Details

Time bar (total: 20.5s)

sample259.0ms

Algorithm
intervals
Results
70.0ms80×body1280valid
62.0ms47×body640valid
30.0ms256×body80valid
6.0ms17×body320valid
5.0ms3×body2560valid
3.0ms14×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
01937
13526
26325
39925
423225
5103425
done500025

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
1.7b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
33.3b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

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 frac-2neg sin-sum pow-exp clear-num fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
24.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
14.0ms
(* (atan2 x.im x.re) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (pow (hypot x.re x.im) y.re) (exp (* (atan2 x.im x.re) y.im)))
36.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(* (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)))

simplify1.1s

Counts
109 → 109
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01851599
13531557
212281451
done50001444

prune840.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (hypot x.re x.im)) y.re)
1.7b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
33.3b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
11×pow1
10×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
9×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 71
Calls
4 calls:
8.0ms
(* (log (hypot x.re x.im)) y.re)
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
14.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (log (hypot x.re x.im)) y.re)
29.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
224.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify884.0ms

Counts
83 → 83
Iterations

Useful iterations: done (880.0ms)

IterNodesCost
0120757
1241741
2828655
done5001649

prune593.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize56.0ms

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))))
1.7b
(* (atan2 x.im x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
33.3b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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:
0.0ms
(log1p (sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
15.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (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)))

series651.0ms

Counts
4 → 12
Calls
4 calls:
375.0ms
(log1p (sin (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)
22.0ms
(* (atan2 x.im x.re) y.im)
217.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify698.0ms

Counts
73 → 73
Iterations

Useful iterations: done (696.0ms)

IterNodesCost
0113789
1215777
2751686
done5000677

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
1.7b
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
1.9b
(* (atan2 x.im x.re) y.im)
33.2b
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-sqr-sqrt
9×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cbrt-prod
2×*-commutative unswap-sqr
1×sin-sum pow1/3 fma-udef
Counts
4 → 64
Calls
4 calls:
2.0ms
(cbrt y.re)
49.0ms
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
14.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

series734.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(cbrt y.re)
116.0ms
(* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re))
33.0ms
(* (atan2 x.im x.re) y.im)
327.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (* (cbrt y.re) (cbrt y.re)) (atan2 x.im x.re)) (cbrt y.re))))

simplify1.5s

Counts
76 → 76
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0126845
1281828
21376642
done5000597

prune664.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.0b

regimes560.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02035
12535
done2535

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.5s2205×body1280valid
1.9s7937×body80valid
1.8s1409×body640valid
353.0ms584×body320valid
142.0ms254×body160valid
111.0ms44×body2560valid