Details

Time bar (total: 11.0s)

sample274.0ms

Algorithm
intervals
Results
90.0ms252×body80valid
54.0ms45×body1280valid
29.0ms34×body640valid
11.0ms18×body320valid
3.0msbody160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
51130
4249
399
263
135
019

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.7b
(* (atan2 x.im x.re) y.re)
1.7b
(pow (exp y.im) (atan2 x.im x.re))
31.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
175×add-sqr-sqrt
173×*-un-lft-identity add-cube-cbrt
153×unpow-prod-down
51×sqr-pow
29×add-exp-log
25×associate-/r*
21×div-exp
11×add-cbrt-cube
div-inv
pow-to-exp pow-exp
pow1 associate-/l*
expm1-log1p-u pow-pow log1p-expm1-u add-log-exp
cbrt-undiv pow-unpow exp-prod associate-*r* associate-*l*
cos-sum clear-num frac-2neg pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 286
Calls
4 calls:
48.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
11.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(pow (exp y.im) (atan2 x.im x.re))
7.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
481.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
33.0ms
(* (atan2 x.im x.re) y.re)
48.0ms
(pow (exp y.im) (atan2 x.im x.re))
240.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify889.0ms

Counts
298 → 298
Iterations
IterNodes
done5000
11415
0529

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp 1) (* (atan2 x.im x.re) y.im)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.1b
(* (atan2 x.im x.re) y.im)
1.7b
(* (atan2 x.im x.re) y.re)
31.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
176×add-sqr-sqrt
172×*-un-lft-identity add-cube-cbrt
150×unpow-prod-down
50×sqr-pow
31×add-exp-log
25×associate-/r*
21×div-exp
13×add-cbrt-cube
div-inv
pow1
pow-to-exp pow-exp associate-/l*
associate-*r* associate-*l*
expm1-log1p-u log1p-expm1-u add-log-exp
cbrt-undiv
pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
cos-sum clear-num frac-2neg associate-/r/ fma-udef
Counts
4 → 284
Calls
4 calls:
42.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp 1) (* (atan2 x.im x.re) y.im)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
10.0ms
(* (atan2 x.im x.re) y.im)
11.0ms
(* (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)))

series825.0ms

Counts
4 → 12
Calls
4 calls:
543.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp 1) (* (atan2 x.im x.re) y.im)) (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
32.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(* (atan2 x.im x.re) y.re)
215.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify790.0ms

Counts
296 → 296
Iterations
IterNodes
done5000
11426
0536

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize2.0ms