Details

Time bar (total: 25.6s)

sample361.0ms

Algorithm
intervals
Results
157.0ms77×body1280valid
52.0ms259×body80valid
38.0ms48×body640valid
16.0ms27×body320valid
1.0ms4×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.2b

localize29.0ms

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)))
1.5b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

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:
18.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
8.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(* (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)))

series546.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
39.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(* (atan2 x.im x.re) y.re)
269.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
109 → 109
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01831590
13481549
212211443
done50001436

prune756.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
1.5b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.9b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite46.0ms

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:
9.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
15.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(* (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)))

series513.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
30.0ms
(* (atan2 x.im x.re) y.im)
26.0ms
(* (atan2 x.im x.re) y.re)
236.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify6.0s

Counts
72 → 72
Iterations

Useful iterations: 3 (973.0ms)

IterNodesCost
0101729
1182720
2565634
34288630
done5000630

prune539.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize47.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.re)
33.5b
(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)))))

rewrite68.0ms

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)
18.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.re)
26.0ms
(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)))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) y.re)
32.0ms
(* (atan2 x.im x.re) y.re)
230.0ms
(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)))))

simplify3.4s

Counts
81 → 81
Iterations

Useful iterations: 3 (536.0ms)

IterNodesCost
0621008
1113998
2352626
32367588
done5001588

prune661.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.5b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.9b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log-pow log1p-expm1-u add-log-exp
3×log-prod exp-prod
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×log-div exp-diff rem-log-exp
Counts
4 → 68
Calls
4 calls:
5.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(* (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)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
23.0ms
(* (atan2 x.im x.re) y.im)
21.0ms
(* (atan2 x.im x.re) y.re)
200.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify745.0ms

Counts
80 → 80
Iterations

Useful iterations: done (741.0ms)

IterNodesCost
0128980
1241931
2839834
done5001824

prune571.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.7b

regimes491.0ms

Accuracy

0% (0.6b remaining)

Error of 3.6b against oracle of 3.0b and baseline of 3.6b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01853
12653
22853
done2853

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.8s1968×body1280valid
1.9s7978×body80valid
1.3s1484×body640valid
350.0ms632×body320valid
86.0ms283×body160valid