Details

Time bar (total: 27.6s)

sample535.0ms

Algorithm
intervals
Results
243.0ms54×body640valid
116.0ms94×body1280valid
44.0ms256×body80valid
13.0ms20×body320valid
6.0ms2×body2560valid
3.0ms9×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.4b

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))
1.0b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

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))
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
10.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series577.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))
37.0ms
(* (atan2 x.im x.re) y.re)
31.0ms
(* (atan2 x.im x.re) y.im)
316.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.6s

Counts
72 → 72
Iterations

Useful iterations: 3 (960.0ms)

IterNodesCost
0101738
1182728
2576646
34394638
done5001638

prune479.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (sin (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)
1.6b
(* (atan2 x.im x.re) y.im)
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

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*
5×expm1-log1p-u
4×log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef sin-sum log1p-expm1 fma-udef
Counts
4 → 61
Calls
4 calls:
1.0ms
(log1p (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
26.0ms
(* (atan2 x.im x.re) y.re)
15.0ms
(* (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)))

series712.0ms

Counts
4 → 12
Calls
4 calls:
386.0ms
(log1p (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
28.0ms
(* (atan2 x.im x.re) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
264.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify648.0ms

Counts
73 → 73
Iterations

Useful iterations: done (645.0ms)

IterNodesCost
0113789
1215777
2751686
done5000677

prune576.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize60.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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 (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
3.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series780.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (atan2 x.im x.re) y.im)
262.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
223.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
269.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.4s

Counts
62 → 62
Iterations

Useful iterations: 3 (540.0ms)

IterNodesCost
070827
1126818
2361728
32318720
done5000720

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize66.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
32.1b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

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:
16.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series731.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (atan2 x.im x.re) y.im)
238.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
233.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
238.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts
62 → 62
Iterations

Useful iterations: 3 (491.0ms)

IterNodesCost
070827
1126818
2361728
32318720
done5000720

prune556.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.2b

regimes698.0ms

Accuracy

81.7% (0.7b remaining)

Error of 6.5b against oracle of 5.9b and baseline of 9.5b

bsearch7.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
035135
144135
done44135

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.9s2244×body1280valid
2.4s7960×body80valid
1.6s1449×body640valid
316.0ms524×body320valid
164.0ms50×body2560valid
85.0ms231×body160valid