Details

analyze40.0ms (1.9%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample745.0ms (35.8%)

Results

675.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify49.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
362×	`div-sub_binary64`
361×	`times-frac_binary64`
137×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	31	10
5	54	10
6	91	10
7	134	10
8	214	10
9	439	10
10	1099	10
11	1804	10
12	2674	10
13	3121	10
14	3277	10
15	3299	10
16	3319	10
17	3319	10

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite42.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
552×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
70×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	140	10
2	2143	10

Stop Event

1×	node limit

Counts

1 → 35

Calls

1 calls:

41.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

simplify24.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

823×	`associate-/l*_binary64`
492×	`associate-/r*_binary64`
361×	`associate-/r/_binary64`
338×	`cancel-sign-sub-inv_binary64`
194×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	417
1	121	399
2	382	339
3	1513	327

Stop Event

1×	node limit

Counts

59 → 49

prune37.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Error

Counts

50 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
▶	0.1b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2)))
	33.1b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
	30.9b	(+.f64 -1 (.f64 (/.f64 x y) (-.f64 -2 (.f64 2 (/.f64 x y)))))
	33.3b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 2)

Compiler

Compiled 779 to 334 computations (57.1% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2)
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.0b	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
✓	0.1b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2))

series95.0ms (4.6%)

Counts

3 → 72

Calls

3 calls:

76.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
10.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2))
9.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2)

rewrite56.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`prod-diff_binary64`
251×	`fma-def_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
128×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	219	40
2	2904	40

Stop Event

1×	node limit

Counts

3 → 98

Calls

3 calls:

54.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2)
54.0ms	(cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
54.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2))

simplify44.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

660×	`associate-/l*_binary64`
615×	`fma-def_binary64`
522×	`associate-/r*_binary64`
151×	`cancel-sign-sub-inv_binary64`
94×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1873
1	444	1843
2	1659	1635

Stop Event

1×	node limit

Counts

170 → 143

prune167.0ms (8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	241	5	246

Error

Counts

246 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.1b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2)))
	33.1b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
▶	30.9b	(+.f64 -1 (.f64 (/.f64 x y) (-.f64 -2 (.f64 2 (/.f64 x y)))))
	33.3b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 2)

Compiler

Compiled 6528 to 2430 computations (62.8% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 x y) (-.f64 -2 (.f64 2 (/.f64 x y))))

series17.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

17.0ms

(*.f64 (/.f64 x y) (-.f64 -2 (*.f64 2 (/.f64 x y))))

rewrite47.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`log-prod_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
151×	`log-pow_binary64`
139×	`prod-diff_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	204	16
2	2761	14

Stop Event

1×	node limit

Counts

1 → 76

Calls

1 calls:

45.0ms

(*.f64 (/.f64 x y) (-.f64 -2 (*.f64 2 (/.f64 x y))))

simplify32.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

711×	`associate-/l/_binary64`
680×	`fma-def_binary64`
401×	`fma-neg_binary64`
338×	`cancel-sign-sub-inv_binary64`
246×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	438
1	46	402
2	118	348
3	338	348
4	1858	312

Stop Event

1×	node limit

Counts

100 → 82

prune58.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	82	5	87

Error

Counts

87 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.1b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2)))
▶	33.1b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
✓	30.9b	(+.f64 -1 (.f64 (/.f64 x y) (-.f64 -2 (.f64 2 (/.f64 x y)))))
	33.3b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 2)

Compiler

Compiled 1728 to 961 computations (44.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
✓	3.2b	(-.f64 (.f64 x x) (.f64 y y))
✓	31.7b	(/.f64 (+.f64 x y) (-.f64 (.f64 x x) (.f64 y y)))

series24.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

8.0ms	(/.f64 (+.f64 x y) (-.f64 (.f64 x x) (.f64 y y)))
8.0ms	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
8.0ms	(-.f64 (.f64 x x) (.f64 y y))

rewrite72.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

603×	`fma-def_binary64`
267×	`egg-rr`
258×	`fma-neg_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	48
1	219	27
2	3520	27

Stop Event

1×	node limit

Counts

3 → 267

Calls

3 calls:

66.0ms	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
66.0ms	(-.f64 (.f64 x x) (.f64 y y))
66.0ms	(/.f64 (+.f64 x y) (-.f64 (.f64 x x) (.f64 y y)))

simplify47.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

499×	`cancel-sign-sub-inv_binary64`
456×	`associate-/r/_binary64`
346×	`associate-/l/_binary64`
273×	`fma-neg_binary64`
190×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1119
1	185	1083
2	600	987
3	2361	966

Stop Event

1×	node limit

Counts

339 → 300

prune178.0ms (8.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	299	1	300
Fresh	1	0	1
Picked	0	1	1
Done	1	2	3
Total	301	4	305

Error

Counts

305 → 4

Alt Table

Status	Error	Program
✓	33.1b	(.f64 (/.f64 (+.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
	12.8b	(fma.f64 (sqrt.f64 (/.f64 x (-.f64 x y))) (sqrt.f64 (/.f64 x (-.f64 x y))) (/.f64 y (-.f64 x y)))
✓	0.1b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 2)))
✓	30.9b	(+.f64 -1 (.f64 (/.f64 x y) (-.f64 -2 (.f64 2 (/.f64 x y)))))

Compiler

Compiled 6687 to 1906 computations (71.5% saved)

regimes159.0ms (7.6%)

Accuracy

Total 0.0b remaining (54.9%)

Threshold costs 0.0b (54.9%)

Counts

58 → 1

Compiler

Compiled 2424 to 1476 computations (39.1% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	16	10
4	17	10

Stop Event

1×

saturated

end111.0ms (5.3%)

Compiler: Compiled 91 to 45 computations (50.5% saved)

Details

analyze40.0ms (1.9%)

sample745.0ms (35.8%)

simplify49.0ms (2.4%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite42.0ms (2%)

simplify24.0ms (1.1%)

prune37.0ms (1.8%)

localize8.0ms (0.4%)

series95.0ms (4.6%)

rewrite56.0ms (2.7%)

simplify44.0ms (2.1%)

prune167.0ms (8%)

localize6.0ms (0.3%)

series17.0ms (0.8%)

rewrite47.0ms (2.2%)

simplify32.0ms (1.5%)

prune58.0ms (2.8%)

localize7.0ms (0.3%)

series24.0ms (1.2%)

rewrite72.0ms (3.5%)

simplify47.0ms (2.3%)

prune178.0ms (8.6%)

regimes159.0ms (7.6%)

simplify5.0ms (0.2%)

end111.0ms (5.3%)

Profiling