Details

Time bar (total: 51.7s)

sample355.0ms

Algorithm
intervals
Results
88.0ms70×body1280valid
52.0ms255×body80valid
49.0ms11×body320valid
43.0ms53×body640valid
3.0ms8×body160valid
3.0ms1×body2560valid

simplify3.7s

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

prune85.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize125.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
1.5b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
30.8b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite57.0ms

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×sin-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
12.0ms
(* y.re (log (hypot x.re x.im)))
12.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series618.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* y.re (log (hypot x.re x.im)))
41.0ms
(* (atan2 x.im x.re) y.re)
41.0ms
(* (atan2 x.im x.re) y.im)
358.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify6.7s

Counts
93 → 93
Iterations
IterNodes
done5001
43517
31403
2583
1267
0142

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize141.0ms

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))))
1.5b
(* (atan2 x.im x.re) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
30.8b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite56.0ms

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×insert-posit16 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 → 65
Calls
4 calls:
2.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
21.0ms
(* (atan2 x.im x.re) y.re)
20.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series1.1s

Counts
4 → 12
Calls
4 calls:
564.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
70.0ms
(* (atan2 x.im x.re) y.re)
70.0ms
(* (atan2 x.im x.re) y.im)
389.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify8.3s

Counts
77 → 77
Iterations
IterNodes
done5003
44122
31322
2498
1221
0118

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

localize217.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
1.2b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
1.6b
(* (atan2 x.im x.re) y.im)
30.7b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt pow1 add-exp-log
9×add-cbrt-cube
8×*-un-lft-identity add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
2×*-commutative unswap-sqr
1×sin-sum pow1/3 fma-udef
Counts
4 → 68
Calls
4 calls:
4.0ms
(cbrt y.re)
48.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
9.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series963.0ms

Counts
4 → 12
Calls
4 calls:
311.0ms
(cbrt y.re)
237.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
42.0ms
(* (atan2 x.im x.re) y.im)
373.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify4.9s

Counts
80 → 80
Iterations
IterNodes
done5001
31919
2659
1274
0130

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

localize211.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.9b
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
1.6b
(* (atan2 x.im x.re) y.im)
30.7b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re)) (cbrt y.re))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt pow1 add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
8×add-cbrt-cube
6×cbrt-prod
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative
1×sin-sum pow1/3 fma-udef unswap-sqr
Counts
4 → 70
Calls
4 calls:
2.0ms
(cbrt y.re)
47.0ms
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
11.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re)) (cbrt y.re))))

series922.0ms

Counts
4 → 12
Calls
4 calls:
325.0ms
(cbrt y.re)
205.0ms
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
49.0ms
(* (atan2 x.im x.re) y.im)
343.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re)) (cbrt y.re))))

simplify5.4s

Counts
82 → 82
Iterations
IterNodes
done5002
32416
2808
1288
0133

prune1.5s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.0b

regimes2.0s

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.4b and baseline of 3.5b

bsearch0.0ms

simplify14.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.1s2218×body1280valid
2.4s7923×body80valid
2.1s1428×body640valid
450.0ms570×body320valid
138.0ms52×body2560valid
78.0ms229×body160valid