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

analyze56.0ms (3.6%)

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)

sample1.3s (80.9%)

Results

1.3s

8256×

body

256

valid

Bogosity

preprocess138.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

82×	`fma-def`
40×	`associate-r`
29×	`*-commutative`
26×	`+-commutative`
24×	`associate--r+`

Problems

129×	No Errors
127×	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	127
1	56	127
2	95	127
3	216	127
4	382	127
5	463	127
6	473	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)

Compiler

Compiled 46 to 15 computations (67.4% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize26.0ms (1.7%)

Compiler: Compiled 12 to 5 computations (58.3% saved)

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)

regimes20.0ms (1.3%)

Accuracy

Total -30.8b remaining (-∞%)

Threshold costs -30.8b (-∞%)

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:

3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	im
3.0ms	re
3.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	(log.f64 (sqrt.f64 (+.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 61 to 37 computations (39.3% 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)

soundness25.0ms (1.6%)

Rules

82×	`fma-def`
40×	`associate-r`
29×	`*-commutative`
26×	`+-commutative`
24×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	127
1	56	127
2	95	127
3	216	127
4	382	127
5	463	127
6	473	127

Stop Event

1×

saturated

Compiler

Compiled 15 to 9 computations (40% saved)

end0.0ms (0%)

preprocess30.0ms (1.9%)

Remove

(sort re im)

(abs im)

(abs re)

Compiler

Compiled 106 to 70 computations (34% saved)

analyze56.0ms (3.6%)

sample1.3s (80.9%)

preprocess138.0ms (8.8%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize26.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes20.0ms (1.3%)

simplify2.0ms (0.1%)

soundness25.0ms (1.6%)

end0.0ms (0%)

preprocess30.0ms (1.9%)

Profiling