Details

analyze1.8s (21.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
3.1%	46.8%	50%	5
4.7%	45.3%	50%	6
5.5%	44.5%	50%	7
5.9%	44.1%	50%	8
6%	43.9%	50%	9
6.1%	43.8%	50%	10
6.2%	43.8%	50%	11
6.2%	43.7%	50%	12
6.2%	43.7%	50%	13
6.2%	43.7%	50%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample5.6s (67.1%)

Results

3.6s	4102×	body	1024	valid
1.1s	2093×	body	512	valid
483.0ms	421×	body	2048	valid
305.0ms	1038×	body	256	valid
86.0ms	602×	body	128	valid

Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
5×	`+-commutative_binary64`
4×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	14	10
2	19	10
3	25	10
4	32	10
5	42	10
6	53	10
7	66	10
8	70	10
9	53	10

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
	61.9b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))

Compiler

Compiled 50 to 38 computations (24% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

series16.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

15.0ms

(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

rewrite63.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

587×	`log1p-udef_binary64`
402×	`expm1-log1p-u_binary64`
400×	`log1p-expm1-u_binary64`
371×	`prod-diff_binary64`
316×	`unpow-prod-down_binary64`

Counts

1 → 1

Calls

1 calls:

63.0ms

(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	124	8
2	1109	1
3	3791	1
4	4959	1
0	0	0
1	0	0

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-/r*_binary64`
379×	`div-sub_binary64`
288×	`fma-def_binary64`
211×	`times-frac_binary64`
195×	`distribute-rgt-in_binary64`

Counts

13 → 24

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	1007
1	406	993
2	1544	781
3	4751	780
4	5424	780

prune28.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Error

0.0b

Counts

26 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
	61.9b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
▶	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 1234 to 941 computations (23.7% saved)

localize6.0ms (0.1%)

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
▶	61.9b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
✓	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 36 to 27 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
✓	6.8b	(log.f64 (-.f64 1 x))
✓	6.8b	(log.f64 (+.f64 1 x))

series21.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

15.0ms	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
3.0ms	(log.f64 (+.f64 1 x))
3.0ms	(log.f64 (-.f64 1 x))

rewrite50.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

815×	`log1p-expm1-u_binary64`
815×	`expm1-log1p-u_binary64`
186×	`prod-diff_binary64`
81×	`add-sqr-sqrt_binary64`
76×	`add-log-exp_binary64`

Counts

3 → 75

Calls

3 calls:

49.0ms	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
49.0ms	(log.f64 (-.f64 1 x))
49.0ms	(log.f64 (+.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	163	18
2	2072	18
3	5394	18
0	0	0
1	0	0

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

518×	`fma-def_binary64`
288×	`times-frac_binary64`
278×	`fma-neg_binary64`
265×	`distribute-rgt-in_binary64`
245×	`sub-neg_binary64`

Counts

111 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	1409
1	567	1361
2	2092	1153
3	4950	1151
4	5064	1151

prune70.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	141	3	144

Error

Counts

144 → 3

Alt Table

Status	Error	Program
✓	61.9b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
▶	1.4b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log1p.f64 x)) 2)) (/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x))))
✓	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 2872 to 1939 computations (32.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x)))
✓	0.3b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log1p.f64 x)) 2)) (/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x))))
✓	0.5b	(pow.f64 (cbrt.f64 (log1p.f64 x)) 2)
✓	0.7b	(cbrt.f64 (log1p.f64 x))

series133.0ms (1.6%)

Counts

4 → 48

Calls

4 calls:

74.0ms	(/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x)))
24.0ms	(pow.f64 (cbrt.f64 (log1p.f64 x)) 2)
17.0ms	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log1p.f64 x)) 2)) (/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x))))
17.0ms	(cbrt.f64 (log1p.f64 x))

rewrite66.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

914×	`expm1-log1p-u_binary64`
912×	`log1p-expm1-u_binary64`
152×	`prod-diff_binary64`
129×	`egg-rr`
113×	`add-sqr-sqrt_binary64`

Counts

4 → 129

Calls

4 calls:

64.0ms	(/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x)))
64.0ms	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log1p.f64 x)) 2)) (/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x))))
64.0ms	(pow.f64 (cbrt.f64 (log1p.f64 x)) 2)
64.0ms	(cbrt.f64 (log1p.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	248	29
2	2437	29
3	5740	29
0	0	0
1	0	0

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
306×	`associate-r_binary64`
269×	`associate-l_binary64`
254×	`associate-/r*_binary64`
227×	`associate-*r/_binary64`

Counts

177 → 224

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	462	4323
1	1570	4048
2	5012	4048

prune198.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	271	3	274

Error

Counts

274 → 3

Alt Table

Status	Error	Program
✓	61.9b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
✓	1.4b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (log1p.f64 x)) 2)) (/.f64 (log1p.f64 (neg.f64 x)) (cbrt.f64 (log1p.f64 x))))
✓	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 10116 to 6912 computations (31.7% saved)

regimes24.0ms (0.3%)

Accuracy

Total 0.0b remaining (32.6%)

Threshold costs 0.0b (32.6%)

Counts

12 → 1

Compiler

Compiled 256 to 196 computations (23.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	10	10
2	12	10
3	13	10
4	13	10

end51.0ms (0.6%)

Compiler: Compiled 49 to 35 computations (28.6% saved)

Details

analyze1.8s (21.4%)

sample5.6s (67.1%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize4.0ms (0%)

series16.0ms (0.2%)

rewrite63.0ms (0.8%)

simplify57.0ms (0.7%)

prune28.0ms (0.3%)

localize6.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series21.0ms (0.2%)

rewrite50.0ms (0.6%)

simplify64.0ms (0.8%)

prune70.0ms (0.8%)

localize9.0ms (0.1%)

series133.0ms (1.6%)

rewrite66.0ms (0.8%)

simplify73.0ms (0.9%)

prune198.0ms (2.4%)

regimes24.0ms (0.3%)

simplify2.0ms (0%)

end51.0ms (0.6%)

Profiling