Metrics for ln(1 + x)

analyze2.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 5 computations (16.7% saved)

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	128	46	0.0ms
ival-add	128	23	0.0ms
ival-log	128	23	0.0ms

sample2.7s (93.5%)

Results

1.8s	2750×	body	1024	valid
454.0ms	3976×	body	256	valid
322.0ms	1346×	body	512	valid
105.0ms	184×	body	2048	valid
0.0ms	1×	body	256	invalid

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	2048	368	0.0ms
const	1024	5868	6.0ms
const	512	8560	8.0ms
const	256	16514	18.0ms
ival-add	2048	184	1.0ms
ival-add	1024	2934	20.0ms
ival-add	512	4280	30.0ms
ival-add	256	8257	63.0ms
ival-log	2048	184	34.0ms
ival-log	1024	2934	743.0ms
ival-log	512	4280	275.0ms
ival-log	256	8257	303.0ms

Bogosity

preprocess102.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

104×	`fma-def`
42×	`sub-neg`
22×	`cancel-sign-sub-inv`
20×	`associate-+l-`
18×	`distribute-lft-neg-in`

Problems

161×	`(log.f64 (+.f64 1 x))`
95×	No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 1 x))
(log.f64 (+.f64 1 x))
(log.f64 (+.f64 1 (neg.f64 x)))
(neg.f64 (log.f64 (+.f64 1 (neg.f64 x))))

Outputs
(log.f64 (+.f64 1 x))
(log1p.f64 x)
(log.f64 (+.f64 1 x))
(log1p.f64 x)
(log.f64 (+.f64 1 (neg.f64 x)))
(log1p.f64 (neg.f64 x))
(neg.f64 (log.f64 (+.f64 1 (neg.f64 x))))
(neg.f64 (log1p.f64 (neg.f64 x)))

Compiler

Compiled 16 to 12 computations (25% saved)

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	2048	32	0.0ms
const	1024	348	0.0ms
const	512	492	0.0ms
const	256	1024	1.0ms
ival-add	2048	16	0.0ms
ival-add	1024	174	1.0ms
ival-add	512	246	2.0ms
ival-add	256	512	4.0ms
ival-log	2048	8	1.0ms
ival-log	1024	87	14.0ms
ival-log	512	123	8.0ms
ival-log	256	256	9.0ms

eval0.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log1p.f64 x)
▶	100.0%	(log1p.f64 x)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize20.0ms (0.7%)

Compiler

Compiled 5 to 3 computations (40% saved)

Mixed Sampling

Click to see full mixed sampling table

op	prec	x	time
const	256	256	0.0ms
ival-log1p	256	256	5.0ms

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Accuracy

100.0%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)

Compiler

Compiled 10 to 7 computations (30% saved)

regimes8.0ms (0.3%)

Accuracy

Total -37.0b remaining (-∞%)

Threshold costs -37b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(log1p.f64 x)
(log.f64 (+.f64 1 x))

Outputs
(log1p.f64 x)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(log.f64 (+.f64 1 x))`
100.0%	1	`(+.f64 1 x)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log1p.f64 x)

Outputs
(log1p.f64 x)

Compiler

Compiled 3 to 2 computations (33.3% saved)

soundness18.0ms (0.6%)

Rules

104×	`fma-def`
42×	`sub-neg`
22×	`cancel-sign-sub-inv`
20×	`associate-+l-`
18×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44

Stop Event

1×

saturated

Compiler

Compiled 7 to 5 computations (28.6% saved)

end0.0ms (0%)

preprocess33.0ms (1.2%)

Compiler: Compiled 56 to 42 computations (25% saved)

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44

analyze2.0ms (0.1%)

sample2.7s (93.5%)

preprocess102.0ms (3.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize20.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes8.0ms (0.3%)

simplify1.0ms (0%)

soundness18.0ms (0.6%)

end0.0ms (0%)

preprocess33.0ms (1.2%)

Profiling

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44

Iter	Nodes	Cost
0	13	44
1	25	44
2	34	44
3	43	44
4	57	44
5	74	44
6	107	44
7	142	44
8	160	44
9	183	44
10	197	44
11	232	44
12	247	44
13	252	44
14	253	44