Details

Time bar (total: 29.2s)

sample455.0ms

Algorithm
intervals
Results
160.0ms74×body1280valid
66.0ms254×body80valid
56.0ms46×body640valid
20.0ms22×body320valid
4.0ms2×body2560valid
3.0ms5×body160valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done2030
62030
5823
4210
395
262
135
019

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
0.7b
(* (atan2 x.im x.re) y.im)
0.9b
(* (atan2 x.im x.re) y.re)
35.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

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)))
5.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (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)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(* y.re (log (hypot x.re x.im)))
30.0ms
(* (atan2 x.im x.re) y.im)
19.0ms
(* (atan2 x.im x.re) y.re)
186.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
93 → 93
Iterations
IterNodes
done2003
42003
31362
2599
1268
0142

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.2b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (expm1 (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.im)
0.9b
(* (atan2 x.im x.re) y.re)
35.1b
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite28.0ms

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 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:
0.0ms
(log1p (expm1 (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
11.0ms
(* (atan2 x.im x.re) y.im)
11.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(log1p (expm1 (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
28.0ms
(* (atan2 x.im x.re) y.im)
33.0ms
(* (atan2 x.im x.re) y.re)
146.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
77 → 77
Iterations
IterNodes
done2003
42003
3904
2397
1193
0108

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize89.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.7b
(* (atan2 x.im x.re) y.im)
0.8b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
35.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite53.0ms

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:
1.0ms
(cbrt y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series630.0ms

Counts
4 → 12
Calls
4 calls:
290.0ms
(cbrt y.re)
30.0ms
(* (atan2 x.im x.re) y.im)
110.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
199.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify1.5s

Counts
80 → 80
Iterations
IterNodes
done2008
42008
31724
2662
1273
0130

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.7b
(* (atan2 x.im x.re) y.im)
0.8b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
35.3b
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (cbrt y.re))))))

rewrite53.0ms

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:
1.0ms
(cbrt y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
2.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (cbrt y.re))))))

series595.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(cbrt y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
120.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
202.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (* (cbrt (* (cbrt y.re) (cbrt y.re))) (cbrt (cbrt y.re))))))

simplify1.6s

Counts
80 → 80
Iterations
IterNodes
done2001
42001
31929
2682
1278
0131

prune1.8s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.2b

regimes799.0ms

Accuracy

0% (0.3b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done25
125
020

end0.0ms

sample11.5s

Algorithm
intervals
Results
4.5s2079×body1280valid
3.5s7982×body80valid
2.1s1466×body640valid
542.0ms554×body320valid
187.0ms258×body160valid
182.0ms48×body2560valid