (sqrt.f64 (hypot.f64 x (.f64 y (sqrt.f64 3)))) (hypot.f64 x (sqrt.f64 (.f64 3 (.f64 y y))))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 4929 to 3720 computations (24.5% saved)

regimes166.0ms (8.4%)

Accuracy

Total 0.1b remaining (92.8%)

Threshold costs 0.1b (92.8%)

Counts

37 → 1

Compiler

Compiled 3063 to 2256 computations (26.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11

Stop Event

1×

saturated

end92.0ms (4.7%)

Compiler: Compiled 132 to 94 computations (28.8% saved)

Details

analyze89.0ms (4.5%)

sample735.0ms (37.4%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite31.0ms (1.6%)

simplify69.0ms (3.5%)

prune26.0ms (1.3%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite28.0ms (1.4%)

simplify58.0ms (3%)

prune18.0ms (0.9%)

localize7.0ms (0.4%)

series91.0ms (4.6%)

rewrite46.0ms (2.3%)

simplify31.0ms (1.6%)

prune84.0ms (4.3%)

localize7.0ms (0.3%)

series127.0ms (6.4%)

rewrite45.0ms (2.3%)

simplify47.0ms (2.4%)

prune138.0ms (7%)

regimes166.0ms (8.4%)

simplify2.0ms (0.1%)

end92.0ms (4.7%)

Profiling