Metrics for ln(1 + x)

analyze7.0ms (0.5%)

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
0%	0%	100%	0%	0%	0%	0%	2
33.3%	25%	50%	0%	0%	25%	0%	3
66.7%	50%	25%	0%	0%	25%	0%	4
83.3%	62.5%	12.5%	0%	0%	25%	0%	5
91.7%	68.7%	6.2%	0%	0%	25%	0%	6
95.8%	71.8%	3.1%	0%	0%	25%	0%	7
97.9%	73.4%	1.6%	0%	0%	25%	0%	8
99%	74.2%	0.8%	0%	0%	25%	0%	9
99.5%	74.6%	0.4%	0%	0%	25%	0%	10
99.7%	74.8%	0.2%	0%	0%	25%	0%	11
99.9%	74.9%	0.1%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 5 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

Operation ival-add, time spent: 5.0ms, 89.0% of total-time

Operation ival-log, time spent: 1.0ms, 18.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample802.0ms (55.8%)

Results

757.0ms	8255×	valid
0.0ms	1×	valid
0.0ms	1×	invalid

Precisions

Click to see histograms. Total time spent on operations: 306.0ms

Operation ival-add, time spent: 157.0ms, 51.0% of total-time

Operation ival-log, time spent: 130.0ms, 42.0% of total-time

Operation const, time spent: 19.0ms, 6.0% of total-time

Bogosity

preprocess351.0ms (24.4%)

Algorithm

1×	egg-herbie

Rules

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

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(+.f64 1 x)`
-	-	`(log.f64 (+.f64 1 x))`
-	-	`1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	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 27 to 20 computations (25.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 186.0ms

Operation ival-add, time spent: 122.0ms, 65.0% of total-time

Operation ival-log, time spent: 52.0ms, 28.0% of total-time

Operation const, time spent: 12.0ms, 6.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	43.3%	(log1p.f64 x)
▶	98.0%	(log.f64 (+.f64 1 x))

Compiler

Compiled 8 to 6 computations (25% saved)

localize202.0ms (14%)

Compiler: Compiled 14 to 9 computations (35.7% saved)
Precisions: Click to see histograms. Total time spent on operations: 135.0ms
Operation ival-add, time spent: 61.0ms, 45.0% of total-time
Operation ival-log1p, time spent: 40.0ms, 30.0% of total-time
Operation ival-log, time spent: 28.0ms, 21.0% of total-time
Operation const, time spent: 6.0ms, 4.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Accuracy

98.8%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	43.3%	(log1p.f64 x)
✓	98.0%	(log.f64 (+.f64 1 x))

Compiler

Compiled 15 to 11 computations (26.7% saved)

regimes7.0ms (0.5%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`(log.f64 (+.f64 1 x))`
98.0%	1	`(+.f64 1 x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes3.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log1p.f64 x)

Outputs
(log1p.f64 x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
43.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	16	22

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

soundness23.0ms (1.6%)

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	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	44

Stop Event

1×

saturated

Compiler

Compiled 7 to 5 computations (28.6% saved)

end0.0ms (0%)

preprocess37.0ms (2.6%)

Compiler: Compiled 64 to 48 computations (25% saved)

Iter	Nodes	Cost
0	13	44
1	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	44

Iter	Nodes	Cost
0	13	44
1	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	44

Iter	Nodes	Cost
0	13	44
1	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	44

Iter	Nodes	Cost
0	13	44
1	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	44

analyze7.0ms (0.5%)

sample802.0ms (55.8%)

preprocess351.0ms (24.4%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize202.0ms (14%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes7.0ms (0.5%)

regimes3.0ms (0.2%)

simplify2.0ms (0.2%)

soundness23.0ms (1.6%)

end0.0ms (0%)

preprocess37.0ms (2.6%)

Profiling

Iter	Nodes	Cost
0	13	44
1	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	44

Iter	Nodes	Cost
0	13	44
1	28	44
2	37	44
3	46	44
4	60	44
5	77	44
6	110	44
7	145	44
8	163	44
9	186	44
10	200	44
11	235	44
12	250	44
13	255	44
14	256	44