Metrics for Hyperbolic arc-cosine

analyze94.0ms (2.1%)

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%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

Operation ival-log, time spent: 15.0ms, 30.0% of total-time

Operation ival-sqrt, time spent: 13.0ms, 26.0% of total-time

Operation ival-mult, time spent: 10.0ms, 20.0% of total-time

Operation ival-add, time spent: 5.0ms, 10.0% of total-time

Operation ival-sub, time spent: 5.0ms, 10.0% of total-time

Operation const, time spent: 1.0ms, 2.0% of total-time

sample2.6s (59.2%)

Results

1.2s	8255×	valid
1.2s	8220×	invalid
0.0ms	1×	valid

Precisions

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

Operation ival-add, time spent: 332.0ms, 25.0% of total-time

Operation ival-sub, time spent: 315.0ms, 24.0% of total-time

Operation ival-log, time spent: 261.0ms, 20.0% of total-time

Operation ival-sqrt, time spent: 225.0ms, 17.0% of total-time

Operation ival-mult, time spent: 145.0ms, 11.0% of total-time

Operation const, time spent: 38.0ms, 3.0% of total-time

Bogosity

preprocess1.3s (30.2%)

Algorithm

1×	egg-herbie

Rules

1468×	`fma-def`
1306×	`distribute-lft-out`
1142×	`distribute-rgt-out--`
1106×	`unsub-neg`
946×	`sub-neg`

FPErrors

Click to see full error table

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	140
1	48	132
2	83	132
3	179	132
4	416	132
5	926	132
6	1721	132
7	3271	132
8	4314	132
9	4981	132
10	5280	132
11	5565	132
12	5717	132
13	5790	132
14	6001	132
15	6768	132
16	7253	132

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 1))))
(log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x -1))))
(log.f64 (-.f64 (sqrt.f64 (fma.f64 x x -1)) x))
(neg.f64 (log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) 1)))))
(neg.f64 (log.f64 (+.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x -1)))))
(neg.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x -1)) x)))

Compiler

Compiled 80 to 43 computations (46.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 885.0ms

Operation ival-sub, time spent: 557.0ms, 63.0% of total-time

Operation ival-sqrt, time spent: 127.0ms, 14.0% of total-time

Operation ival-add, time spent: 102.0ms, 12.0% of total-time

Operation ival-log, time spent: 54.0ms, 6.0% of total-time

Operation ival-mult, time spent: 30.0ms, 3.0% of total-time

Operation const, time spent: 15.0ms, 2.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.1%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 10 to 7 computations (30% saved)

localize334.0ms (7.6%)

Compiler: Compiled 35 to 18 computations (48.6% saved)
Precisions: Click to see histograms. Total time spent on operations: 255.0ms
Operation ival-sub, time spent: 100.0ms, 39.0% of total-time
Operation ival-sqrt, time spent: 61.0ms, 24.0% of total-time
Operation ival-add, time spent: 51.0ms, 20.0% of total-time
Operation ival-log, time spent: 23.0ms, 9.0% of total-time
Operation ival-mult, time spent: 13.0ms, 5.0% of total-time
Operation const, time spent: 8.0ms, 3.0% 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

53.1%

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.1%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`unsub-neg`
4×	`sub-neg`
4×	`neg-mul-1`
3×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	20	36
2	24	36
3	27	36
4	30	36
5	33	36

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))

Compiler

Compiled 10 to 7 computations (30% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess30.0ms (0.7%)

Compiler: Compiled 40 to 28 computations (30% saved)

analyze94.0ms (2.1%)

sample2.6s (59.2%)

preprocess1.3s (30.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize334.0ms (7.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess30.0ms (0.7%)

Profiling