Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.1s (40.8%)

Results

1.0s	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify34.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

756×	`fma-def_binary64`
559×	`hypot-def_binary64`
544×	`distribute-rgt-out_binary64`
436×	`associate-l_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	30	4
3	53	4
4	121	4
5	361	4
6	1334	4
7	2593	4
8	3960	4
9	4922	4

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 12 computations (40% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(hypot.f64 x x)

rewrite28.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
230×	`add-cbrt-cube_binary64`
227×	`add-cube-cbrt_binary64`
222×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	700	4

Stop Event

1×	node limit

Counts

1 → 40

Calls

1 calls:

27.0ms

(hypot.f64 x x)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

52 → 43

prune28.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	36	7	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	8	44

Error

0.0b

Counts

44 → 8

Alt Table

Status	Error	Program
	31.7b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	31.0b	(*.f64 (sqrt.f64 2) x)
	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.1b	(hypot.f64 x x)
	43.6b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 513 to 251 computations (51.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

series18.0ms (0.7%)

Counts

2 → 0

Calls

2 calls:

11.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
7.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite38.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
339×	`pow1_binary64`
263×	`unpow-prod-down_binary64`
191×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	124	10
2	1142	10

Stop Event

1×	node limit

Counts

2 → 88

Calls

2 calls:

37.0ms	(sqrt.f64 (hypot.f64 x x))
37.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

88 → 88

prune62.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	130	9	139

Error

0.0b

Counts

139 → 9

Alt Table

Status	Error	Program
	31.7b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	31.0b	(*.f64 (sqrt.f64 2) x)
▶	0.4b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
	43.6b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.1b	(hypot.f64 x x)
	31.9b	(pow.f64 (*.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x x) 1/4)) 2)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 1599 to 854 computations (46.6% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/4)
	0.1b	(hypot.f64 x x)
✓	0.2b	(pow.f64 (hypot.f64 x x) 3/4)
✓	0.4b	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

series328.0ms (12.3%)

Counts

3 → 36

Calls

3 calls:

164.0ms	(pow.f64 (hypot.f64 x x) 3/4)
160.0ms	(pow.f64 (hypot.f64 x x) 1/4)
3.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

rewrite38.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
305×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	162	18
2	1753	18

Stop Event

1×	node limit

Counts

3 → 64

Calls

3 calls:

37.0ms	(pow.f64 (hypot.f64 x x) 1/4)
37.0ms	(pow.f64 (hypot.f64 x x) 3/4)
37.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

401×	`associate-l_binary64`
374×	`associate-r_binary64`
322×	`fma-def_binary64`
240×	`unswap-sqr_binary64`
177×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	464
1	74	464
2	156	416
3	331	320
4	821	312
5	1983	312

Stop Event

1×	node limit

Counts

100 → 77

prune102.0ms (3.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	5	1	6
Picked	1	0	1
Done	0	2	2
Total	164	8	172

Error

Counts

172 → 8

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4)) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	31.7b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	4.4b	(*.f64 (pow.f64 (pow.f64 (E.f64) (log.f64 (hypot.f64 x x))) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.1b	(hypot.f64 x x)
	0.7b	(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)) (pow.f64 (hypot.f64 x x) 3/4))
	0.6b	(.f64 (.f64 (pow.f64 (hypot.f64 x x) 1/8) (pow.f64 (hypot.f64 x x) 1/8)) (pow.f64 (hypot.f64 x x) 3/4))
	1.2b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) 3/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3/4)))

Compiler

Compiled 2722 to 1421 computations (47.8% saved)

localize22.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
	0.2b	(pow.f64 (hypot.f64 x x) 3/4)
✓	0.3b	(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4))
✓	0.4b	(.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4)) (pow.f64 (hypot.f64 x x) 3/4))

series165.0ms (6.2%)

Counts

2 → 24

Calls

2 calls:

161.0ms

(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4))

4.0ms

(*.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4)) (pow.f64 (hypot.f64 x x) 3/4))

rewrite91.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

831×	`log1p-expm1-u_binary64`
831×	`expm1-log1p-u_binary64`
105×	`add-cbrt-cube_binary64`
104×	`add-sqr-sqrt_binary64`
104×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	248	11
2	2811	11

Stop Event

1×	node limit

Counts

2 → 34

Calls

2 calls:

90.0ms

(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4))

90.0ms

(*.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4)) (pow.f64 (hypot.f64 x x) 3/4))

simplify34.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

517×	`fma-def_binary64`
471×	`div-sub_binary64`
360×	`fma-neg_binary64`
230×	`associate-l_binary64`
220×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	272
1	54	272
2	110	248
3	236	200
4	598	196
5	1397	196
6	3675	196

Stop Event

1×	node limit

Counts

58 → 42

prune162.0ms (6.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	225	8	233

Error

Counts

233 → 8

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 1/4) (pow.f64 (pow.f64 (hypot.f64 x x) 3/4) 1/4)) (pow.f64 (hypot.f64 x x) 3/4))
	0.6b	(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/8) 2) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	31.7b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	4.4b	(*.f64 (pow.f64 (pow.f64 (E.f64) (log.f64 (hypot.f64 x x))) 1/4) (pow.f64 (hypot.f64 x x) 3/4))
✓	0.1b	(hypot.f64 x x)
	0.7b	(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)) (pow.f64 (hypot.f64 x x) 3/4))
	1.2b	(.f64 (pow.f64 (hypot.f64 x x) 1/4) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) 3/4) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 3/4)))

Compiler

Compiled 5460 to 3173 computations (41.9% saved)

regimes243.0ms (9.1%)

Accuracy

Total 0.1b remaining (76.3%)

Threshold costs 0.1b (76.3%)

Counts

55 → 1

Compiler

Compiled 3038 to 1998 computations (34.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4

Stop Event

1×

saturated

end104.0ms (3.9%)

Compiler: Compiled 116 to 73 computations (37.1% saved)

Details

analyze6.0ms (0.2%)

sample1.1s (40.8%)

simplify34.0ms (1.3%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite28.0ms (1%)

simplify11.0ms (0.4%)

prune28.0ms (1%)

localize7.0ms (0.3%)

series18.0ms (0.7%)

rewrite38.0ms (1.4%)

simplify7.0ms (0.2%)

prune62.0ms (2.3%)

localize8.0ms (0.3%)

series328.0ms (12.3%)

rewrite38.0ms (1.4%)

simplify33.0ms (1.2%)

prune102.0ms (3.8%)

localize22.0ms (0.8%)

series165.0ms (6.2%)

rewrite91.0ms (3.4%)

simplify34.0ms (1.3%)

prune162.0ms (6.1%)

regimes243.0ms (9.1%)

simplify2.0ms (0.1%)

end104.0ms (3.9%)

Profiling