Details

Time bar (total: 29.9s)

sample264.0ms

Algorithm
intervals
Results
92.0ms70×body1280valid
33.0ms255×body80valid
29.0ms53×body640valid
4.0ms11×body320valid
4.0ms1×body2560valid
2.0ms8×body160valid

simplify2.3s

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize37.0ms

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)))

rewrite38.0ms

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:
16.0ms
(* y.re (log (hypot x.re x.im)))
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* y.re (log (hypot x.re x.im)))
28.0ms
(* (atan2 x.im x.re) y.re)
31.0ms
(* (atan2 x.im x.re) y.im)
226.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.4s

Counts
93 → 93
Iterations
IterNodes
done5000
43768
31505
2616
1270
0142

prune858.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize75.0ms

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)))

rewrite24.0ms

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:
0.0ms
(log1p (sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (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)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(log1p (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.re)
29.0ms
(* (atan2 x.im x.re) y.im)
172.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts
77 → 77
Iterations
IterNodes
done5006
44440
31373
2500
1221
0118

prune748.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

localize84.0ms

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))))

rewrite41.0ms

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:
2.0ms
(cbrt y.re)
27.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
7.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series625.0ms

Counts
4 → 12
Calls
4 calls:
276.0ms
(cbrt y.re)
117.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
29.0ms
(* (atan2 x.im x.re) y.im)
203.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.0s

Counts
80 → 80
Iterations
IterNodes
done5008
31860
2667
1273
0130

prune786.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

localize69.0ms

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))))

rewrite55.0ms

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:
1.0ms
(cbrt y.re)
34.0ms
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
14.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(sin (fma y.im (log (hypot x.re x.im)) (* (* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re)) (cbrt y.re))))

series618.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(cbrt y.re)
121.0ms
(* (* (atan2 x.im x.re) (cbrt y.re)) (cbrt y.re))
26.0ms
(* (atan2 x.im x.re) y.im)
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))))

simplify3.0s

Counts
82 → 82
Iterations
IterNodes
done5000
32395
2808
1287
0133

prune714.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.0b

regimes731.0ms

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 3.5b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.8s2218×body1280valid
2.1s7923×body80valid
1.3s1428×body640valid
660.0ms52×body2560valid
419.0ms570×body320valid
83.0ms229×body160valid