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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze87.0ms (3.3%)

Memory

15.8MiB live, 62.0MiB allocated; 52ms collecting garbage

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 11 to 6 computations (45.5% saved)

sample1.1s (40.7%)

Memory

-12.9MiB live, 643.7MiB allocated; 345ms collecting garbage

Samples

759.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 489.0ms

ival-hypot: 366.0ms (74.9% of total)

ival-log: 121.0ms (24.8% of total)

adjust: 2.0ms (0.4% of total)

Bogosity

preprocess87.0ms (3.2%)

Memory

45.9MiB live, 45.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
1	71	56
2	177	56
3	260	56
4	644	56
5	3845	56

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.3%	(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Symmetry

(abs re)

(abs im)

(sort re im)

Compiler

Compiled 18 to 14 computations (22.2% saved)

series160.0ms (6%)

Memory

-28.9MiB live, 111.4MiB allocated; 38ms collecting garbage

Counts

7 → 53

Calls

Call 1

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

Outputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 6 binary64)))) (.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 4 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (sqrt.f64 (pow.f64 im #s(literal 2 binary64))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (+ (* re re) (* im im)) (pow.f64 im #s(literal 2 binary64)))
#s(approx (+ (* re re) (* im im)) (+.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))
#s(approx (* re re) (pow.f64 re #s(literal 2 binary64)))
#s(approx re re)
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 im #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 im #s(literal 6 binary64)))) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (+ (* re re) (* im im)) (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 im #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 im #s(literal 6 binary64)))) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 6 binary64)))) (.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 4 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (sqrt.f64 (pow.f64 re #s(literal 2 binary64))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx im im)
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 re #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 re #s(literal 6 binary64)))) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (+ (* re re) (* im im)) (*.f64 (pow.f64 im #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 re #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 re #s(literal 6 binary64)))) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))))

Calls

6 calls:

Time	Variable	Point
23.0ms	re	0
4.0ms	re	inf
4.0ms	im	-inf
3.0ms	im	inf
3.0ms	im	0

rewrite152.0ms (5.7%)

Memory

1.6MiB live, 187.4MiB allocated; 40ms collecting garbage

Counts

7 → 42

Calls

Call 1

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

Outputs
(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(fabs.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(hypot.f64 re im)
(hypot.f64 im re)
(hypot.f64 (neg.f64 re) im)
(hypot.f64 (neg.f64 re) (neg.f64 im))
(hypot.f64 (neg.f64 re) (fabs.f64 im))
(hypot.f64 (fabs.f64 re) im)
(hypot.f64 (fabs.f64 re) (neg.f64 im))
(hypot.f64 (fabs.f64 re) (fabs.f64 im))
(hypot.f64 (neg.f64 im) re)
(hypot.f64 (neg.f64 im) (neg.f64 re))
(hypot.f64 (neg.f64 im) (fabs.f64 re))
(hypot.f64 (fabs.f64 im) re)
(hypot.f64 (fabs.f64 im) (neg.f64 re))
(hypot.f64 (fabs.f64 im) (fabs.f64 re))
(hypot.f64 re (neg.f64 im))
(hypot.f64 re (fabs.f64 im))
(hypot.f64 im (neg.f64 re))
(hypot.f64 im (fabs.f64 re))
(pow.f64 (fma.f64 re re (*.f64 im im)) #s(literal 1/2 binary64))
(sqrt.f64 (fma.f64 re re (*.f64 im im)))
(+.f64 (.f64 re re) (.f64 im im))
(+.f64 (.f64 im im) (.f64 re re))
(-.f64 (.f64 re re) (neg.f64 (.f64 im im)))
(-.f64 (.f64 re re) (.f64 (neg.f64 im) im))
(fma.f64 (neg.f64 re) (neg.f64 re) (*.f64 im im))
(fma.f64 (fabs.f64 re) (fabs.f64 re) (*.f64 im im))
(fma.f64 (neg.f64 im) (neg.f64 im) (*.f64 re re))
(fma.f64 (fabs.f64 im) (fabs.f64 im) (*.f64 re re))
(fma.f64 re re (*.f64 im im))
(fma.f64 im im (*.f64 re re))
(*.f64 re re)
(*.f64 (neg.f64 re) (neg.f64 re))
(*.f64 (fabs.f64 re) (fabs.f64 re))
(pow.f64 re #s(literal 2 binary64))
re
(*.f64 im im)
(*.f64 (neg.f64 im) (neg.f64 im))
(*.f64 (fabs.f64 im) (fabs.f64 im))
(pow.f64 im #s(literal 2 binary64))
im

eval19.0ms (0.7%)

