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
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: 1.0ms

ival-log: 1.0ms (112.6% of total)

ival-add: 0.0ms (0% of total)

const: 0.0ms (0% of total)

sample1.6s (74.7%)

Results

1.1s	5273×	1	valid
201.0ms	2983×	0	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 858.0ms

ival-log: 639.0ms (74.5% of total)

ival-add: 107.0ms (12.5% of total)

backward-pass: 93.0ms (10.8% of total)

const: 19.0ms (2.2% of total)

Bogosity

preprocess40.0ms (1.9%)

Algorithm

1×	egg-herbie

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

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)))

explain148.0ms (6.9%)

FPErrors

Click to see full error table

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

Results

25.0ms	266×	256	valid
73.0ms	162×	1024	valid
14.0ms	66×	512	valid
10.0ms	18×	2048	valid

Compiler

Compiled 27 to 20 computations (25.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-log: 67.0ms (81.2% of total)

ival-add: 13.0ms (15.7% of total)

const: 2.0ms (2.4% of total)

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)

localize298.0ms (14%)

Results

10.0ms	133×	256	valid
33.0ms	81×	1024	valid
244.0ms	33×	512	valid
4.0ms	9×	2048	valid

Compiler

Compiled 5 to 3 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 549.0ms

composed: 275.0ms (50.1% of total)

ival-log: 270.0ms (49.2% of total)

ival-add: 3.0ms (0.5% of total)

const: 1.0ms (0.2% of total)

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)

regimes3.0ms (0.1%)

Accuracy

Total -34.5b remaining (-∞%)

Threshold costs -34.5b (-∞%)

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×

saturated

Calls

Call 1

Inputs
(log1p.f64 x)

Outputs
(log1p.f64 x)

soundness12.0ms (0.6%)

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×	done
1×	saturated

Compiler

Compiled 10 to 7 computations (30% saved)

preprocess32.0ms (1.5%)

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

ln(1 + x)

analyze2.0ms (0.1%)

sample1.6s (74.7%)

preprocess40.0ms (1.9%)

explain148.0ms (6.9%)

eval0.0ms (0%)

prune1.0ms (0%)

localize298.0ms (14%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes3.0ms (0.1%)

simplify2.0ms (0.1%)

soundness12.0ms (0.6%)

preprocess32.0ms (1.5%)

end0.0ms (0%)

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