Details

Time bar (total: 30.9s)

sample318.0ms

Algorithm
intervals
Results
112.0ms53×body1280valid
39.0ms256×body80valid
31.0ms50×body640valid
6.0ms16×body320valid
3.0ms10×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
0.8b
(* (atan2 x.im x.re) y.im)
1.1b
(* (atan2 x.im x.re) y.re)
33.8b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×times-frac
12×unpow-prod-down
10×add-exp-log add-cbrt-cube
8×pow1
7×associate-/l*
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×div-exp associate-/r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cbrt-undiv pow-to-exp cos-sum frac-2neg pow-exp clear-num fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
17.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
14.0ms
(* (atan2 x.im x.re) y.im)
14.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series528.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
27.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(* (atan2 x.im x.re) y.re)
242.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts
109 → 109
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01831590
13331549
28381441
324071436
done50011435

prune620.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
0.8b
(* (atan2 x.im x.re) y.im)
1.1b
(* (atan2 x.im x.re) y.re)
33.8b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×cos-sum
Counts
4 → 60
Calls
4 calls:
0.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
8.0ms
(* (atan2 x.im x.re) y.im)
13.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series533.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
34.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(* (atan2 x.im x.re) y.re)
244.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify5.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (427.0ms)

IterNodesCost
0101729
1177720
2414634
3809630
41501630
54377630
done5000630

prune479.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

localize45.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
1.1b
(* (atan2 x.im x.re) y.re)
1.1b
(* (atan2 x.im x.re) y.re)
33.8b
(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 69
Calls
4 calls:
8.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.re)
30.0ms
(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (atan2 x.im x.re) y.re)
29.0ms
(* (atan2 x.im x.re) y.re)
32.0ms
(* (atan2 x.im x.re) y.re)
297.0ms
(cos (* (* (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (cbrt (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))

simplify3.8s

Counts
81 → 81
Iterations

Useful iterations: 3 (204.0ms)

IterNodesCost
0621008
1109998
2239620
3424588
4606588
51030588
62152588
done5000588

prune670.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.9b

localize72.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (atan2 x.im x.re) y.re)
33.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.8b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×expm1-log1p-u 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 → 50
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
8.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series664.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (atan2 x.im x.re) y.re)
234.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
222.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
186.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts
62 → 62
Iterations

Useful iterations: done (3.8s)

IterNodesCost
078866
1150857
2352765
3787756
41975750
done5000747

prune592.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.9b

regimes247.0ms

Accuracy

0% (0.6b remaining)

Error of 3.4b against oracle of 2.8b and baseline of 3.4b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01853
12653
22853
done2853

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.4s2082×body1280valid
2.4s7986×body80valid
1.2s1444×body640valid
334.0ms687×body320valid
105.0ms322×body160valid