Memory: 19.4MiB live, 19.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 862 to 378 computations (79.7% saved)

prune6.0ms (0.2%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Accuracy

100.0%

Counts

91 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (hypot.f64 re im))
	46.3%	(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
▶	0.0%	(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re)))
▶	0.0%	(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im)))
▶	10.2%	#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
▶	99.2%	#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))

Compiler

Compiled 140 to 112 computations (20% saved)

series344.0ms (12.9%)

Memory

-23.4MiB live, 135.9MiB allocated; 78ms collecting garbage

Counts

20 → 56

Calls

Call 1

Inputs
(log.f64 (hypot.f64 re im))
(hypot.f64 re im)
re
im
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im)))
#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im))
(*.f64 #s(literal -1 binary64) im)
#s(literal -1 binary64)
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re)))
#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re))
(*.f64 #s(literal -1 binary64) re)
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)))
(log.f64 (/.f64 #s(literal 1 binary64) im))
(/.f64 #s(literal 1 binary64) im)
#s(literal 1 binary64)
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)))
(log.f64 (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) re)

Outputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 6 binary64)))) (.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 4 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (sqrt.f64 (pow.f64 im #s(literal 2 binary64))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx re re)
#s(approx (* -1 re) (*.f64 #s(literal -1 binary64) re))
#s(approx (* -1 (log (/ 1 re))) (log.f64 re))
#s(approx (log (/ 1 re)) (*.f64 #s(literal -1 binary64) (log.f64 re)))
#s(approx (/ 1 re) (/.f64 #s(literal 1 binary64) re))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 im #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 im #s(literal 6 binary64)))) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (log (/ 1 re)) (log.f64 (/.f64 #s(literal 1 binary64) re)))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 im #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 im #s(literal 6 binary64)))) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 6 binary64)))) (.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 4 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (sqrt.f64 (pow.f64 re #s(literal 2 binary64))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx im im)
#s(approx (* -1 im) (*.f64 #s(literal -1 binary64) im))
#s(approx (* -1 (log (/ 1 im))) (log.f64 im))
#s(approx (log (/ 1 im)) (*.f64 #s(literal -1 binary64) (log.f64 im)))
#s(approx (/ 1 im) (/.f64 #s(literal 1 binary64) im))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 re #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 re #s(literal 6 binary64)))) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (log (/ 1 im)) (log.f64 (/.f64 #s(literal 1 binary64) im)))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 re #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 re #s(literal 6 binary64)))) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))))

Calls

6 calls:

Time	Variable	Point
84.0ms	im	-inf
63.0ms	re	0
28.0ms	im	0
17.0ms	re	inf
10.0ms	re	-inf

rewrite140.0ms (5.3%)

Memory

6.6MiB live, 53.5MiB allocated; 3ms collecting garbage

Counts

20 → 61

Calls

Call 1

Inputs
(log.f64 (hypot.f64 re im))
(hypot.f64 re im)
re
im
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im)))
#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im))
(*.f64 #s(literal -1 binary64) im)
#s(literal -1 binary64)
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re)))
#s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re))
(*.f64 #s(literal -1 binary64) re)
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)))
(log.f64 (/.f64 #s(literal 1 binary64) im))
(/.f64 #s(literal 1 binary64) im)
#s(literal 1 binary64)
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)))
(log.f64 (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) re)

