Details

Time bar (total: 28.2s)

sample228.0ms

Algorithm
intervals
Results
52.0ms55×body1280valid
41.0ms258×body80valid
21.0ms32×body640valid
9.0ms17×body320valid
3.0ms9×body160valid

simplify2.2s

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

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.0b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) y.im)
32.6b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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 insert-posit16 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 → 81
Calls
4 calls:
7.0ms
(* y.re (log (hypot x.re x.im)))
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (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)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* y.re (log (hypot x.re x.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
21.0ms
(* (atan2 x.im x.re) y.im)
205.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
93 → 93
Iterations
IterNodes
done5001
32037
2736
1298
0150

prune798.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize100.0ms

Local error

Found 4 expressions with local error:

7.0b
(cbrt (* (atan2 x.im x.re) y.re))
7.0b
(cbrt (* (atan2 x.im x.re) y.re))
7.0b
(cbrt (* (atan2 x.im x.re) y.re))
32.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×cos-sum fma-udef
Counts
4 → 47
Calls
4 calls:
3.0ms
(cbrt (* (atan2 x.im x.re) y.re))
4.0ms
(cbrt (* (atan2 x.im x.re) y.re))
6.0ms
(cbrt (* (atan2 x.im x.re) y.re))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(cbrt (* (atan2 x.im x.re) y.re))
62.0ms
(cbrt (* (atan2 x.im x.re) y.re))
98.0ms
(cbrt (* (atan2 x.im x.re) y.re))
190.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify2.7s

Counts
59 → 59
Iterations
IterNodes
done5003
42134
3675
2292
1150
082

prune660.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.0b

localize116.0ms

Local error

Found 4 expressions with local error:

18.7b
(sin (* (atan2 x.im x.re) y.re))
19.1b
(cos (* (atan2 x.im x.re) y.re))
22.9b
(sin (* y.im (log (hypot x.re x.im))))
23.0b
(cos (* y.im (log (hypot x.re x.im))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×distribute-rgt-in cos-sum distribute-lft-in sin-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
8.0ms
(sin (* (atan2 x.im x.re) y.re))
8.0ms
(cos (* (atan2 x.im x.re) y.re))
9.0ms
(sin (* y.im (log (hypot x.re x.im))))
10.0ms
(cos (* y.im (log (hypot x.re x.im))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sin (* (atan2 x.im x.re) y.re))
67.0ms
(cos (* (atan2 x.im x.re) y.re))
124.0ms
(sin (* y.im (log (hypot x.re x.im))))
131.0ms
(cos (* y.im (log (hypot x.re x.im))))

simplify2.3s

Counts
64 → 64
Iterations
IterNodes
done5000
41441
3559
2280
1188
0134

prune756.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize160.0ms

Local error

Found 4 expressions with local error:

22.4b
(cos (* y.im (log (cbrt (hypot x.re x.im)))))
22.4b
(sin (* y.im (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im))))))
22.5b
(sin (* y.im (log (cbrt (hypot x.re x.im)))))
22.9b
(sin (* y.im (log (hypot x.re x.im))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
32×log-prod
20×sin-sum
16×distribute-rgt-in distribute-lft-in
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×cbrt-prod cos-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
12.0ms
(cos (* y.im (log (cbrt (hypot x.re x.im)))))
9.0ms
(sin (* y.im (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im))))))
10.0ms
(sin (* y.im (log (cbrt (hypot x.re x.im)))))
14.0ms
(sin (* y.im (log (hypot x.re x.im))))

series638.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(cos (* y.im (log (cbrt (hypot x.re x.im)))))
207.0ms
(sin (* y.im (log (* (cbrt (hypot x.re x.im)) (cbrt (hypot x.re x.im))))))
144.0ms
(sin (* y.im (log (cbrt (hypot x.re x.im)))))
99.0ms
(sin (* y.im (log (hypot x.re x.im))))

simplify3.4s

Counts
84 → 84
Iterations
IterNodes
done5000
43966
31224
2550
1358
0243

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

regimes886.0ms

Accuracy

0% (0.3b remaining)

Error of 3.5b against oracle of 3.2b and baseline of 3.5b

bsearch0.0ms

simplify26.0ms

Iterations
IterNodes
done60
160
045

end0.0ms

sample8.0s

Algorithm
intervals
Results
2.8s2023×body1280valid
2.4s7979×body80valid
1.3s1440×body640valid
589.0ms325×body160valid
404.0ms665×body320valid