Details

Time bar (total: 30.5s)

sample407.0ms

Algorithm
intervals
Results
113.0ms259×body80valid
80.0ms62×body1280valid
38.0ms43×body640valid
15.0ms23×body320valid
6.0ms16×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01937
13526
26325
39625
421525
584325
done500025

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.7b

localize60.0ms

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))
1.4b
(* (atan2 x.im x.re) y.re)
2.3b
(* (atan2 x.im x.re) y.im)
34.6b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite40.0ms

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:
1.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
14.0ms
(* (atan2 x.im x.re) y.re)
13.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(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:
211.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
27.0ms
(* (atan2 x.im x.re) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
274.0ms
(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 (426.0ms)

IterNodesCost
0101729
1177720
2412634
3803630
41494630
54360630
done5000630

prune535.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize75.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.re)
2.3b
(* (atan2 x.im x.re) y.im)
34.8b
(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)))))

rewrite97.0ms

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:
14.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
43.0ms
(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)))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
252.0ms
(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)))))

simplify4.9s

Counts
81 → 81
Iterations

Useful iterations: 3 (312.0ms)

IterNodesCost
0851008
1156998
2375620
3669588
4925588
51602588
63531588
done5001588

prune676.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize61.0ms

Local error

Found 4 expressions with local error:

6.0b
(cbrt (atan2 x.im x.re))
6.0b
(cbrt (atan2 x.im x.re))
6.0b
(cbrt (atan2 x.im x.re))
34.6b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum fma-udef
Counts
4 → 49
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))
3.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(cbrt (atan2 x.im x.re))
81.0ms
(cbrt (atan2 x.im x.re))
76.0ms
(cbrt (atan2 x.im x.re))
232.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.8s

Counts
61 → 61
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
054529
182516
2134456
3235445
4567445
52110445
done5000445

prune450.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize47.0ms

Local error

Found 4 expressions with local error:

6.0b
(cbrt (atan2 x.im x.re))
6.0b
(cbrt (atan2 x.im x.re))
6.0b
(cbrt (atan2 x.im x.re))
34.6b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×cos-sum fma-udef
Counts
4 → 49
Calls
4 calls:
2.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cbrt (atan2 x.im x.re))
5.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(cbrt (atan2 x.im x.re))
54.0ms
(cbrt (atan2 x.im x.re))
75.0ms
(cbrt (atan2 x.im x.re))
222.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts
61 → 61
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
054529
182516
2134456
3235445
4567445
52110445
done5000445

prune516.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

regimes487.0ms

Accuracy

75.5% (0.8b remaining)

Error of 5.9b against oracle of 5.1b and baseline of 8.4b

bsearch4.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
038117
149117
done49117

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.1s2021×body1280valid
2.1s7972×body80valid
1.3s1427×body640valid
408.0ms674×body320valid
110.0ms326×body160valid