Outputs
(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(fabs.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(hypot.f64 re im)
(hypot.f64 im re)
(hypot.f64 (neg.f64 re) im)
(hypot.f64 (neg.f64 re) (neg.f64 im))
(hypot.f64 (neg.f64 re) (fabs.f64 im))
(hypot.f64 (fabs.f64 re) im)
(hypot.f64 (fabs.f64 re) (neg.f64 im))
(hypot.f64 (fabs.f64 re) (fabs.f64 im))
(hypot.f64 (neg.f64 im) re)
(hypot.f64 (neg.f64 im) (neg.f64 re))
(hypot.f64 (neg.f64 im) (fabs.f64 re))
(hypot.f64 (fabs.f64 im) re)
(hypot.f64 (fabs.f64 im) (neg.f64 re))
(hypot.f64 (fabs.f64 im) (fabs.f64 re))
(hypot.f64 re (neg.f64 im))
(hypot.f64 re (fabs.f64 im))
(hypot.f64 im (neg.f64 re))
(hypot.f64 im (fabs.f64 re))
(pow.f64 (fma.f64 re re (*.f64 im im)) #s(literal 1/2 binary64))
(sqrt.f64 (fma.f64 re re (*.f64 im im)))
re
im
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im))
(*.f64 #s(literal -1 binary64) im)
(*.f64 im #s(literal -1 binary64))
(neg.f64 im)
#s(literal -1 binary64)
(neg.f64 #s(literal 1 binary64))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(*.f64 #s(literal -1 binary64) re)
(*.f64 re #s(literal -1 binary64))
(neg.f64 re)
#s(approx (log (sqrt (+ (* re re) (* im im)))) (neg.f64 (neg.f64 (log.f64 im))))
(*.f64 (neg.f64 (log.f64 im)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (log.f64 im)))
(log.f64 (pow.f64 (/.f64 #s(literal 1 binary64) im) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (log.f64 im)))
(log.f64 (/.f64 #s(literal 1 binary64) im))
(neg.f64 (log.f64 im))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) im))
(/.f64 #s(literal 1 binary64) im)
(/.f64 #s(literal -1 binary64) (neg.f64 im))
(pow.f64 im #s(literal -1 binary64))
#s(literal 1 binary64)
(cosh.f64 #s(literal 0 binary64))
(exp.f64 #s(literal 0 binary64))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (neg.f64 (neg.f64 (log.f64 re))))
(*.f64 (neg.f64 (log.f64 re)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (log.f64 re)))
(log.f64 (pow.f64 (/.f64 #s(literal 1 binary64) re) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (log.f64 re)))
(log.f64 (/.f64 #s(literal 1 binary64) re))
(neg.f64 (log.f64 re))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) re))
(/.f64 #s(literal 1 binary64) re)
(/.f64 #s(literal -1 binary64) (neg.f64 re))
(pow.f64 re #s(literal -1 binary64))

eval23.0ms (0.9%)

Memory: -30.8MiB live, 15.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 2 304 to 435 computations (81.1% saved)

prune24.0ms (0.9%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	0	1	1
Picked	4	1	5
Done	0	0	0
Total	111	6	117

Accuracy

100.0%

Counts

117 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (hypot.f64 re im))
▶	46.3%	(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
▶	0.0%	(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
▶	0.0%	(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
▶	10.2%	#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 re))) (log.f64 re)))
▶	99.2%	#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 im))) (log.f64 im)))

Compiler

Compiled 144 to 112 computations (22.2% saved)

series280.0ms (10.5%)

Memory

40.7MiB live, 184.1MiB allocated; 24ms collecting garbage

Counts

18 → 55

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 im))) (log.f64 im)))
#s(approx (* -1 (log (/ 1 im))) (log.f64 im))
(log.f64 im)
im
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 re))) (log.f64 re)))
#s(approx (* -1 (log (/ 1 re))) (log.f64 re))
(log.f64 re)
re
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im))
(neg.f64 im)
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(neg.f64 re)
(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(sqrt.f64 (fma.f64 re re (*.f64 im im)))
(fma.f64 re re (*.f64 im im))
(*.f64 im im)

Outputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 6 binary64)))) (.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 4 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (* -1 (log (/ 1 re))) (log.f64 re))
#s(approx re re)
#s(approx (sqrt (+ (* re re) (* im im))) (sqrt.f64 (pow.f64 im #s(literal 2 binary64))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) (.f64 (pow.f64 re #s(literal 2 binary64)) (fma.f64 (pow.f64 re #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 im #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (neg re) (*.f64 #s(literal -1 binary64) re))
#s(approx (+ (* re re) (* im im)) (pow.f64 im #s(literal 2 binary64)))
#s(approx (+ (* re re) (* im im)) (+.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 im #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 im #s(literal 6 binary64)))) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (+ (* re re) (* im im)) (pow.f64 re #s(literal 2 binary64)))
#s(approx (+ (* re re) (* im im)) (*.f64 (pow.f64 re #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) re)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 im #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 im #s(literal 6 binary64)))) (pow.f64 re #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 re (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 4 binary64)) (pow.f64 re #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 6 binary64)) (pow.f64 re #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 re #s(literal 2 binary64))))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/6 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 6 binary64)))) (.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 4 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 2 binary64))))))))
#s(approx (* -1 (log (/ 1 im))) (log.f64 im))
#s(approx im im)
#s(approx (sqrt (+ (* re re) (* im im))) (sqrt.f64 (pow.f64 re #s(literal 2 binary64))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 3 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (+.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) (.f64 (pow.f64 im #s(literal 2 binary64)) (fma.f64 (pow.f64 im #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 im #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 5 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (pow.f64 re #s(literal 2 binary64))) #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 re #s(literal 2 binary64)))))))))
#s(approx (neg im) (*.f64 #s(literal -1 binary64) im))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 re #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 re #s(literal 6 binary64)))) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (+ (* re re) (* im im)) (*.f64 (pow.f64 im #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal -1 binary64) im)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/720 binary64) (/.f64 (fma.f64 #s(literal 30 binary64) (pow.f64 re #s(literal 6 binary64)) (.f64 #s(literal 90 binary64) (pow.f64 re #s(literal 6 binary64)))) (pow.f64 im #s(literal 6 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64)))))))))
#s(approx (sqrt (+ (* re re) (* im im))) (.f64 #s(literal -1 binary64) (.f64 im (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 re #s(literal 4 binary64)) (pow.f64 im #s(literal 4 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 re #s(literal 6 binary64)) (pow.f64 im #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 re #s(literal 2 binary64)) (pow.f64 im #s(literal 2 binary64))))))))))

Calls

6 calls:

Time	Variable	Point
56.0ms	im	-inf
26.0ms	re	inf
24.0ms	re	0
19.0ms	im	0
15.0ms	re	-inf

rewrite178.0ms (6.7%)

Memory

-1.9MiB live, 96.9MiB allocated; 11ms collecting garbage

Counts

18 → 50

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 im))) (log.f64 im)))
#s(approx (* -1 (log (/ 1 im))) (log.f64 im))
(log.f64 im)
im
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 re))) (log.f64 re)))
#s(approx (* -1 (log (/ 1 re))) (log.f64 re))
(log.f64 re)
re
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im))
(neg.f64 im)
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(neg.f64 re)
(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(sqrt.f64 (fma.f64 re re (*.f64 im im)))
(fma.f64 re re (*.f64 im im))
(*.f64 im im)

Outputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (neg (neg (log im))) (log.f64 im)))
#s(approx (neg (neg (log im))) (log.f64 im))
(log.f64 im)
im
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (neg (neg (log re))) (log.f64 re)))
#s(approx (neg (neg (log re))) (log.f64 re))
(log.f64 re)
re
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im))
(neg.f64 im)
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
#s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re))
(neg.f64 re)
(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(fabs.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(hypot.f64 re im)
(hypot.f64 im re)
(hypot.f64 (neg.f64 re) im)
(hypot.f64 (neg.f64 re) (neg.f64 im))
(hypot.f64 (neg.f64 re) (fabs.f64 im))
(hypot.f64 (fabs.f64 re) im)
(hypot.f64 (fabs.f64 re) (neg.f64 im))
(hypot.f64 (fabs.f64 re) (fabs.f64 im))
(hypot.f64 (neg.f64 im) re)
(hypot.f64 (neg.f64 im) (neg.f64 re))
(hypot.f64 (neg.f64 im) (fabs.f64 re))
(hypot.f64 (fabs.f64 im) re)
(hypot.f64 (fabs.f64 im) (neg.f64 re))
(hypot.f64 (fabs.f64 im) (fabs.f64 re))
(hypot.f64 re (neg.f64 im))
(hypot.f64 re (fabs.f64 im))
(hypot.f64 im (neg.f64 re))
(hypot.f64 im (fabs.f64 re))
(pow.f64 (fma.f64 re re (*.f64 im im)) #s(literal 1/2 binary64))
(sqrt.f64 (fma.f64 re re (*.f64 im im)))
(+.f64 (.f64 re re) (.f64 im im))
(+.f64 (.f64 im im) (.f64 re re))
(-.f64 (.f64 re re) (neg.f64 (.f64 im im)))
(-.f64 (.f64 re re) (.f64 (neg.f64 im) im))
(fma.f64 re re (*.f64 im im))
(fma.f64 (neg.f64 re) (neg.f64 re) (*.f64 im im))
(fma.f64 (fabs.f64 re) (fabs.f64 re) (*.f64 im im))
(fma.f64 (neg.f64 im) (neg.f64 im) (*.f64 re re))
(fma.f64 (fabs.f64 im) (fabs.f64 im) (*.f64 re re))
(fma.f64 im im (*.f64 re re))
(*.f64 im im)
(*.f64 (neg.f64 im) (neg.f64 im))
(*.f64 (fabs.f64 im) (fabs.f64 im))
(pow.f64 im #s(literal 2 binary64))

