Details

Time bar (total: 22.4s)

sample873.0ms

Algorithm
intervals
Results
302.0ms45×body640valid
168.0ms64×body1280valid
128.0ms264×body80valid
24.0ms24×body320valid
6.0ms10×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done2008
5823
4210
395
262
135
019

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.5b
(* (atan2 x.im x.re) y.im)
1.7b
(* (atan2 x.im x.re) y.re)
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite47.0ms

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:
14.0ms
(* y.re (log (hypot x.re x.im)))
11.0ms
(* (atan2 x.im x.re) y.im)
11.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(* y.re (log (hypot x.re x.im)))
31.0ms
(* (atan2 x.im x.re) y.im)
33.0ms
(* (atan2 x.im x.re) y.re)
186.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify946.0ms

Counts
93 → 93
Iterations
IterNodes
done2000
31949
2719
1296
0150

prune823.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize106.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.re)
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 54
Calls
4 calls:
11.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (atan2 x.im x.re) y.re)
171.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
161.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
165.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify732.0ms

Counts
66 → 66
Iterations
IterNodes
done2001
31000
2363
1156
080

prune793.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
1.5b
(* (atan2 x.im x.re) y.im)
1.7b
(* (atan2 x.im x.re) y.re)
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
4×expm1-log1p-u log-pow insert-posit16 log1p-expm1-u add-log-exp
3×log-prod exp-prod
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
1×log-div exp-diff rem-log-exp
Counts
4 → 72
Calls
4 calls:
4.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
6.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
30.0ms
(* (atan2 x.im x.re) y.im)
30.0ms
(* (atan2 x.im x.re) y.re)
156.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify959.0ms

Counts
84 → 84
Iterations
IterNodes
done2001
31451
2552
1245
0133

prune686.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize63.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.re)
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cos-sum associate-*r* associate-*l* fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 54
Calls
4 calls:
9.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series581.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (atan2 x.im x.re) y.re)
187.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
185.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
186.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify744.0ms

Counts
66 → 66
Iterations
IterNodes
done2001
31000
2363
1156
080

prune786.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

regimes492.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done25
125
020

end0.0ms

sample10.7s

Algorithm
intervals
Results
3.9s2044×body1280valid
2.9s7974×body80valid
2.4s1473×body640valid
767.0ms674×body320valid
181.0ms295×body160valid