Details

Time bar (total: 29.0s)

sample363.0ms

Algorithm
intervals
Results
111.0ms256×body80valid
95.0ms53×body640valid
66.0ms43×body1280valid
13.0ms16×body320valid
2.0ms6×body160valid

simplify2.3s

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

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
0.9b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.re)
29.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite54.0ms

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:
8.0ms
(* y.re (log (hypot x.re x.im)))
24.0ms
(* (atan2 x.im x.re) y.im)
12.0ms
(* (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)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* y.re (log (hypot x.re x.im)))
19.0ms
(* (atan2 x.im x.re) y.im)
25.0ms
(* (atan2 x.im x.re) y.re)
188.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.3s

Counts
93 → 93
Iterations
IterNodes
done5001
31949
2719
1296
0150

prune831.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize97.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.9b
(* (atan2 x.im x.re) y.im)
1.3b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite53.0ms

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×cos-sum pow1/3 fma-udef
Counts
4 → 68
Calls
4 calls:
1.0ms
(cbrt y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(cbrt y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
108.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
188.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.2s

Counts
80 → 80
Iterations
IterNodes
done5001
32399
2788
1301
0138

prune726.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.1b

localize103.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
30.0b
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log
7×add-cbrt-cube
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cos-sum associate-*l* pow-prod-down prod-exp cbrt-unprod fma-udef
1×associate-*r* *-commutative unswap-sqr
Counts
4 → 55
Calls
4 calls:
437.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

series728.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re)))
205.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
202.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))
185.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (* (atan2 x.im x.re) (* (cbrt y.re) (cbrt y.re))) (cbrt y.re))))

simplify2.8s

Counts
67 → 67
Iterations
IterNodes
done5000
43921
31035
2440
1196
093

prune844.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.im)
1.2b
(* (atan2 x.im x.re) y.re)
4.6b
(log (exp (* y.re (log (hypot x.re x.im)))))
29.7b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt log-prod
11×*-un-lft-identity add-cube-cbrt
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* exp-sum
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum exp-prod exp-to-pow rem-log-exp fma-udef
Counts
4 → 76
Calls
4 calls:
8.0ms
(* (atan2 x.im x.re) y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
20.0ms
(* (atan2 x.im x.re) y.re)
105.0ms
(log (exp (* y.re (log (hypot x.re x.im)))))
167.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts
88 → 88
Iterations
IterNodes
done5000
31727
2663
1312
0164

prune810.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.0b

regimes504.0ms

Accuracy

0% (0.0b remaining)

Error of 3.2b against oracle of 3.2b and baseline of 3.2b

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done26
126
021

end0.0ms

sample10.7s

Algorithm
intervals
Results
4.5s1961×body1280valid
2.8s8009×body80valid
2.0s1444×body640valid
676.0ms638×body320valid
182.0ms291×body160valid