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)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation ival-log, time spent: 0.0ms, 0.0% of total-time

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

sample2.5s (82%)

Results

353.0ms	3954×	256	valid
1.3s	2755×	1024	valid
341.0ms	1349×	512	valid
110.0ms	198×	2048	valid
0.0ms	2×	256	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

Operation ival-log, time spent: 1.3s, 89.0% of total-time

Operation ival-add, time spent: 127.0ms, 9.0% of total-time

Operation const, time spent: 27.0ms, 2.0% of total-time

Bogosity

preprocess203.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

10×	`sub-neg`
8×	`fma-define`
7×	`+-commutative`
5×	`associate-+l-`
4×	`associate--r+`

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
173	-	-	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	-	`x`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 #s(literal 1 binary64) x)`

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	74	44
6	91	44
7	95	44

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 #s(literal 1 binary64) x))
(log.f64 (+.f64 #s(literal 1 binary64) x))
(log.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x)))
(neg.f64 (log.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x))))

Outputs
(log.f64 (+.f64 #s(literal 1 binary64) x))
(log1p.f64 x)
(log.f64 (+.f64 #s(literal 1 binary64) x))
(log1p.f64 x)
(log.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x)))
(log1p.f64 (neg.f64 x))
(neg.f64 (log.f64 (+.f64 #s(literal 1 binary64) (neg.f64 x))))
(neg.f64 (log1p.f64 (neg.f64 x)))

Results

26.0ms	226×	256	valid
82.0ms	188×	1024	valid
23.0ms	90×	512	valid
4.0ms	8×	2048	valid

Compiler

Compiled 27 to 20 computations (25.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

Operation ival-log, time spent: 66.0ms, 76.0% of total-time

Operation ival-add, time spent: 18.0ms, 21.0% of total-time

Operation const, time spent: 3.0ms, 3.0% of total-time

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)

Compiler

Compiled 3 to 2 computations (33.3% saved)

localize283.0ms (9.4%)

Results

10.0ms	117×	256	valid
104.0ms	91×	1024	valid
160.0ms	45×	512	valid
1.0ms	3×	2048	valid

Compiler

Compiled 5 to 3 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 211.0ms

Operation composed, time spent: 106.0ms, 50.0% of total-time

Operation ival-log, time spent: 100.0ms, 47.0% of total-time

Operation ival-add, time spent: 4.0ms, 2.0% of total-time

Operation const, time spent: 1.0ms, 0.0% of total-time

eval0.0ms (0%)

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

prune2.0ms (0.1%)

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)

regimes3.0ms (0.1%)

Accuracy

Total -40.1b remaining (-∞%)

Threshold costs -40.1b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(log1p.f64 x)
(log.f64 (+.f64 #s(literal 1 binary64) x))

Outputs
(log1p.f64 x)

Calls

3 calls:

1.0ms	x
1.0ms	(+.f64 #s(literal 1 binary64) x)
1.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
100.0%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify2.0ms (0.1%)

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)

soundness12.0ms (0.4%)

Rules

10×	`sub-neg`
8×	`fma-define`
7×	`+-commutative`
5×	`associate-+l-`
4×	`associate--r+`

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	74	44
6	91	44
7	95	44

Stop Event

1×

saturated

Compiler

Compiled 7 to 5 computations (28.6% saved)

end0.0ms (0%)

preprocess33.0ms (1.1%)

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

analyze2.0ms (0.1%)

sample2.5s (82%)

preprocess203.0ms (6.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize283.0ms (9.4%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes3.0ms (0.1%)

simplify2.0ms (0.1%)

soundness12.0ms (0.4%)

end0.0ms (0%)

preprocess33.0ms (1.1%)

Profiling