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)

sample667.0ms (38.7%)

Results

639.0ms

8256×

body

128

valid

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

prune3.0ms (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)

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(hypot.f64 x x)

rewrite27.0ms (1.5%)

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)

simplify10.0ms (0.6%)

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

prune21.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	5	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Error

0.0b

Counts

44 → 6

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	2.9b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 469 to 223 computations (52.5% 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)

series21.0ms (1.2%)

Counts

2 → 0

Calls

2 calls:

11.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
10.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite31.0ms (1.8%)

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:

30.0ms	(sqrt.f64 (hypot.f64 x x))
30.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

simplify36.0ms (2.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

88 → 88

prune54.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	130	7	137

Error

0.0b

Counts

137 → 7

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	19.1b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)) 2)
	2.9b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
▶	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 1557 to 826 computations (46.9% saved)

localize5.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.3b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series372.0ms (21.6%)

Counts

3 → 36

Calls

3 calls:

200.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
169.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))

rewrite39.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`log1p-expm1-u_binary64`
439×	`expm1-log1p-u_binary64`
333×	`unpow-prod-down_binary64`
224×	`log-prod_binary64`
131×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	142	19
2	1333	19

Stop Event

1×	node limit

Counts

3 → 121

Calls

3 calls:

37.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
37.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
37.0ms	(cbrt.f64 (hypot.f64 x x))

simplify42.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

427×	`associate-l_binary64`
423×	`fma-neg_binary64`
337×	`associate-r_binary64`
281×	`fma-def_binary64`
276×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	500
1	67	500
2	144	452
3	371	332
4	1203	324
5	4386	324

Stop Event

1×	node limit

Counts

157 → 134

prune105.0ms (6.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	282	1	283
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	282	8	290

Error

0.0b

Counts

290 → 8

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	32.0b	(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x x))) 3/2)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	19.1b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)) 2)
▶	2.9b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
✓	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 5002 to 2016 computations (59.7% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	2.8b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))

series8.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(log1p.f64 (hypot.f64 x x))
4.0ms	(expm1.f64 (log1p.f64 (hypot.f64 x x)))

rewrite33.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

324×	`expm1-log1p-u_binary64`
323×	`log1p-expm1-u_binary64`
289×	`add-log-exp_binary64`
288×	`add-exp-log_binary64`
283×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	79	10
2	909	10

Stop Event

1×	node limit

Counts

2 → 79

Calls

2 calls:

31.0ms	(log1p.f64 (hypot.f64 x x))
31.0ms	(expm1.f64 (log1p.f64 (hypot.f64 x x)))

simplify28.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-neg_binary64`
248×	`sub-neg_binary64`
168×	`unswap-sqr_binary64`
167×	`times-frac_binary64`
164×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	468
1	176	382
2	609	365
3	2447	363

Stop Event

1×	node limit

Counts

103 → 103

prune57.0ms (3.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	146	8	154

Error

0.0b

Counts

154 → 8

Alt Table

Status	Error	Program
✓	0.1b	(hypot.f64 x x)
	32.0b	(pow.f64 (cbrt.f64 (*.f64 x (+.f64 x x))) 3/2)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	19.1b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x x) 3/2)) 2)
✓	2.9b	(expm1.f64 (log1p.f64 (hypot.f64 x x)))
	35.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
✓	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	27.9b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 1847 to 1041 computations (43.6% saved)

regimes67.0ms (3.9%)

Accuracy

Total 0.1b remaining (75.8%)

Threshold costs 0.1b (75.8%)

Counts

21 → 1

Compiler

Compiled 718 to 488 computations (32% 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

end74.0ms (4.3%)

Compiler: Compiled 70 to 45 computations (35.7% saved)

Details

analyze4.0ms (0.2%)

sample667.0ms (38.7%)

simplify6.0ms (0.3%)

prune3.0ms (0.2%)

localize2.0ms (0.1%)

series4.0ms (0.2%)

rewrite27.0ms (1.5%)

simplify10.0ms (0.6%)

prune21.0ms (1.2%)

localize4.0ms (0.2%)

series21.0ms (1.2%)

rewrite31.0ms (1.8%)

simplify36.0ms (2.1%)

prune54.0ms (3.1%)

localize5.0ms (0.3%)

series372.0ms (21.6%)

rewrite39.0ms (2.3%)

simplify42.0ms (2.4%)

prune105.0ms (6.1%)

localize4.0ms (0.2%)

series8.0ms (0.5%)

rewrite33.0ms (1.9%)

simplify28.0ms (1.6%)

prune57.0ms (3.3%)

regimes67.0ms (3.9%)

simplify2.0ms (0.1%)

end74.0ms (4.3%)

Profiling