Metrics for math.log/1 on complex, real part

analyze72.0ms (4.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
18.8%	18.7%	81.2%	0.1%	0%	0%	0%	5
34.4%	34.3%	65.6%	0.1%	0%	0%	0%	6
54.7%	54.6%	45.3%	0.1%	0%	0%	0%	7
64.8%	64.8%	35.1%	0.1%	0%	0%	0%	8
76.2%	76.1%	23.8%	0.1%	0%	0%	0%	9
81.8%	81.8%	18.1%	0.1%	0%	0%	0%	10
87.8%	87.7%	12.2%	0.1%	0%	0%	0%	11
90.8%	90.7%	9.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 12 to 8 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

Operation ival-mult, time spent: 17.0ms, 43.0% of total-time

Operation ival-log, time spent: 9.0ms, 23.0% of total-time

Operation ival-sqrt, time spent: 8.0ms, 20.0% of total-time

Operation ival-add, time spent: 4.0ms, 10.0% of total-time

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

sample1.4s (78.3%)

Results

1.1s	8255×	256	valid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 435.0ms

Operation ival-log, time spent: 153.0ms, 35.0% of total-time

Operation ival-mult, time spent: 140.0ms, 32.0% of total-time

Operation ival-sqrt, time spent: 79.0ms, 18.0% of total-time

Operation ival-add, time spent: 54.0ms, 12.0% of total-time

Operation const, time spent: 9.0ms, 2.0% of total-time

Bogosity

preprocess198.0ms (11.2%)

Algorithm

1×	egg-herbie

Rules

52×	`fma-neg`
45×	`fma-define`
15×	`neg-sub0`
14×	`distribute-lft-neg-in`
14×	`unsub-neg`

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
129	-	1	(5.2174599389134434e-164 4.933983366155964e-158)	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
0	-	0	-	`(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))`
0	-	0	-	`im`
0	-	0	-	`(*.f64 im im)`
0	-	0	-	`(*.f64 re re)`
0	-	0	-	`re`
0	-	0	-	`(+.f64 (.f64 re re) (.f64 im im))`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	127
1	55	127
2	102	127
3	187	127
4	284	127
5	323	127
6	333	127

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im)))))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im)))))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im))))))
(log.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))))

Outputs
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im))))
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im)))))
(log.f64 (hypot.f64 re im))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (neg.f64 re) (neg.f64 re)) (.f64 im im)))))
(neg.f64 (log.f64 (hypot.f64 re im)))
(neg.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 (neg.f64 im) (neg.f64 im))))))
(neg.f64 (log.f64 (hypot.f64 re im)))
(log.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))))
(log.f64 (hypot.f64 re im))

Symmetry

(abs re)

(abs im)

(sort re im)

Results

99.0ms	511×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 81 to 23 computations (71.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

Operation ival-log, time spent: 9.0ms, 34.0% of total-time

Operation ival-mult, time spent: 9.0ms, 34.0% of total-time

Operation ival-sqrt, time spent: 5.0ms, 19.0% of total-time

Operation ival-add, time spent: 3.0ms, 11.0% of total-time

Operation const, time spent: 1.0ms, 4.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (hypot.f64 re im))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize39.0ms (2.2%)

Results

30.0ms	255×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

Operation composed, time spent: 9.0ms, 41.0% of total-time

Operation ival-log, time spent: 5.0ms, 23.0% of total-time

Operation ival-mult, time spent: 4.0ms, 18.0% of total-time

Operation ival-add, time spent: 2.0ms, 9.0% of total-time

Operation ival-sqrt, time spent: 2.0ms, 9.0% of total-time

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

eval0.0ms (0%)

Compiler: Compiled 2 to 2 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%	(log.f64 (hypot.f64 re im))

Compiler

Compiled 21 to 13 computations (38.1% saved)

regimes10.0ms (0.6%)

Accuracy

Total -31.0b remaining (-∞%)

Threshold costs -31b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(log.f64 (hypot.f64 re im))
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Outputs
(log.f64 (hypot.f64 re im))

Calls

7 calls:

2.0ms	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
1.0ms	re
1.0ms	im
1.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
1.0ms	(+.f64 (.f64 re re) (.f64 im im))

Results

Accuracy	Segments	Branch
100.0%	1	`re`
100.0%	1	`im`
100.0%	1	`(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
100.0%	1	`(+.f64 (.f64 re re) (.f64 im im))`
100.0%	1	`(*.f64 re re)`
100.0%	1	`(*.f64 im im)`

Compiler

Compiled 46 to 28 computations (39.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f64 (hypot.f64 re im))

Outputs
(log.f64 (hypot.f64 re im))

Compiler

Compiled 6 to 4 computations (33.3% saved)

soundness24.0ms (1.4%)

Rules

52×	`fma-neg`
45×	`fma-define`
15×	`neg-sub0`
14×	`distribute-lft-neg-in`
14×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	127
1	55	127
2	102	127
3	187	127
4	284	127
5	323	127
6	333	127

Stop Event

1×

saturated

Compiler

Compiled 15 to 9 computations (40% saved)

end0.0ms (0%)

preprocess34.0ms (1.9%)

Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 106 to 70 computations (34% saved)

analyze72.0ms (4.1%)

sample1.4s (78.3%)

preprocess198.0ms (11.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize39.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes10.0ms (0.6%)

simplify2.0ms (0.1%)

soundness24.0ms (1.4%)

end0.0ms (0%)

preprocess34.0ms (1.9%)

Profiling