Details

Time bar (total: 28.5s)

sample364.0ms

Algorithm
intervals
Results
165.0ms77×body1280valid
53.0ms256×body80valid
40.0ms47×body640valid
16.0ms22×body320valid
2.0ms7×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.4b

localize41.0ms

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))
1.0b
(* (atan2 x.im x.re) y.re)
2.1b
(* (atan2 x.im x.re) y.im)
31.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite36.0ms

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×sin-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)
12.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
36.0ms
(* (atan2 x.im x.re) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
321.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.9s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
0101738
1182728
2576646
34394638
done5001638

prune806.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))
0.7b
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
2.1b
(* (atan2 x.im x.re) y.im)
31.8b
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt associate-*r*
10×pow-prod-down prod-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod *-commutative
2×unswap-sqr
1×sin-sum fma-udef
Counts
4 → 77
Calls
4 calls:
158.0ms
(* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))
47.0ms
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
14.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

series517.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))
136.0ms
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
32.0ms
(* (atan2 x.im x.re) y.im)
306.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

simplify1.6s

Counts
89 → 89
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01371193
13151169
218071006
done5001782

prune707.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.7b
(* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))
2.1b
(* (atan2 x.im x.re) y.im)
31.8b
(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity associate-*r* add-cbrt-cube
7×pow-prod-down prod-exp cbrt-unprod
6×cbrt-prod
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×*-commutative
1×sin-sum pow1/3 fma-udef unswap-sqr
Counts
4 → 69
Calls
4 calls:
1.0ms
(cbrt y.re)
81.0ms
(* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))
15.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

series671.0ms

Counts
4 → 12
Calls
4 calls:
338.0ms
(cbrt y.re)
37.0ms
(* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))
26.0ms
(* (atan2 x.im x.re) y.im)
269.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt y.re) (* (atan2 x.im x.re) (cbrt y.re))) (cbrt y.re))))

simplify1.5s

Counts
81 → 81
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0130971
1291951
21311755
done5000595

prune763.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

localize50.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (atan2 x.im x.re) y.im)
31.9b
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
31.9b
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
31.9b
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite18.0ms

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×sin-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
8.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series564.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (atan2 x.im x.re) y.im)
181.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
187.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
160.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify2.6s

Counts
62 → 62
Iterations

Useful iterations: 3 (449.0ms)

IterNodesCost
071827
1128818
2367728
32383720
done5001720

prune615.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

regimes791.0ms

Accuracy

87.3% (0.4b remaining)

Error of 6.2b against oracle of 5.8b and baseline of 8.8b

bsearch5.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
034109
145109
done45109

end0.0ms

sample9.3s

Algorithm
intervals
Results
3.2s2185×body1280valid
2.7s7969×body80valid
1.9s1400×body640valid
365.0ms557×body320valid
116.0ms209×body160valid
111.0ms44×body2560valid