Details

Time bar (total: 30.4s)

sample509.0ms

Algorithm
intervals
Results
210.0ms258×body80valid
58.0ms47×body1280valid
37.0ms39×body640valid
10.0ms17×body320valid
5.0ms10×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (atan2 x.im x.re) y.im)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(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)))

rewrite86.0ms

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:
11.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (atan2 x.im x.re) y.im)
60.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
227.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.1s

Counts
68 → 68
Iterations

Useful iterations: 3 (378.0ms)

IterNodesCost
095836
1193778
2437690
3816677
41651677
54087677
done5001677

prune408.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
0.9b
(* (atan2 x.im x.re) y.im)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
41.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
24.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
14.0ms
(* (atan2 x.im x.re) y.im)
28.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
155.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
66.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.3s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01321042
1282985
2691871
31455860
44042859
done5000859

prune424.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* (atan2 x.im x.re) y.im))
0.9b
(* (atan2 x.im x.re) y.im)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
1×exp-prod exp-to-pow pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
2 → 28
Calls
2 calls:
17.0ms
(exp (* (atan2 x.im x.re) y.im))
13.0ms
(* (atan2 x.im x.re) y.im)

series62.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(exp (* (atan2 x.im x.re) y.im))
32.0ms
(* (atan2 x.im x.re) y.im)

simplify2.5s

Counts
34 → 34
Iterations

Useful iterations: 3 (242.0ms)

IterNodesCost
048260
191250
2252223
3600221
41624221
done5000221

prune154.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
3.7b
(cbrt (atan2 x.im x.re))
3.7b
(cbrt (atan2 x.im x.re))
3.7b
(cbrt (atan2 x.im x.re))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
24.0ms
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
2.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cbrt (atan2 x.im x.re))
2.0ms
(cbrt (atan2 x.im x.re))

series312.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (cbrt (atan2 x.im x.re)) (cbrt (atan2 x.im x.re)))
86.0ms
(cbrt (atan2 x.im x.re))
72.0ms
(cbrt (atan2 x.im x.re))
59.0ms
(cbrt (atan2 x.im x.re))

simplify6.1s

Counts
85 → 85
Iterations

Useful iterations: done (6.1s)

IterNodesCost
049804
184719
2252595
3920569
44302560
done5001540

prune426.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes365.0ms

Accuracy

61% (6.4b remaining)

Error of 10.0b against oracle of 3.6b and baseline of 20.1b

bsearch832.0ms

Steps
ItersRangePoint
11
-1.8064072260362412e-290
5.147296625674691e-303
2.9106186824831246e-307
8
-9.07075452395602e-152
-2.051209900968979e-156
-8.840626789860417e-152
8
-1.4044621988311022e-69
-8.006417948394775e-74
-1.085931852353555e-71
8
-1163.8105601768866
-1.1154561922801245
-1.448187283069528

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
055117
172107
274107
done74107

end0.0ms

sample8.2s

Algorithm
intervals
Results
2.8s1936×body1280valid
2.3s7997×body80valid
1.4s1402×body640valid
784.0ms663×body320valid
103.0ms305×body160valid