Details

Time bar (total: 33.1s)

sample355.0ms

Algorithm
intervals
Results
106.0ms258×body80valid
97.0ms73×body1280valid
30.0ms29×body640valid
14.0ms22×body320valid
4.0ms11×body160valid
3.0ms1×body2560valid

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5000
5823
4210
395
262
135
019

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.1b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite50.0ms

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×sin-sum log-pow fma-udef
Counts
4 → 77
Calls
4 calls:
28.0ms
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* y.re (log (hypot x.re x.im)))
21.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(* (atan2 x.im x.re) y.re)
234.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
89 → 89
Iterations
IterNodes
done5001
31871
2630
1270
0138

prune900.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
1.1b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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×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 y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
8.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
33.0ms
(* (atan2 x.im x.re) y.im)
33.0ms
(* (atan2 x.im x.re) y.re)
202.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.2s

Counts
73 → 73
Iterations
IterNodes
done5005
44320
31302
2501
1217
0114

prune806.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize170.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite15.0ms

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×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:
6.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series607.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.re)
184.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
211.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
177.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.1s

Counts
62 → 62
Iterations
IterNodes
done5001
53736
41610
3591
2256
1124
069

prune910.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.3b

localize119.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.6b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

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×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:
12.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.re)
188.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
163.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
179.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.3s

Counts
62 → 62
Iterations
IterNodes
done5001
53736
41610
3591
2256
1124
069

prune816.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.3b

regimes567.0ms

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.7b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.1s2111×body1280valid
1.8s1489×body640valid
1.8s7906×body80valid
723.0ms558×body320valid
148.0ms40×body2560valid
76.0ms232×body160valid