Details

Time bar (total: 25.8s)

sample362.0ms

Algorithm
intervals
Results
92.0ms55×body1280valid
89.0ms40×body640valid
73.0ms250×body80valid
14.0ms15×body320valid
5.0ms11×body160valid

simplify2.3s

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
1.4b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
35.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite34.0ms

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:
7.0ms
(* y.re (log (hypot x.re x.im)))
13.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* y.re (log (hypot x.re x.im)))
20.0ms
(* (atan2 x.im x.re) y.re)
24.0ms
(* (atan2 x.im x.re) y.im)
181.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify967.0ms

Counts
93 → 93
Iterations
IterNodes
done5001
21092
1302
0150

prune839.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize81.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
35.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
35.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 54
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (atan2 x.im x.re) y.im)
144.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
158.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (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)))

simplify3.3s

Counts
66 → 66
Iterations
IterNodes
done5001
34405
2595
1160
082

prune708.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.2b

localize68.0ms

Local error

Found 4 expressions with local error:

4.6b
(cbrt (atan2 x.im x.re))
4.6b
(cbrt (atan2 x.im x.re))
4.6b
(cbrt (atan2 x.im x.re))
34.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum fma-udef
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(cbrt (atan2 x.im x.re))
51.0ms
(cbrt (atan2 x.im x.re))
47.0ms
(cbrt (atan2 x.im x.re))
177.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify1.4s

Counts
65 → 65
Iterations
IterNodes
done5000
31456
2353
1129
070

prune602.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.2b

localize79.0ms

Local error

Found 4 expressions with local error:

4.6b
(cbrt (atan2 x.im x.re))
4.6b
(cbrt (atan2 x.im x.re))
4.6b
(cbrt (atan2 x.im x.re))
34.6b
(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum fma-udef
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
1.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

series356.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(cbrt (atan2 x.im x.re))
71.0ms
(cbrt (atan2 x.im x.re))
61.0ms
(cbrt (atan2 x.im x.re))
148.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (* (* (cbrt (cbrt (atan2 x.im x.re))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (cbrt (atan2 x.im x.re)))) (cbrt (atan2 x.im x.re))) (* (cbrt (atan2 x.im x.re)) y.re))))

simplify1.6s

Counts
65 → 65
Iterations
IterNodes
done5000
31867
2388
1135
072

prune551.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.2b

regimes454.0ms

Accuracy

0% (0.0b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done23
123
018

end0.0ms

sample10.9s

Algorithm
intervals
Results
4.5s1988×body1280valid
2.8s7962×body80valid
2.2s1502×body640valid
646.0ms609×body320valid
263.0ms333×body160valid