Details

Time bar (total: 29.8s)

sample485.0ms

Algorithm
intervals
Results
272.0ms256×body80valid
58.0ms63×body1280valid
26.0ms45×body640valid
8.0ms21×body320valid
5.0ms11×body160valid

simplify2.5s

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

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
0.6b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) y.im)
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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:
12.0ms
(* y.re (log (hypot x.re x.im)))
10.0ms
(* (atan2 x.im x.re) y.re)
10.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* y.re (log (hypot x.re x.im)))
20.0ms
(* (atan2 x.im x.re) y.re)
27.0ms
(* (atan2 x.im x.re) y.im)
226.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts
89 → 89
Iterations
IterNodes
done5000
32437
2751
1298
0146

prune830.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.5b

localize106.0ms

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)))))
0.6b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) y.im)
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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:
7.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
11.0ms
(* (atan2 x.im x.re) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(log (exp (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
38.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)
164.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
80 → 80
Iterations
IterNodes
done5000
31418
2543
1241
0129

prune843.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.5b

localize118.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.im)
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

rewrite25.0ms

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 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 → 50
Calls
4 calls:
12.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

series581.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (atan2 x.im x.re) y.im)
193.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
160.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))
194.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* y.re (atan2 x.im x.re))))

simplify3.7s

Counts
62 → 62
Iterations
IterNodes
done5002
43716
31054
2378
1160
081

prune791.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.5b

localize163.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.im)
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
30.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite25.0ms

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 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 → 50
Calls
4 calls:
11.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(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)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series629.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (atan2 x.im x.re) y.im)
196.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
229.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
179.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify3.8s

Counts
62 → 62
Iterations
IterNodes
done5005
44310
31085
2373
1158
080

prune890.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.5b

regimes684.0ms

Accuracy

0% (0.0b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done22
122
018

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.5s1987×body1280valid
1.7s7979×body80valid
1.6s1444×body640valid
624.0ms703×body320valid
103.0ms291×body160valid