Metrics for ln(1 + x)

analyze3.0ms (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: 2.0ms

Operation ival-log, time spent: 1.0ms, 64.0% of total-time

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

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

sample3.0s (87.7%)

Results

730.0ms	3999×	256	valid
1.5s	2730×	1024	valid
497.0ms	1360×	512	valid
133.0ms	166×	2048	valid
0.0ms	4×	256	invalid
0.0ms	1×	1024	valid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

Operation ival-log, time spent: 1.4s, 81.0% of total-time

Operation ival-add, time spent: 313.0ms, 18.0% of total-time

Operation const, time spent: 26.0ms, 1.0% of total-time

Bogosity

preprocess250.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

20×	`sub-neg`
16×	`fma-define`
14×	`+-commutative`
10×	`associate-+l-`
8×	`associate--r+`

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
168	-	1	(0.011932286649523116)	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	0	-	`x`
0	-	0	-	`#s(literal 1 binary64)`
0	-	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)))

Compiler

Compiled 27 to 20 computations (25.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

Operation ival-log, time spent: 61.0ms, 79.0% of total-time

Operation ival-add, time spent: 13.0ms, 17.0% of total-time

Operation const, time spent: 3.0ms, 4.0% 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)

localize65.0ms (1.9%)

Compiler: Compiled 5 to 3 computations (40% saved)
Precisions: Click to see histograms. Total time spent on operations: 87.0ms
Operation composed, time spent: 44.0ms, 50.0% of total-time
Operation ival-log, time spent: 31.0ms, 35.0% of total-time
Operation ival-add, time spent: 11.0ms, 13.0% of total-time
Operation const, time spent: 1.0ms, 1.0% of total-time

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)

regimes30.0ms (0.9%)

Accuracy

Total -38.4b remaining (-∞%)

Threshold costs -38.4b (-∞%)

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:

26.0ms	x
2.0ms	(+.f64 #s(literal 1 binary64) x)
2.0ms	(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)

soundness11.0ms (0.3%)

Rules

20×	`sub-neg`
16×	`fma-define`
14×	`+-commutative`
10×	`associate-+l-`
8×	`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%)

preprocess55.0ms (1.6%)

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

analyze3.0ms (0.1%)

sample3.0s (87.7%)

preprocess250.0ms (7.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize65.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes30.0ms (0.9%)

simplify2.0ms (0.1%)

soundness11.0ms (0.3%)

end0.0ms (0%)

preprocess55.0ms (1.6%)

Profiling