Metrics for Hyperbolic arc-(co)tangent

analyze4.0ms (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
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 14 to 12 computations (14.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

Operation ival-log, time spent: 1.0ms, 46.0% of total-time

Operation ival-div, time spent: 1.0ms, 46.0% of total-time

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

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

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

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

sample1.2s (22.2%)

Results

1.1s	8255×	valid
0.0ms	4×	invalid
0.0ms	1×	valid

Precisions

Click to see histograms. Total time spent on operations: 616.0ms

Operation ival-add, time spent: 156.0ms, 25.0% of total-time

Operation ival-sub, time spent: 139.0ms, 23.0% of total-time

Operation ival-div, time spent: 134.0ms, 22.0% of total-time

Operation ival-log, time spent: 117.0ms, 19.0% of total-time

Operation ival-mult, time spent: 35.0ms, 6.0% of total-time

Operation const, time spent: 35.0ms, 6.0% of total-time

Bogosity

preprocess1.9s (35.1%)

Algorithm

1×	egg-herbie

Rules

1946×	`fma-def`
1402×	`fma-neg`
1276×	`associate-+r+`
794×	`distribute-lft-in`
714×	`unsub-neg`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(+.f64 1 x)`
-	-	`(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))`
-	-	`(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))`
-	-	`(/.f64 (+.f64 1 x) (-.f64 1 x))`
-	-	`(/.f64 1 2)`
-	-	`(-.f64 1 x)`
-	-	`2`
-	-	`1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	144
1	51	124
2	85	124
3	168	124
4	391	124
5	915	124
6	2246	124
7	3420	124
8	4980	124
9	5860	124
10	6148	124
11	6388	124
12	6525	124
13	6639	124
14	6926	124
15	7106	124
16	7192	124
17	7503	124
18	7623	124
19	7651	124
20	7671	124
21	7679	124
22	7679	124

Stop Event

1×	node limit

Calls

Call 1

Inputs
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(neg.f64 (*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x))))))

Outputs
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x)))))
(*.f64 1/2 (log.f64 (/.f64 (-.f64 1 x) (-.f64 1 (neg.f64 x)))))
(*.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
(*.f64 -1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
(neg.f64 (*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 (neg.f64 x)) (-.f64 1 (neg.f64 x))))))
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))

Symmetry

(negabs x)

Compiler

Compiled 95 to 75 computations (21.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.3s

Operation ival-log, time spent: 404.0ms, 32.0% of total-time

Operation ival-div, time spent: 323.0ms, 25.0% of total-time

Operation ival-add, time spent: 242.0ms, 19.0% of total-time

Operation ival-sub, time spent: 236.0ms, 19.0% of total-time

Operation const, time spent: 39.0ms, 3.0% of total-time

Operation ival-mult, time spent: 26.0ms, 2.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 19 to 15 computations (21.1% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	11.4%	(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
▶	95.6%	(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))

Compiler

Compiled 20 to 16 computations (20% saved)

localize1.1s (19.8%)

Compiler: Compiled 59 to 34 computations (42.4% saved)
Precisions: Click to see histograms. Total time spent on operations: 925.0ms
Operation ival-log1p, time spent: 342.0ms, 37.0% of total-time
Operation ival-log, time spent: 198.0ms, 21.0% of total-time
Operation ival-sub, time spent: 149.0ms, 16.0% of total-time
Operation ival-add, time spent: 125.0ms, 14.0% of total-time
Operation ival-div, time spent: 56.0ms, 6.0% of total-time
Operation ival-mult, time spent: 28.0ms, 3.0% of total-time
Operation const, time spent: 19.0ms, 2.0% of total-time
Operation ival-neg, time spent: 8.0ms, 1.0% of total-time

eval0.0ms (0%)

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

prune3.0ms (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

98.6%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	11.4%	(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))
✓	95.6%	(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))

Compiler

Compiled 51 to 41 computations (19.6% saved)

regimes15.0ms (0.3%)

