Details

analyze399.0ms (9.5%)

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)

sample3.2s (76.8%)

Results

1.5s	2544×	body	1024	valid
764.0ms	1292×	body	2048	valid
479.0ms	1278×	body	512	valid
282.0ms	2448×	body	128	valid
141.0ms	650×	body	256	valid
31.0ms	44×	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

46.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	46.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 x (hypot.f64 1 x))
✓	3.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite39.0ms (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	16
1	121	16
2	1537	16

Stop Event

1×	node limit

Counts

2 → 62

Calls

2 calls:

38.0ms	(+.f64 x (hypot.f64 1 x))
38.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

simplify29.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

415×	`associate-/r*_binary64`
385×	`associate-l_binary64`
364×	`cancel-sign-sub-inv_binary64`
300×	`fma-neg_binary64`
277×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	411
1	254	397
2	724	391
3	2290	391

Stop Event

1×	node limit

Counts

86 → 106

prune52.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	4	107

Error

0.0b

Counts

107 → 4

Alt Table

Status	Error	Program
	49.1b	(log.f64 (/.f64 -1/2 x))
✓	46.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	49.3b	(+.f64 (log.f64 2) (log.f64 x))
▶	29.3b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 1436 to 1069 computations (25.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

rewrite33.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
282×	`unpow-prod-down_binary64`
223×	`log-prod_binary64`
142×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	126	8
2	1355	8

Stop Event

1×	node limit

Counts

1 → 36

Calls

1 calls:

32.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

simplify29.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1047×	`fma-def_binary64`
818×	`unswap-sqr_binary64`
241×	`associate-l_binary64`
194×	`fma-neg_binary64`
174×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	105
1	23	105
2	61	87
3	194	87
4	429	87
5	1190	87
6	2374	87
7	3266	87

Stop Event

1×	node limit

Counts

48 → 41

prune23.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Error

0.0b

Counts

45 → 4

Alt Table

Status	Error	Program
▶	49.1b	(log.f64 (/.f64 -1/2 x))
✓	46.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	49.3b	(+.f64 (log.f64 2) (log.f64 x))
✓	29.3b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 537 to 416 computations (22.5% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	49.1b	(log.f64 (/.f64 -1/2 x))
✓	46.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	49.3b	(+.f64 (log.f64 2) (log.f64 x))
✓	29.3b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 31 to 24 computations (22.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (log.f64 2) (log.f64 x))

series44.0ms (1%)

Counts

1 → 12

Calls

1 calls:

43.0ms

(+.f64 (log.f64 2) (log.f64 x))

rewrite34.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

587×	`log1p-expm1-u_binary64`
587×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
158×	`fma-def_binary64`
110×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	127	6
2	1574	6

Stop Event

1×	node limit

Counts

1 → 39

Calls

1 calls:

33.0ms

(+.f64 (log.f64 2) (log.f64 x))

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1420×	`fma-neg_binary64`
658×	`fma-def_binary64`
309×	`distribute-rgt-in_binary64`
292×	`unsub-neg_binary64`
272×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	96
1	30	96
2	50	96
3	115	96
4	337	96
5	1087	96
6	2028	96
7	3587	96
8	3970	96
9	4114	96
10	4141	96
11	4147	96
12	4147	96

Stop Event

1×	node limit

Counts

51 → 42

prune19.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	42	4	46

Error

0.0b

Counts

46 → 4

Alt Table

Status	Error	Program
✓	49.1b	(log.f64 (/.f64 -1/2 x))
✓	46.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	49.3b	(/.f64 (+.f64 (pow.f64 (log1p.f64 1) 3) (pow.f64 (log.f64 x) 3)) (+.f64 (pow.f64 (log.f64 x) 2) (-.f64 (pow.f64 (log1p.f64 1) 2) (*.f64 (log1p.f64 1) (log.f64 x)))))
✓	29.3b	(fma.f64 (pow.f64 x 3) -1/6 x)

Compiler

Compiled 504 to 390 computations (22.6% saved)

regimes62.0ms (1.5%)

Accuracy

Total 0.1b remaining (62.1%)

Threshold costs 0.1b (62.1%)

Counts

15 → 3

Compiler

Compiled 423 to 319 computations (24.6% saved)

bsearch38.0ms (0.9%)

Steps

Iters	Range		Point
9	7.628700423801858e-10	0.05704294867570225	0.0010462575660624225
10	-80329480.11588429	-3.614078377920913e-6	-1.2603231646087443

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	35
1	23	35

Stop Event

1×

saturated

end72.0ms (1.7%)

Compiler: Compiled 95 to 71 computations (25.3% saved)

Details

analyze399.0ms (9.5%)

sample3.2s (76.8%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite39.0ms (0.9%)

simplify29.0ms (0.7%)

prune52.0ms (1.2%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite33.0ms (0.8%)

simplify29.0ms (0.7%)

prune23.0ms (0.6%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series44.0ms (1%)

rewrite34.0ms (0.8%)

simplify60.0ms (1.4%)

prune19.0ms (0.5%)

regimes62.0ms (1.5%)

bsearch38.0ms (0.9%)

simplify2.0ms (0.1%)

end72.0ms (1.7%)

Profiling