eval11.0ms (0.4%)

Memory: -31.8MiB live, 15.3MiB allocated; 1ms collecting garbage
Compiler: Compiled 1 951 to 401 computations (79.4% saved)

prune3.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	92	6	98

Accuracy

100.0%

Counts

98 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (hypot.f64 re im))
✓	46.3%	(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
✓	0.0%	(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
✓	0.0%	(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
✓	10.2%	#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 re))) (log.f64 re)))
✓	99.2%	#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 im))) (log.f64 im)))

Compiler

Compiled 74 to 58 computations (21.6% saved)

regimes45.0ms (1.7%)

Memory

20.1MiB live, 67.4MiB allocated; 1ms collecting garbage

Accuracy

Total -63.5b remaining (-11781%)

Threshold costs -63.5b (-11781%)

Counts

10 → 1

11 → 1

Calls

Call 1

Inputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 im))) (log.f64 im)))
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 re))) (log.f64 re)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re)))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))

Outputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 im))) (log.f64 im)))

Call 2

Inputs
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 im))) (log.f64 im)))
#s(approx (log (sqrt (+ (* re re) (* im im)))) #s(approx (* -1 (log (/ 1 re))) (log.f64 re)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 im)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (neg.f64 re)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) im)))
(log.f64 #s(approx (sqrt (+ (* re re) (* im im))) (*.f64 #s(literal -1 binary64) re)))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) im))))
#s(approx (log (sqrt (+ (* re re) (* im im)))) (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(literal 1 binary64) re))))
(log.f64 (sqrt.f64 (fma.f64 re re (*.f64 im im))))
(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
(log.f64 (hypot.f64 re im))

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

Calls

14 calls:

4.0ms	(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	im

Results

Accuracy	Segments	Branch
99.2%	1	`(*.f64 im im)`
99.2%	1	`(*.f64 re re)`
99.2%	1	`(+.f64 (.f64 re re) (.f64 im im))`
99.2%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
99.2%	1	`(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))`
99.2%	1	`re`
99.2%	1	`im`
100.0%	1	`(*.f64 im im)`
100.0%	1	`(*.f64 re re)`
100.0%	1	`(+.f64 (.f64 re re) (.f64 im im))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))`
100.0%	1	`(log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))`
100.0%	1	`re`
100.0%	1	`im`

Compiler

Compiled 205 to 109 computations (46.8% saved)

derivations0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 23 to 17 computations (26.1% saved)

preprocess23.0ms (0.9%)

Memory: -7.0MiB live, 39.9MiB allocated; 2ms collecting garbage
Compiler: Compiled 170 to 138 computations (18.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze87.0ms (3.3%)

sample1.1s (40.7%)

preprocess87.0ms (3.2%)

series160.0ms (6%)

rewrite152.0ms (5.7%)

eval19.0ms (0.7%)

prune6.0ms (0.2%)

series344.0ms (12.9%)

rewrite140.0ms (5.3%)

eval23.0ms (0.9%)

prune24.0ms (0.9%)

series280.0ms (10.5%)

rewrite178.0ms (6.7%)

eval11.0ms (0.4%)

prune3.0ms (0.1%)

regimes45.0ms (1.7%)

derivations0.0ms (0%)

preprocess23.0ms (0.9%)

end0.0ms (0%)

Profiling