Counts

3 → 2

Calls

Call 1

Inputs
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))

Outputs
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x))))

Calls

4 calls:

5.0ms	x
3.0ms	(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
3.0ms	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
3.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))

Results

Accuracy	Segments	Branch
98.6%	2	`x`
97.3%	2	`(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))`
97.3%	2	`(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))`
97.3%	2	`(/.f64 (+.f64 1 x) (-.f64 1 x))`

Compiler

Compiled 32 to 25 computations (21.9% saved)

regimes10.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))

Outputs
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))

Calls

4 calls:

4.0ms	(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
2.0ms	x
2.0ms	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
2.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))

Results

Accuracy	Segments	Branch
95.6%	1	`(*.f64 (/.f64 1 2) (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))`
95.6%	1	`(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))`
95.6%	1	`(/.f64 (+.f64 1 x) (-.f64 1 x))`
95.6%	1	`x`

Compiler

Compiled 32 to 25 computations (21.9% saved)

bsearch20.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	2.4753953991159742e-29	1.3411824532466086e-27

Results

17.0ms	111×	0	valid
0.0ms	1×	0	valid

Compiler

Compiled 171 to 140 computations (18.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

Operation ival-log, time spent: 3.0ms, 32.0% of total-time

Operation ival-sub, time spent: 2.0ms, 22.0% of total-time

Operation ival-div, time spent: 2.0ms, 22.0% of total-time

Operation ival-add, time spent: 2.0ms, 22.0% of total-time

Operation ival-mult, time spent: 1.0ms, 11.0% of total-time

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative`
8×	`sub-neg`
8×	`*-commutative`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	113
1	38	113
2	44	113
3	47	113
4	48	113

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 x 4549352020500247/89202980794122492566142873090593446023921664) (*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))) (*.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))))

(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))

Outputs
(if (<=.f64 x 4549352020500247/89202980794122492566142873090593446023921664) (.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))) (.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))))
(if (<=.f64 x 4549352020500247/89202980794122492566142873090593446023921664) (.f64 1/2 (log.f64 (/.f64 (+.f64 x 1) (-.f64 1 x)))) (.f64 1/2 (-.f64 (log1p.f64 x) (log1p.f64 (neg.f64 x)))))
(*.f64 1/2 (log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
(*.f64 1/2 (log.f64 (/.f64 (+.f64 x 1) (-.f64 1 x))))

Compiler

Compiled 34 to 27 computations (20.6% saved)

soundness1.1s (21.1%)

Rules

1946×	`fma-def`
1946×	`fma-def`
1402×	`fma-neg`
1402×	`fma-neg`
1276×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	144
1	51	124
2	85	124
3	168	124
4	391	124
5	915	124
6	2246	124
7	3420	124
8	4980	124
9	5860	124
10	6148	124
11	6388	124
12	6525	124
13	6639	124
14	6926	124
15	7106	124
16	7192	124
17	7503	124
18	7623	124
19	7651	124
20	7671	124
21	7679	124
22	7679	124
0	22	144
1	51	124
2	85	124
3	168	124
4	391	124
5	915	124
6	2246	124
7	3420	124
8	4980	124
9	5860	124
10	6148	124
11	6388	124
12	6525	124
13	6639	124
14	6926	124
15	7106	124
16	7192	124
17	7503	124
18	7623	124
19	7651	124
20	7671	124
21	7679	124
22	7679	124

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 84 to 65 computations (22.6% saved)

end0.0ms (0%)

preprocess38.0ms (0.7%)

Compiler: Compiled 184 to 146 computations (20.7% saved)

analyze4.0ms (0.1%)

sample1.2s (22.2%)

preprocess1.9s (35.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize1.1s (19.8%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes15.0ms (0.3%)

regimes10.0ms (0.2%)

bsearch20.0ms (0.4%)

simplify4.0ms (0.1%)

soundness1.1s (21.1%)

end0.0ms (0%)

preprocess38.0ms (0.7%)

Profiling