Details

Time bar (total: 27.8s)

sample250.0ms

Algorithm
intervals
Results
66.0ms42×body640valid
62.0ms61×body1280valid
35.0ms248×body80valid
11.0ms21×body320valid
2.0ms8×body160valid

simplify1.9s

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

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.7b

localize41.0ms

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))
32.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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 sin-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))
10.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(pow (exp y.im) (atan2 x.im x.re))
7.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))
20.0ms
(* (atan2 x.im x.re) y.re)
46.0ms
(pow (exp y.im) (atan2 x.im x.re))
214.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify878.0ms

Counts
74 → 74
Iterations
IterNodes
done5000
21092
1247
0119

prune821.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.7b

localize70.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.re)
3.7b
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
3.7b
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
32.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt pow-unpow
24×*-un-lft-identity add-cube-cbrt
18×times-frac
8×pow1 pow-pow
6×exp-prod unpow-prod-down add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×pow-to-exp pow-exp div-inv sqr-pow
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 94
Calls
4 calls:
11.0ms
(* (atan2 x.im x.re) y.re)
9.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
7.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (atan2 x.im x.re) y.re)
56.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
66.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
180.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify814.0ms

Counts
106 → 106
Iterations
IterNodes
done5001
21277
1338
0139

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

localize128.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (cbrt y.im) (/ 2 (atan2 x.im x.re)))
3.2b
(pow (exp (* (cbrt y.im) (cbrt y.im))) (/ (cbrt y.im) (/ 2 (atan2 x.im x.re))))
3.7b
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
32.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
282×times-frac
160×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
96×pow-unpow
81×cbrt-prod
16×div-inv
13×associate-/r*
9×add-exp-log
7×pow-pow add-cbrt-cube
6×pow1 unpow-prod-down associate-/l*
5×add-log-exp
4×expm1-log1p-u exp-prod log1p-expm1-u
3×cbrt-undiv div-exp
2×pow-to-exp pow-exp associate-/r/ sqr-pow
1×clear-num frac-2neg exp-to-pow sin-sum fma-udef
Counts
4 → 257
Calls
4 calls:
17.0ms
(/ (cbrt y.im) (/ 2 (atan2 x.im x.re)))
24.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (/ (cbrt y.im) (/ 2 (atan2 x.im x.re))))
5.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (cbrt y.im) (/ 2 (atan2 x.im x.re)))
188.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (/ (cbrt y.im) (/ 2 (atan2 x.im x.re))))
48.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
157.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify701.0ms

Counts
269 → 269
Iterations
IterNodes
done5001
11295
0422

prune3.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

localize135.0ms

Local error

Found 4 expressions with local error:

3.2b
(pow (exp (* (cbrt y.im) (cbrt y.im))) (/ (cbrt y.im) (/ 2 (atan2 x.im x.re))))
3.7b
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
3.7b
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
32.9b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
109×pow-unpow
92×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
39×cbrt-prod
11×pow-pow
9×unpow-prod-down div-inv
7×pow1 exp-prod
5×add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×pow-to-exp pow-exp sqr-pow
1×exp-to-pow sin-sum associate-/r/ fma-udef
Counts
4 → 175
Calls
4 calls:
25.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (/ (cbrt y.im) (/ 2 (atan2 x.im x.re))))
9.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
17.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(pow (exp (* (cbrt y.im) (cbrt y.im))) (/ (cbrt y.im) (/ 2 (atan2 x.im x.re))))
69.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
70.0ms
(pow (exp y.im) (/ (atan2 x.im x.re) 2))
149.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.6s

Counts
187 → 187
Iterations
IterNodes
done5000
24716
11036
0322

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.6b

regimes1.1s

Accuracy

57.1% (2.2b remaining)

Error of 6.8b against oracle of 4.6b and baseline of 9.7b

bsearch354.0ms

Steps
ItersRangePoint
6
1.0614652160556683e-07
1.0953845066771504e-06
1.0702928080317355e-06
8
-2.2683617134564615e+39
-1.439813619911313e+35
-1.8741626089457186e+38

simplify10.0ms

Iterations
IterNodes
done56
156
044

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.9s2261×body1280valid
1.7s8009×body80valid
1.4s1409×body640valid
417.0ms558×body320valid
129.0ms54×body2560valid
82.0ms244×body160valid