Details

Time bar (total: 24.4s)

sample1.3s

Algorithm
intervals
Results
948.0ms69×body1280valid
49.0ms258×body80valid
43.0ms22×body320valid
31.0ms32×body640valid
5.0ms13×body160valid

simplify2.4s

Counts
1 → 1
Iterations
IterNodes
done5001
51130
4249
399
263
135
019

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
1.1b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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 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 → 77
Calls
4 calls:
13.0ms
(* 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)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* y.re (log (hypot x.re x.im)))
30.0ms
(* (atan2 x.im x.re) y.im)
21.0ms
(* (atan2 x.im x.re) y.re)
246.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify993.0ms

Counts
89 → 89
Iterations
IterNodes
done5001
21096
1298
0146

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.2b

localize45.0ms

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)))))
1.1b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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 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 → 68
Calls
4 calls:
11.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
5.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
21.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(* (atan2 x.im x.re) y.re)
211.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
80 → 80
Iterations
IterNodes
done5000
2846
1243
0129

prune774.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.2b

localize118.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.re)
1.8b
(* (atan2 x.im x.re) y.re)
33.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
33.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite20.0ms

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 log1p-expm1-u add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 60
Calls
4 calls:
8.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.re)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (atan2 x.im x.re) y.re)
32.0ms
(* (atan2 x.im x.re) y.re)
182.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
169.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.1s

Counts
72 → 72
Iterations
IterNodes
done5000
33485
2528
1154
078

prune923.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b
(expm1 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
1.1b
(* (atan2 x.im x.re) y.im)
1.8b
(* (atan2 x.im x.re) y.re)
33.4b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

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×log1p-expm1-u
4×expm1-log1p-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum expm1-log1p fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
0.0ms
(expm1 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
5.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(* (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)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(expm1 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re))))
32.0ms
(* (atan2 x.im x.re) y.im)
20.0ms
(* (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)))

simplify1.2s

Counts
73 → 73
Iterations
IterNodes
done5001
2958
1261
0125

prune795.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.2b

regimes567.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done23
123
019

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.0s1955×body1280valid
2.1s7929×body80valid
1.7s1507×body640valid
361.0ms636×body320valid
103.0ms309×body160valid