Details

Time bar (total: 28.6s)

sample367.0ms

Algorithm
intervals
Results
80.0ms43×body640valid
70.0ms62×body1280valid
44.0ms259×body80valid
12.0ms23×body320valid
6.0ms16×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize33.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (atan2 x.im x.re) y.im)
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite59.0ms

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:
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)))
32.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
53.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
206.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.2s

Counts
68 → 68
Iterations

Useful iterations: 3 (298.0ms)

IterNodesCost
095836
1193778
2437690
3816677
41651677
54087677
done5001677

prune491.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.3b

localize22.0ms

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)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.3b
(* (atan2 x.im x.re) y.im)
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite87.0ms

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:
37.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
8.0ms
(* (atan2 x.im x.re) y.im)
24.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
148.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
35.0ms
(* (atan2 x.im x.re) y.im)
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.5s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.9s)

IterNodesCost
01321042
1282985
2691871
31455860
44042859
done5000859

prune474.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (/ -1 x.re) (- y.re))
0.3b
(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
2.3b
(* (atan2 x.im x.re) y.im)

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
67×add-sqr-sqrt
65×add-cube-cbrt unpow-prod-down *-un-lft-identity
17×associate-/l*
12×add-exp-log
10×pow-unpow
7×add-cbrt-cube
6×pow1 div-exp div-inv
5×sqr-pow
4×pow-exp
3×distribute-lft-neg-in distribute-rgt-neg-in associate-*r* associate-*l* associate-/r* add-log-exp
2×neg-sub0 pow-to-exp pow-neg associate-/l/ pow-sub
1×cbrt-undiv neg-mul-1 pow-pow frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
3 → 143
Calls
3 calls:
13.0ms
(pow (/ -1 x.re) (- y.re))
40.0ms
(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
23.0ms
(* (atan2 x.im x.re) y.im)

series301.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(pow (/ -1 x.re) (- y.re))
164.0ms
(/ (pow (/ -1 x.re) (- y.re)) (exp (* (atan2 x.im x.re) y.im)))
31.0ms
(* (atan2 x.im x.re) y.im)

simplify4.0s

Counts
152 → 152
Iterations

Useful iterations: done (4.0s)

IterNodesCost
02812867
15412740
213952652
347102636
done50012492

prune831.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

localize84.0ms

Local error

Found 4 expressions with local error:

6.0b
(cbrt (atan2 x.im x.re))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.6b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube add-log-exp
3×cbrt-prod
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow1/3
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (atan2 x.im x.re))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
13.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(cbrt (atan2 x.im x.re))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
214.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify2.1s

Counts
61 → 61
Iterations

Useful iterations: 3 (190.0ms)

IterNodesCost
082777
1158718
2319638
3642622
41613622
done5000622

prune544.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

regimes384.0ms

Accuracy

50.1% (8.0b remaining)

Error of 11.7b against oracle of 3.7b and baseline of 19.8b

bsearch562.0ms

Steps
ItersRangePoint
10
-1.9739641733344554e-305
8.845804037490812e-301
-1.59374399213355e-310
9
-1.4140900430281582e-101
-5.0983811848635975e-111
-3.3320972694784386e-105
5
-274393.4748245095
-128623.8930200133
-146157.60732674622

simplify14.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
048144
163138
done63138

end0.0ms

sample7.7s

Algorithm
intervals
Results
2.8s2021×body1280valid
2.0s7972×body80valid
1.2s1427×body640valid
847.0ms674×body320valid
98.0ms326×body160valid