Metrics for Kahan's exp quotient

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
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

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

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

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

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

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

sample1.6s (78.2%)

Results

246.0ms	3076×	256	valid
611.0ms	2082×	1024	valid
204.0ms	2002×	256	infinite
227.0ms	984×	512	valid
30.0ms	112×	2048	valid

Precisions

Click to see histograms. Total time spent on operations: 696.0ms

Operation ival-exp, time spent: 322.0ms, 46.0% of total-time

Operation ival-div, time spent: 209.0ms, 30.0% of total-time

Operation ival-sub, time spent: 142.0ms, 20.0% of total-time

Operation const, time spent: 22.0ms, 3.0% of total-time

Bogosity

preprocess251.0ms (12.6%)

Algorithm

1×	egg-herbie

Rules

318×	`fma-define`
191×	`fma-neg`
111×	`times-frac`
97×	`div-sub`
64×	`distribute-rgt-in`

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
139	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	-	`x`
0	-	-	`(exp.f64 x)`
0	-	-	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`
0	-	-	`#s(literal 1 binary64)`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	43	80
2	88	80
3	240	80
4	630	80
5	971	80
6	1341	80
7	1585	80
8	1656	80

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64)) (neg.f64 x))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64)) (neg.f64 x)))

Outputs
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64)) (neg.f64 x))
(/.f64 (expm1.f64 (neg.f64 x)) (neg.f64 x))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64)) (neg.f64 x)))
(/.f64 (expm1.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(/.f64 (expm1.f64 (neg.f64 x)) x)

Results

22.0ms	190×	256	valid
48.0ms	138×	1024	valid
11.0ms	102×	256	infinite
13.0ms	70×	512	valid
4.0ms	12×	2048	valid

Compiler

Compiled 39 to 23 computations (41% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

Operation ival-exp, time spent: 25.0ms, 52.0% of total-time

Operation ival-sub, time spent: 12.0ms, 25.0% of total-time

Operation ival-div, time spent: 8.0ms, 17.0% of total-time

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

eval0.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

prune3.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 5 to 3 computations (40% saved)

localize45.0ms (2.2%)

Results

8.0ms	99×	256	valid
16.0ms	69×	1024	valid
5.0ms	51×	256	infinite
6.0ms	35×	512	valid
0.0ms	2×	2048	valid

Compiler

Compiled 9 to 4 computations (55.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

Operation composed, time spent: 14.0ms, 47.0% of total-time

Operation ival-exp, time spent: 9.0ms, 30.0% of total-time

Operation ival-div, time spent: 4.0ms, 14.0% of total-time

Operation ival-sub, time spent: 3.0ms, 10.0% of total-time

Operation const, time spent: 1.0ms, 3.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (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%	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes2.0ms (0.1%)

Accuracy

Total -32.5b remaining (-∞%)

Threshold costs -32.5b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Outputs
(/.f64 (expm1.f64 x) x)

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)

Outputs
(/.f64 (expm1.f64 x) x)

Compiler

Compiled 5 to 3 computations (40% saved)

soundness90.0ms (4.5%)

Rules

318×	`fma-define`
191×	`fma-neg`
111×	`times-frac`
97×	`div-sub`
64×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	43	80
2	88	80
3	240	80
4	630	80
5	971	80
6	1341	80
7	1585	80
8	1656	80

Stop Event

1×

saturated

Compiler

Compiled 11 to 7 computations (36.4% saved)

end0.0ms (0%)

preprocess39.0ms (2%)

Compiler: Compiled 70 to 46 computations (34.3% saved)

analyze2.0ms (0.1%)

sample1.6s (78.2%)

preprocess251.0ms (12.6%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize45.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes2.0ms (0.1%)

simplify2.0ms (0.1%)

soundness90.0ms (4.5%)

end0.0ms (0%)

preprocess39.0ms (2%)

Profiling