Details

analyze436.0ms (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.4s (69.2%)

Results

1.5s	2537×	body	1024	valid
796.0ms	1285×	body	2048	valid
506.0ms	1288×	body	512	valid
295.0ms	2463×	body	128	valid
154.0ms	637×	body	256	valid
34.0ms	46×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9

Stop Event

1×

saturated

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

43.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.5b	(+.f64 x (hypot.f64 1 x))
✓	2.6b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(hypot.f64 1 x)

rewrite45.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`log1p-expm1-u_binary64`
575×	`expm1-log1p-u_binary64`
462×	`prod-diff_binary64`
165×	`fma-def_binary64`
105×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
1	121	20
2	1537	20

Stop Event

1×	node limit

Counts

3 → 81

Calls

3 calls:

43.0ms	(hypot.f64 1 x)
43.0ms	(+.f64 x (hypot.f64 1 x))
43.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

447×	`cancel-sign-sub-inv_binary64`
436×	`fma-neg_binary64`
413×	`associate-/r*_binary64`
338×	`sub-neg_binary64`
314×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	569
1	306	549
2	863	537
3	2779	537

Stop Event

1×	node limit

Counts

117 → 145

prune79.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	4	146

Error

0.0b

Counts

146 → 4

Alt Table

Status	Error	Program
✓	43.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	58.9b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))
▶	28.6b	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))
	51.1b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 1950 to 1448 computations (25.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	16.8b	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 (pow.f64 x 3) -1/6 x)
3.0ms	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))

rewrite38.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

836×	`log1p-expm1-u_binary64`
836×	`expm1-log1p-u_binary64`
103×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	214	23
2	2285	23

Stop Event

1×	node limit

Counts

2 → 47

Calls

2 calls:

37.0ms	(fma.f64 (pow.f64 x 3) -1/6 x)
37.0ms	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))

simplify33.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-neg_binary64`
416×	`unswap-sqr_binary64`
405×	`cancel-sign-sub-inv_binary64`
333×	`associate-l_binary64`
304×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	264
1	43	260
2	102	228
3	309	228
4	735	228
5	2023	228
6	3560	228

Stop Event

1×	node limit

Counts

71 → 57

prune30.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
✓	43.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	58.9b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))
✓	28.6b	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))
▶	51.1b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 955 to 736 computations (22.9% saved)

localize19.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
✓	0.4b	(/.f64 1/8 (pow.f64 x 3))
✓	12.3b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

series9.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

3.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
3.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite54.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

914×	`prod-diff_binary64`
193×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	231	31
2	3097	31

Stop Event

1×	node limit

Counts

3 → 104

Calls

3 calls:

52.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x))
52.0ms	(/.f64 1/8 (pow.f64 x 3))
52.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
524×	`cancel-sign-sub-inv_binary64`
352×	`sub-neg_binary64`
306×	`associate-/r*_binary64`
237×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	410
1	181	402
2	523	400
3	1888	396

Stop Event

1×	node limit

Counts

128 → 131

prune67.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Error

0.0b

Counts

135 → 4

Alt Table

Status	Error	Program
✓	43.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	58.9b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))
✓	28.6b	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))
✓	51.1b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 2196 to 1746 computations (20.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x)))
✓	0.9b	(-.f64 x (hypot.f64 1 x))
✓	2.6b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))
✓	15.0b	(-.f64 (*.f64 x x) (fma.f64 x x 1))

series12.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))
3.0ms	(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x)))
3.0ms	(-.f64 (*.f64 x x) (fma.f64 x x 1))
2.0ms	(-.f64 x (hypot.f64 1 x))

rewrite75.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

453×	`fma-def_binary64`
290×	`egg-rr`
263×	`fma-neg_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	60
1	224	34
2	3372	34

Stop Event

1×	node limit

Counts

4 → 290

Calls

4 calls:

70.0ms	(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x)))
70.0ms	(-.f64 x (hypot.f64 1 x))
70.0ms	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))
70.0ms	(-.f64 (*.f64 x x) (fma.f64 x x 1))

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

424×	`associate-/r*_binary64`
414×	`cancel-sign-sub-inv_binary64`
337×	`fma-neg_binary64`
305×	`sub-neg_binary64`
248×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	592
1	270	568
2	775	562
3	2458	562

Stop Event

1×	node limit

Counts

338 → 341

prune181.0ms (3.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	341	4	345

Error

0.0b

Counts

345 → 4

Alt Table

Status	Error	Program
✓	43.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	58.9b	(log.f64 (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x 1)) (-.f64 x (hypot.f64 1 x))))
✓	28.6b	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 x))
✓	51.1b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

Compiler

Compiled 7437 to 4783 computations (35.7% saved)

regimes114.0ms (2.4%)

Accuracy

Total 0.0b remaining (22%)

Threshold costs 0.0b (22%)

Counts

26 → 3

Compiler

Compiled 1014 to 781 computations (23% saved)

bsearch41.0ms (0.9%)

Steps

Iters	Range		Point
9	1.2657313602955984e-9	0.2007625494085178	0.007834703990068876
8	-0.22645862137088205	-0.0007928517292319593	-0.007430164824513489

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

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	25	48
1	30	48
2	33	48
3	35	48
4	36	48

Stop Event

1×

saturated

end101.0ms (2.1%)

Compiler: Compiled 114 to 83 computations (27.2% saved)

Details

analyze436.0ms (9%)

sample3.4s (69.2%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite45.0ms (0.9%)

simplify44.0ms (0.9%)

prune79.0ms (1.6%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite38.0ms (0.8%)

simplify33.0ms (0.7%)

prune30.0ms (0.6%)

localize19.0ms (0.4%)

series9.0ms (0.2%)

rewrite54.0ms (1.1%)

simplify25.0ms (0.5%)

prune67.0ms (1.4%)

localize9.0ms (0.2%)

series12.0ms (0.2%)

rewrite75.0ms (1.5%)

simplify42.0ms (0.9%)

prune181.0ms (3.7%)

regimes114.0ms (2.4%)

bsearch41.0ms (0.9%)

simplify3.0ms (0.1%)

end101.0ms (2.1%)

Profiling