Details

Time bar (total: 2.4m)

sample4.1s

Algorithm
intervals
Results
3.8s988×body10240exit
141.0ms256×body80valid

simplify745.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
744.0ms
(* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re))))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

25.9b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
0.3b
(* (atan2 x.im x.re) y.re)
0.3b
(* y.re (log (hypot x.re x.im)))
0.2b
(* (atan2 x.im x.re) y.im)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
Slowest
7.0ms
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
105.0ms
(* y.re (log (hypot x.re x.im)))
32.0ms
(* (atan2 x.im x.re) y.im)
29.0ms
(* (atan2 x.im x.re) y.re)

simplify1.8s

Counts
48 → 93
Calls
48 calls:
Slowest
330.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
295.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.im y.im) y.im))
269.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
267.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
163.0ms
(cos (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

25.9b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.8b
(log (exp (* y.re (log (hypot x.re x.im)))))
0.3b
(* (atan2 x.im x.re) y.re)
0.3b
(* y.re (log (hypot x.re x.im)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
21×log-prod
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×pow1
8×add-cbrt-cube add-exp-log
7×associate-*r*
6×distribute-rgt-in distribute-lft-in associate-*l* exp-sum
5×add-log-exp
4×expm1-log1p-u log-pow insert-posit16 log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum exp-prod exp-to-pow rem-log-exp fma-udef
Counts
4 → 83
Calls
4 calls:
Slowest
7.0ms
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
100.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
95.0ms
(* y.re (log (hypot x.re x.im)))
30.0ms
(* (atan2 x.im x.re) y.re)

simplify3.0s

Counts
50 → 95
Calls
50 calls:
Slowest
323.0ms
(- 1 (+ (* y.im (* (atan2 x.im x.re) (* y.re (log x.im)))) (* 1/2 (* (pow y.im 2) (pow (log x.im) 2)))))
321.0ms
(* (* (* (atan2 x.im x.re) (atan2 x.im x.re)) (atan2 x.im x.re)) (* (* y.re y.re) y.re))
260.0ms
(* (* (* y.re y.re) y.re) (* (* (log (hypot x.re x.im)) (log (hypot x.re x.im))) (log (hypot x.re x.im))))
234.0ms
(log (exp (* (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))) y.re)))
214.0ms
(log (exp (* y.re (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im)))))))

prune1.8s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.0m30557×body10240exit
3.8s8000×body80valid