Details

Time bar (total: 20.5s)

sample976.0ms

Algorithm
intervals
Results
702.0ms42×body640valid
79.0ms57×body1280valid
48.0ms249×body80valid
15.0ms25×body320valid
3.0ms7×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5001
51130
4249
399
263
135
019

prune52.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))
0.9b
(* (atan2 x.im x.re) y.re)
3.7b
(pow (exp y.im) (atan2 x.im x.re))
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow-pow log1p-expm1-u add-log-exp
3×pow-unpow exp-prod unpow-prod-down associate-*r* associate-*l*
2×fma-udef
1×pow-to-exp cos-sum pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod unswap-sqr sqr-pow
Counts
4 → 62
Calls
4 calls:
0.0ms
(fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))
11.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(pow (exp y.im) (atan2 x.im x.re))
8.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))
23.0ms
(* (atan2 x.im x.re) y.re)
40.0ms
(pow (exp y.im) (atan2 x.im x.re))
185.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
74 → 74
Iterations
IterNodes
done5000
21242
1274
0127

prune794.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma y.im (log (hypot x.re x.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 y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

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*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×cos-sum
Counts
4 → 60
Calls
4 calls:
0.0ms
(fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))
5.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))
32.0ms
(* (atan2 x.im x.re) y.re)
32.0ms
(* (atan2 x.im x.re) y.im)
198.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify600.0ms

Counts
72 → 72
Iterations
IterNodes
done5000
2826
1219
0113

prune690.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
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)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow unpow-prod-down cube-prod
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cube-mult pow-to-exp cos-sum pow-pow unpow3 pow-exp fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 75
Calls
4 calls:
3.0ms
(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
5.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(* (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)))

series689.0ms

Counts
4 → 12
Calls
4 calls:
403.0ms
(pow (cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re))) 3)
31.0ms
(* (atan2 x.im x.re) y.re)
28.0ms
(* (atan2 x.im x.re) y.im)
227.0ms
(cos (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify785.0ms

Counts
87 → 87
Iterations
IterNodes
done5001
21137
1283
0118

prune985.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize101.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (log (exp (cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re)))))) 3)
0.9b
(* y.re (atan2 x.im x.re))
1.7b
(* (atan2 x.im x.re) y.im)
33.2b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×pow1
9×add-cbrt-cube add-exp-log
8×log-pow
7×unpow-prod-down cube-prod
6×exp-prod associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cube-mult pow-to-exp cos-sum pow-pow unpow3 pow-exp fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 83
Calls
4 calls:
10.0ms
(pow (log (exp (cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re)))))) 3)
8.0ms
(* y.re (atan2 x.im x.re))
5.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series504.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(pow (log (exp (cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re)))))) 3)
12.0ms
(* y.re (atan2 x.im x.re))
24.0ms
(* (atan2 x.im x.re) y.im)
207.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify1.0s

Counts
95 → 95
Iterations
IterNodes
done5001
21792
1415
0154

prune958.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

regimes905.0ms

Accuracy

55.2% (2.1b remaining)

Error of 6.2b against oracle of 4.2b and baseline of 8.8b

bsearch7.0ms

simplify8.0ms

Iterations
IterNodes
done40
140
030

end0.0ms

sample7.7s

Algorithm
intervals
Results
3.4s2090×body1280valid
2.1s8037×body80valid
1.1s1444×body640valid
368.0ms646×body320valid
99.0ms318×body160valid