Details

Time bar (total: 25.4s)

sample298.0ms

Algorithm
intervals
Results
111.0ms61×body1280valid
38.0ms255×body80valid
28.0ms37×body640valid
9.0ms2×body2560valid
8.0ms19×body320valid
1.0ms3×body160valid

simplify1.7s

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
0.7b
(* (atan2 x.im x.re) y.re)
2.7b
(pow (exp y.im) (atan2 x.im x.re))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
343×times-frac
175×add-sqr-sqrt
173×*-un-lft-identity add-cube-cbrt
153×unpow-prod-down
51×sqr-pow
29×add-exp-log
25×associate-/r*
21×div-exp
11×add-cbrt-cube
9×div-inv
8×pow-to-exp pow-exp
7×pow1 associate-/l*
4×expm1-log1p-u pow-pow log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow exp-prod associate-*r* associate-*l*
1×clear-num frac-2neg sin-sum pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 286
Calls
4 calls:
48.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (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)
7.0ms
(pow (exp y.im) (atan2 x.im x.re))
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series953.0ms

Counts
4 → 12
Calls
4 calls:
657.0ms
(/ (pow (hypot x.re x.im) y.re) (/ (pow (exp y.im) (atan2 x.im x.re)) (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
25.0ms
(* (atan2 x.im x.re) y.re)
43.0ms
(pow (exp y.im) (atan2 x.im x.re))
228.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify759.0ms

Counts
298 → 298
Iterations
IterNodes
done5000
11403
0526

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize150.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (exp (atan2 x.im x.re)) y.im)
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u pow-pow add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×pow-unpow exp-prod unpow-prod-down sin-sum fma-udef
1×pow-to-exp pow-exp sqr-pow
Counts
4 → 52
Calls
4 calls:
7.0ms
(pow (exp (atan2 x.im x.re)) y.im)
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)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(pow (exp (atan2 x.im x.re)) y.im)
176.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
182.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
143.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
64 → 64
Iterations
IterNodes
done5001
32008
2498
1183
085

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize207.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (exp (atan2 x.im x.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-prod sin-sum fma-udef
1×pow1/3
Counts
4 → 43
Calls
4 calls:
2.0ms
(cbrt (exp (atan2 x.im x.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (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)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(cbrt (exp (atan2 x.im x.re)))
194.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
190.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
173.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify551.0ms

Counts
55 → 55
Iterations
IterNodes
done5000
4688
3209
2122
188
059

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize249.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (exp (atan2 x.im x.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×cbrt-prod sin-sum fma-udef
1×pow1/3
Counts
4 → 43
Calls
4 calls:
3.0ms
(cbrt (exp (atan2 x.im x.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)))
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series562.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(cbrt (exp (atan2 x.im x.re)))
150.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
168.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
167.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify478.0ms

Counts
55 → 55
Iterations
IterNodes
done5000
4688
3209
2122
188
059

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.3b

regimes1.2s

Accuracy

58.3% (2.3b remaining)

Error of 6.4b against oracle of 4.1b and baseline of 9.7b

bsearch8.0ms

simplify8.0ms

Iterations
IterNodes
done43
143
034

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.0s2184×body1280valid
2.3s7979×body80valid
1.4s1363×body640valid
655.0ms44×body2560valid
311.0ms564×body320valid
105.0ms242×body160valid