Details

Time bar (total: 38.1s)

sample539.0ms

Algorithm
intervals
Results
179.0ms62×body1280valid
54.0ms259×body80valid
49.0ms52×body640valid
18.0ms23×body320valid
5.0ms11×body160valid

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
done5001
5823
4210
395
262
135
019

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize102.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
1.2b
(* y.re (atan2 x.im x.re))
1.7b
(* (atan2 x.im x.re) y.im)
36.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1
10×add-exp-log associate-*r* add-cbrt-cube
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:
17.0ms
(* y.re (log (hypot x.re x.im)))
14.0ms
(* y.re (atan2 x.im x.re))
14.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series515.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* y.re (log (hypot x.re x.im)))
20.0ms
(* y.re (atan2 x.im x.re))
38.0ms
(* (atan2 x.im x.re) y.im)
306.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify3.1s

Counts
89 → 89
Iterations
IterNodes
done5001
32066
2745
1294
0146

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.3b

localize108.0ms

Local error

Found 4 expressions with local error:

0.4b
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))))
1.2b
(* y.re (atan2 x.im x.re))
1.7b
(* (atan2 x.im x.re) y.im)
36.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1
8×add-exp-log add-cbrt-cube
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:
20.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))))
15.0ms
(* y.re (atan2 x.im x.re))
14.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series917.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))))
24.0ms
(* y.re (atan2 x.im x.re))
36.0ms
(* (atan2 x.im x.re) y.im)
600.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify3.1s

Counts
80 → 80
Iterations
IterNodes
done5001
31666
2588
1248
0130

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize150.0ms

Local error

Found 4 expressions with local error:

1.2b
(* y.re (atan2 x.im x.re))
1.7b
(* (atan2 x.im x.re) y.im)
36.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
36.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
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:
14.0ms
(* y.re (atan2 x.im x.re))
15.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series570.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* y.re (atan2 x.im x.re))
35.0ms
(* (atan2 x.im x.re) y.im)
258.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
254.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify3.6s

Counts
72 → 72
Iterations
IterNodes
done5000
31794
2556
1211
0103

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize229.0ms

Local error

Found 4 expressions with local error:

3.3b
(cbrt (atan2 x.im x.re))
3.3b
(cbrt (atan2 x.im x.re))
36.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
36.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×cos-sum pow1/3 fma-udef
Counts
4 → 46
Calls
4 calls:
2.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cbrt (atan2 x.im x.re))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series684.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(cbrt (atan2 x.im x.re))
90.0ms
(cbrt (atan2 x.im x.re))
261.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
247.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify3.8s

Counts
58 → 58
Iterations
IterNodes
done5001
42173
3634
2249
1120
067

prune994.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

regimes1.0s

Accuracy

0% (0.0b remaining)

Error of 3.4b against oracle of 3.3b and baseline of 3.4b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done23
123
019

end0.0ms

sample11.0s

Algorithm
intervals
Results
3.8s7964×body80valid
3.3s2015×body1280valid
2.4s1450×body640valid
549.0ms625×body320valid
125.0ms282×body160valid