Details

Time bar (total: 28.0s)

sample391.0ms

Algorithm
intervals
Results
104.0ms48×body640valid
91.0ms65×body1280valid
59.0ms257×body80valid
15.0ms22×body320valid
4.0ms8×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
01937
13137
25336
38536
422036
5102336
done500036

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize83.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite110.0ms

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×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
14.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
57.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series494.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (atan2 x.im x.re) y.im)
72.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
316.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify3.6s

Counts
68 → 68
Iterations

Useful iterations: 3 (856.0ms)

IterNodesCost
095836
1197778
2554692
32818677
done5000677

prune862.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 66
Calls
4 calls:
18.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
26.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
26.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series547.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
192.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
40.0ms
(* (atan2 x.im x.re) y.im)
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.1s

Counts
78 → 78
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01301070
1300990
21018908
done5000899

prune840.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
1.6b
(* (atan2 x.im x.re) y.im)
31.7b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.5b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×cbrt-prod
14×add-cube-cbrt *-un-lft-identity
10×pow1
9×sqrt-prod
8×add-exp-log associate-*l* add-cbrt-cube
6×unpow-prod-down cube-prod associate-*r*
4×sqrt-div add-log-exp
2×cube-div cbrt-div flip3-+ pow1/3 pow-prod-down prod-exp log-pow *-commutative cbrt-unprod flip-+ unswap-sqr
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 82
Calls
4 calls:
26.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series353.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
38.0ms
(* (atan2 x.im x.re) y.im)
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
72.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify2.1s

Counts
94 → 94
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01461404
13641042
21785958
done5001956

prune989.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.1b

localize41.0ms

Local error

Found 2 expressions with local error:

0.1b
(* y.re (log (/ -1 x.re)))
1.6b
(* (atan2 x.im x.re) y.im)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
26×log-prod
24×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
13×distribute-rgt-in distribute-lft-in
7×pow1 associate-*r*
6×add-exp-log associate-*l* add-cbrt-cube
2×pow-prod-down prod-exp *-commutative cbrt-unprod div-inv add-log-exp unswap-sqr
1×log-pow
Counts
2 → 63
Calls
2 calls:
26.0ms
(* y.re (log (/ -1 x.re)))
14.0ms
(* (atan2 x.im x.re) y.im)

series117.0ms

Counts
2 → 6
Calls
2 calls:
73.0ms
(* y.re (log (/ -1 x.re)))
43.0ms
(* (atan2 x.im x.re) y.im)

simplify1.0s

Counts
69 → 69
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0161749
1320715
2975657
done5000643

prune506.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.1b

regimes848.0ms

Accuracy

74.5% (5.5b remaining)

Error of 9.0b against oracle of 3.5b and baseline of 25.1b

bsearch830.0ms

Steps
ItersRangePoint
10
4.735830173312099e-12
58383.88522329229
6.8690697371453956e-06
9
9.064035183044125e-119
1.28399272252935e-112
1.097546056989818e-112
8
-2.156528177776517e-300
-3.3603542884328756e-305
-3.431420414734735e-305

simplify19.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
04177
15859
26359
done6359

end0.0ms

sample10.6s

Algorithm
intervals
Results
3.7s2035×body1280valid
2.8s7977×body80valid
1.9s1473×body640valid
992.0ms665×body320valid
129.0ms290×body160valid