Details

analyze4.0ms (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 5 computations (50% saved)

sample660.0ms (30.2%)

Results

632.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(hypot.f64 x x)

rewrite27.0ms (1.2%)

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:

26.0ms

(hypot.f64 x x)

simplify11.0ms (0.5%)

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

prune23.0ms (1.1%)

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

Compiler

Compiled 513 to 251 computations (51.1% saved)

localize4.0ms (0.2%)

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 (0.8%)

Counts

2 → 0

Calls

2 calls:

12.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
6.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite34.0ms (1.5%)

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:

32.0ms	(sqrt.f64 (hypot.f64 x x))
32.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

88 → 88

prune58.0ms (2.7%)

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

Compiler

Compiled 1599 to 854 computations (46.6% saved)

localize8.0ms (0.4%)

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))

series329.0ms (15.1%)

Counts

3 → 36

Calls

3 calls:

166.0ms	(pow.f64 (hypot.f64 x x) 3/4)
159.0ms	(pow.f64 (hypot.f64 x x) 1/4)
4.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

rewrite40.0ms (1.8%)

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:

39.0ms	(pow.f64 (hypot.f64 x x) 1/4)
39.0ms	(pow.f64 (hypot.f64 x x) 3/4)
39.0ms	(*.f64 (pow.f64 (hypot.f64 x x) 1/4) (pow.f64 (hypot.f64 x x) 3/4))

simplify34.0ms (1.6%)

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

prune139.0ms (6.4%)

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
	31.7b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	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)))
	0.7b	(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)) (pow.f64 (hypot.f64 x x) 3/4))
	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))
▶	0.5b	(.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 (.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))
✓	0.1b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 2722 to 1421 computations (47.8% saved)

localize16.0ms (0.7%)

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))

series218.0ms (10%)

Counts

2 → 24

Calls

2 calls:

214.0ms

(*.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))

rewrite46.0ms (2.1%)

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:

46.0ms

(*.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))

46.0ms

(*.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))

simplify37.0ms (1.7%)

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

prune159.0ms (7.3%)

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
	31.7b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	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)))
	0.6b	(*.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/8) 2) (pow.f64 (hypot.f64 x x) 3/4))
	0.7b	(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 3)) (pow.f64 (hypot.f64 x x) 3/4))
	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))
✓	0.5b	(.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))
✓	0.1b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Compiler

Compiled 5460 to 3173 computations (41.9% saved)

regimes190.0ms (8.7%)

Accuracy

Total 0.1b remaining (76.3%)

Threshold costs 0.1b (76.3%)

Counts

55 → 1

Compiler

Compiled 3038 to 1972 computations (35.1% 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

end106.0ms (4.9%)

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

Details

analyze4.0ms (0.2%)

sample660.0ms (30.2%)

simplify6.0ms (0.3%)

prune4.0ms (0.2%)

localize2.0ms (0.1%)

series3.0ms (0.2%)

rewrite27.0ms (1.2%)

simplify11.0ms (0.5%)

prune23.0ms (1.1%)

localize4.0ms (0.2%)

series18.0ms (0.8%)

rewrite34.0ms (1.5%)

simplify7.0ms (0.3%)

prune58.0ms (2.7%)

localize8.0ms (0.4%)

series329.0ms (15.1%)

rewrite40.0ms (1.8%)

simplify34.0ms (1.6%)

prune139.0ms (6.4%)

localize16.0ms (0.7%)

series218.0ms (10%)

rewrite46.0ms (2.1%)

simplify37.0ms (1.7%)

prune159.0ms (7.3%)

regimes190.0ms (8.7%)

simplify2.0ms (0.1%)

end106.0ms (4.9%)

Profiling