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-div, 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-exp, time spent: 0.0ms, 0.0% of total-time

sample1.5s (76.4%)

Results

371.0ms	2960×	256	valid
562.0ms	2104×	1024	valid
234.0ms	2031×	256	infinite
164.0ms	1034×	512	valid
37.0ms	126×	2048	valid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 649.0ms

Operation ival-exp, time spent: 414.0ms, 64.0% of total-time

Operation ival-div, time spent: 122.0ms, 19.0% of total-time

Operation ival-sub, time spent: 91.0ms, 14.0% of total-time

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

Bogosity

preprocess212.0ms (11.1%)

Algorithm

1×	egg-herbie

Rules

1782×	`div-sub`
1494×	`fma-neg`
1012×	`times-frac`
636×	`distribute-lft-neg-in`
552×	`distribute-rgt-neg-in`

FPErrors

Click to see full error table

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	39	88
2	68	86
3	147	80
4	384	80
5	1036	80
6	4095	80
7	7627	80

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x)))

Outputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x))
(/.f64 (expm1.f64 (neg.f64 x)) (neg.f64 x))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) 1) (neg.f64 x)))
(/.f64 (neg.f64 (expm1.f64 (neg.f64 x))) (neg.f64 x))
(*.f64 1 (/.f64 (expm1.f64 (neg.f64 x)) x))
(/.f64 (expm1.f64 (neg.f64 x)) x)

Compiler

Compiled 39 to 23 computations (41% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

Operation ival-exp, time spent: 18.0ms, 47.0% of total-time

Operation ival-sub, time spent: 10.0ms, 26.0% of total-time

Operation ival-div, time spent: 8.0ms, 21.0% of total-time

Operation const, time spent: 2.0ms, 5.0% of total-time

eval0.0ms (0%)

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

prune1.0ms (0%)

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)

localize22.0ms (1.1%)

Compiler: Compiled 9 to 4 computations (55.6% saved)
Precisions: Click to see histograms. Total time spent on operations: 5.0ms
Operation ival-div, time spent: 2.0ms, 43.0% of total-time
Operation ival-expm1, time spent: 2.0ms, 43.0% of total-time
Operation const, time spent: 0.0ms, 0.0% 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)

regimes6.0ms (0.3%)

Accuracy

Total -33.1b remaining (-∞%)

Threshold costs -33.1b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)

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

Calls

2 calls:

3.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 (exp.f64 x) 1) 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)

soundness169.0ms (8.8%)

Rules

1782×	`div-sub`
1494×	`fma-neg`
1012×	`times-frac`
636×	`distribute-lft-neg-in`
552×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	39	88
2	68	86
3	147	80
4	384	80
5	1036	80
6	4095	80
7	7627	80

Stop Event

1×	node limit

Compiler

Compiled 11 to 7 computations (36.4% saved)

end0.0ms (0%)

preprocess37.0ms (1.9%)

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

analyze2.0ms (0.1%)

sample1.5s (76.4%)

preprocess212.0ms (11.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize22.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes6.0ms (0.3%)

simplify2.0ms (0.1%)

soundness169.0ms (8.8%)

end0.0ms (0%)

preprocess37.0ms (1.9%)

Profiling