Details

Time bar (total: 16.6s)

sample368.0ms

Algorithm
intervals
Results
40.0ms69×body1280valid
23.0ms55×body640valid
21.0ms256×body80valid
6.0ms22×body320valid
3.0ms16×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01937
13137
25336
38436
420136
584136
done500036

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize31.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
153.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.2s

Counts
68 → 68
Iterations

Useful iterations: 3 (191.0ms)

IterNodesCost
095836
1193778
2438690
3878677
41626677
53671677
done5000677

prune337.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.3b

localize17.0ms

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)
1.5b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

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:
3.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
94.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.0s

Counts
78 → 78
Iterations

Useful iterations: 3 (458.0ms)

IterNodesCost
01301070
1292990
2770908
32006892
44758892
done5000892

prune289.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.5b
(* (atan2 x.im x.re) y.im)
2.8b
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1
8×add-exp-log log-pow add-cbrt-cube
7×associate-*l*
6×exp-prod associate-*r* sqrt-prod
4×add-log-exp
3×log-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 70
Calls
4 calls:
3.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify1.6s

Counts
82 → 82
Iterations

Useful iterations: 3 (315.0ms)

IterNodesCost
0130987
1258843
2615748
31237740
42317740
done5000740

prune323.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.9b

localize28.0ms

Local error

Found 4 expressions with local error:

30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
33.9b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cos-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
6.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
145.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
139.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
144.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.8s

Counts
51 → 51
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
068978
1139948
2273824
3555815
41187815
52898815
done5001815

prune323.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.9b

regimes419.0ms

Accuracy

82.8% (5.5b remaining)

Error of 8.7b against oracle of 3.2b and baseline of 35.0b

bsearch91.0ms

Steps
ItersRangePoint
8
-3.6767631255749315e-308
2.7751932276321228e-306
3.68045830903155e-310

simplify4.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02333
13429
23629
done3629

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s2058×body1280valid
805.0ms8020×body80valid
548.0ms1423×body640valid
177.0ms672×body320valid
62.0ms329×body160valid