Details

Time bar (total: 11.1s)

sample199.0ms

Algorithm
intervals
Results
67.0ms252×body80valid
34.0ms45×body1280valid
18.0ms34×body640valid
8.0ms18×body320valid
2.0msbody160valid

simplify1.8s

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.4b

localize46.0ms

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)))

rewrite78.0ms

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:
33.0ms
(/ (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)
6.0ms
(pow (exp y.im) (atan2 x.im x.re))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series887.0ms

Counts
4 → 12
Calls
4 calls:
530.0ms
(/ (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)))))
26.0ms
(* (atan2 x.im x.re) y.re)
60.0ms
(pow (exp y.im) (atan2 x.im x.re))
270.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify812.0ms

Counts
298 → 298
Iterations
IterNodes
done5000
11415
0529

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize68.0ms

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)))

rewrite80.0ms

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:
28.0ms
(/ (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)))))
11.0ms
(* (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)))

series762.0ms

Counts
4 → 12
Calls
4 calls:
542.0ms
(/ (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)))))
33.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (atan2 x.im x.re) y.re)
168.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify725.0ms

Counts
296 → 296
Iterations
IterNodes
done5000
11426
0536

prune2.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize1.0ms