Details

Time bar (total: 31.3s)

sample331.0ms

Algorithm
intervals
Results
104.0ms57×body1280valid
39.0ms249×body80valid
30.0ms42×body640valid
13.0ms25×body320valid
2.0ms7×body160valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
019784
135654
263654
399654
4249654
51130654
done5001654

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
0.9b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow fma-udef
Counts
4 → 77
Calls
4 calls:
7.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(* (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)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* y.re (log (hypot x.re x.im)))
28.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
244.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
89 → 89
Iterations

Useful iterations: done (1.1s)

IterNodesCost
013625222
126524705
287324623
done500024278

prune952.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
0.9b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (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 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
1.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
11.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series633.0ms

Counts
4 → 12
Calls
4 calls:
356.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
31.0ms
(* (atan2 x.im x.re) y.re)
31.0ms
(* (atan2 x.im x.re) y.im)
215.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.7s

Counts
73 → 73
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
010524316
119423851
259723771
3451323561
done500123561

prune810.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize139.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
33.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 50
Calls
4 calls:
9.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (atan2 x.im x.re) y.im)
248.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
233.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))
217.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts
62 → 62
Iterations

Useful iterations: 3 (610.0ms)

IterNodesCost
06824704
112224590
237924510
3262324315
done500024315

prune855.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
0.9b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
1.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
12.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series618.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(expm1 (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))))
22.0ms
(* (atan2 x.im x.re) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
220.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify4.8s

Counts
73 → 73
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
010524316
119423851
259723771
3451323561
done500123561

prune708.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

regimes719.0ms

Accuracy

0% (0.3b remaining)

Error of 3.2b against oracle of 2.9b and baseline of 3.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0221114
1271114
done271114

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.0s2090×body1280valid
2.2s8037×body80valid
1.7s1444×body640valid
321.0ms646×body320valid
104.0ms318×body160valid