Details

Time bar (total: 16.6s)

sample357.0ms

Algorithm
intervals
Results
36.0ms59×body1280valid
23.0ms250×body80valid
21.0ms50×body640valid
5.0ms16×body320valid
2.0ms1×body2560valid
1.0ms6×body160valid

simplify349.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01937
13526
26325
39825
421525
588225
done500025

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
0.6b
(* (atan2 x.im x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt
13×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
5×prod-exp
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac associate-/r* cbrt-unprod
2×cbrt-undiv pow-prod-down *-commutative unswap-sqr
1×pow-to-exp frac-2neg sin-sum pow-exp clear-num fma-udef div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
6.0ms
(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (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)))

series602.0ms

Counts
4 → 12
Calls
4 calls:
397.0ms
(/ (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))) (exp (* (atan2 x.im x.re) y.im)))
16.0ms
(* (atan2 x.im x.re) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
172.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify447.0ms

Counts
87 → 87
Iterations

Useful iterations: done (444.0ms)

IterNodesCost
01531462
13371430
211431222
done50001215

prune368.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize26.0ms

Local error

Found 4 expressions with local error:

20.7b
(cos (* (atan2 x.im x.re) y.re))
20.7b
(sin (* (atan2 x.im x.re) y.re))
22.5b
(sin (* (log (hypot x.re x.im)) y.im))
22.5b
(cos (* (log (hypot x.re x.im)) y.im))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 36
Calls
4 calls:
2.0ms
(cos (* (atan2 x.im x.re) y.re))
2.0ms
(sin (* (atan2 x.im x.re) y.re))
2.0ms
(sin (* (log (hypot x.re x.im)) y.im))
2.0ms
(cos (* (log (hypot x.re x.im)) y.im))

series338.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(cos (* (atan2 x.im x.re) y.re))
36.0ms
(sin (* (atan2 x.im x.re) y.re))
122.0ms
(sin (* (log (hypot x.re x.im)) y.im))
125.0ms
(cos (* (log (hypot x.re x.im)) y.im))

simplify3.8s

Counts
48 → 48
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
065431
189425
2131371
3199368
4397368
51165368
done5000368

prune318.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (exp (* (atan2 x.im x.re) y.im)) (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
0.6b
(* (atan2 x.im x.re) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt
13×add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×associate-*r* associate-*l*
5×prod-exp
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac cbrt-unprod associate-/l*
2×cbrt-undiv pow-prod-down *-commutative unswap-sqr
1×pow-to-exp frac-2neg sin-sum pow-exp clear-num associate-/r* fma-udef div-inv
Counts
4 → 75
Calls
4 calls:
5.0ms
(/ (exp (* (atan2 x.im x.re) y.im)) (* (pow (hypot x.re x.im) y.re) (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))))
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
367.0ms
(/ (exp (* (atan2 x.im x.re) y.im)) (* (pow (hypot x.re x.im) y.re) (sin (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)
17.0ms
(* (atan2 x.im x.re) y.im)
155.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify464.0ms

Counts
87 → 87
Iterations

Useful iterations: done (462.0ms)

IterNodesCost
01801492
14041457
212661259
done50001253

prune392.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.7b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite7.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
1.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
1.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (atan2 x.im x.re) y.im)
151.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
155.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
154.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts
62 → 62
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
070827
1124818
2288726
3539720
4963720
52457720
done5001720

prune368.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.4b

regimes292.0ms

Accuracy

12.1% (4.9b remaining)

Error of 8.4b against oracle of 3.5b and baseline of 9.1b

bsearch195.0ms

Steps
ItersRangePoint
7
1.3309592285936424e+88
4.572907920869157e+89
2.2092076921331203e+89
8
-1.9084804576299814e+188
-1.7196627288471757e+184
-3.853834220586221e+184

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046100
161100
263100
done63100

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2240×body1280valid
686.0ms7959×body80valid
594.0ms1492×body640valid
160.0ms577×body320valid
63.0ms42×body2560valid
43.0ms223×body160valid