Details

Time bar (total: 7.0s)

sample420.0ms

Algorithm
intervals
Results
41.0ms256×body80valid
36.0ms63×body1280valid
14.0ms37×body640valid
4.0ms17×body320valid
2.0ms10×body160valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117
done500117

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
162.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify78.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207454
1556413
21286411
32863411
45002411
done5002411

prune379.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.1b

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
29.4b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.3b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square cos-sum sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
Counts
4 → 68
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
18.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify89.0ms

Counts
80 → 80
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0253387
1722347
21719345
33543345
45002345
done5002345

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
1.4b
(* (atan2 x.im x.re) y.im)
5.8b
(exp (log (hypot x.re x.im)))
31.3b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite35.0ms

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 exp-prod log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow rem-exp-log
Counts
4 → 67
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(exp (log (hypot x.re x.im)))
16.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
46.0ms
(exp (log (hypot x.re x.im)))
158.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify58.0ms

Counts
79 → 79
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
0198344
1529303
21170303
31995299
45001299
done5001299

prune364.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
1.3b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
5.8b
(exp (log (hypot x.re x.im)))
31.3b
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-sqr-sqrt
11×add-exp-log
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*l*
4×expm1-log1p-u exp-prod associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×*-commutative unswap-sqr
1×cos-sum log-pow rem-exp-log
Counts
4 → 68
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
22.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
3.0ms
(exp (log (hypot x.re x.im)))
18.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
88.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
47.0ms
(exp (log (hypot x.re x.im)))
159.0ms
(cos (+ (* (log (hypot x.re x.im)) y.im) (* (atan2 x.im x.re) y.re)))

simplify65.0ms

Counts
80 → 80
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0242425
1737366
22739362
35001353
done5001353

prune388.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

regimes288.0ms

Accuracy

0% (0.5b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03024
13024
done3024

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s2048×body1280valid
644.0ms7966×body80valid
547.0ms1440×body640valid
179.0ms648×body320valid
54.0ms302×body160valid