Details

analyze9.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample310.0ms (8.1%)

Algorithm

1×

intervals

Results

55.0ms	139×	body	1024	valid
13.0ms	63×	body	512	valid
5.0ms	10×	body	2048	valid
4.0ms	30×	body	256	valid
1.0ms	14×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify221.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

3656×	`fma-def_binary64`
1088×	`fma-neg_binary64`
739×	`distribute-rgt-in_binary64`
501×	`distribute-lft-in_binary64`
425×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	18	10
2	28	10
3	41	10
4	70	10
5	92	10
6	140	10
7	245	10
8	414	10
9	537	10
10	694	10
11	940	10
12	1451	10
13	1750	10
14	1999	10
15	2072	10
16	2086	10
17	2086	10
18	3526	10
19	2536	10
20	2614	10
21	2622	10
22	2630	10
23	2630	10
24	2830	10
25	3322	10
26	3370	10
27	3344	10
28	5722	10

prune4.0ms (0.1%)

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 eps)) (log1p.f64 eps))
	59.5b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 47 to 35 computations (25.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`

Counts

1 → 33

Calls

1 calls:

3.0ms

(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

954×	`fma-neg_binary64`
405×	`distribute-rgt-in_binary64`
378×	`cancel-sign-sub-inv_binary64`
338×	`fma-def_binary64`
286×	`associate-l_binary64`

Counts

45 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	904
1	263	641
2	755	588
3	2436	586
4	4287	586
5	4920	586

prune25.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
▶	0.3b	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	0.0b	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
	59.5b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 1038 to 421 computations (59.4% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	0.4b	(*.f64 eps -2/3)

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
2.0ms	(*.f64 eps -2/3)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

3.0ms	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
3.0ms	(*.f64 eps -2/3)

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
586×	`distribute-neg-out_binary64`
552×	`times-frac_binary64`
295×	`associate-l_binary64`
287×	`*-commutative_binary64`

Counts

66 → 71

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	674
1	142	594
2	413	594
3	1198	594
4	2262	594
5	4618	594
6	5585	594

prune40.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	71	3	74

Error

Counts

74 → 3

Alt Table

Status	Error	Program
✓	0.3b	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	0.0b	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
▶	59.5b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 958 to 647 computations (32.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
✓	4.7b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
2.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
30×	`log-prod_binary64`
25×	`add-cube-cbrt_binary64`

Counts

2 → 96

Calls

2 calls:

7.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
5.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

simplify148.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-neg_binary64`
329×	`fma-def_binary64`
307×	`sub-neg_binary64`
306×	`div-exp_binary64`
171×	`distribute-rgt-neg-in_binary64`

Counts

120 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2246
1	422	2118
2	1082	2055
3	2942	2055
4	4638	2055
5	4992	2055
6	4963	2055
7	5384	2055

prune69.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	161	3	164

Error

Counts

164 → 3

Alt Table

Status	Error	Program
✓	0.3b	(.f64 eps (fma.f64 eps (.f64 eps -2/3) -2))
✓	0.0b	(-.f64 (log1p.f64 (neg.f64 eps)) (log1p.f64 eps))
✓	59.5b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Compiler

Compiled 2585 to 1938 computations (25% saved)

regimes17.0ms (0.4%)

Accuracy

Total 0.0b remaining (53.8%)

Threshold costs 0.0b (53.8%)

Counts

6 → 1

Compiler

Compiled 170 to 127 computations (25.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	17	10
3	20	10
4	21	10
5	21	10

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample2.8s (72.6%)

Algorithm

1×

intervals

Results

1.7s	4093×	body	1024	valid
474.0ms	1976×	body	512	valid
217.0ms	395×	body	2048	valid
121.0ms	969×	body	256	valid
41.0ms	567×	body	128	valid

Compiler

Compiled 43 to 32 computations (25.6% saved)

Details

analyze9.0ms (0.2%)

sample310.0ms (8.1%)

simplify221.0ms (5.8%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify69.0ms (1.8%)

prune25.0ms (0.7%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify70.0ms (1.8%)

prune40.0ms (1%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite19.0ms (0.5%)

simplify148.0ms (3.9%)

prune69.0ms (1.8%)

regimes17.0ms (0.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.8s (72.6%)

Profiling