Details

Time bar (total: 27.9s)

sample331.0ms

Algorithm
intervals
Results
94.0ms260×body80valid
87.0ms82×body1280valid
33.0ms49×body640valid
16.0ms32×body320valid
3.0ms9×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.6b

localize54.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite73.0ms

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:
18.0ms
(* (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)))
35.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (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)))
261.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify4.0s

Counts
68 → 68
Iterations

Useful iterations: 3 (362.0ms)

IterNodesCost
095836
1193778
2437690
3816677
41651677
54087677
done5001677

prune531.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.1b

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)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
2.0b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite75.0ms

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:
35.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
13.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
124.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
55.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.4s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01321042
1282985
2691871
31455860
44042859
done5000859

prune528.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize23.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
6×add-exp-log sqrt-div add-cbrt-cube
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 63
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)))
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (atan2 x.im x.re) y.im)
72.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.6s

Counts
75 → 75
Iterations

Useful iterations: 3 (267.0ms)

IterNodesCost
067794
1147710
2366642
3708624
41474624
53831624
done5001624

prune555.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
0.0b
(exp (* (atan2 x.im x.re) y.im))
2.0b
(* (atan2 x.im x.re) y.im)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
7×add-exp-log add-cbrt-cube associate-/l*
5×pow1 add-log-exp
4×sqr-pow
3×div-exp associate-*r* associate-*l* associate-/r*
1×cbrt-undiv pow-to-exp exp-prod exp-to-pow frac-2neg pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv rem-exp-log unswap-sqr
Counts
3 → 73
Calls
3 calls:
17.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
8.0ms
(exp (* (atan2 x.im x.re) y.im))
15.0ms
(* (atan2 x.im x.re) y.im)

series200.0ms

Counts
3 → 9
Calls
3 calls:
143.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
29.0ms
(exp (* (atan2 x.im x.re) y.im))
28.0ms
(* (atan2 x.im x.re) y.im)

simplify2.4s

Counts
82 → 82
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01401140
12581099
26741035
322511026
done50001024

prune320.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

regimes450.0ms

Accuracy

61% (7.7b remaining)

Error of 11.7b against oracle of 4.0b and baseline of 23.8b

bsearch201.0ms

Steps
ItersRangePoint
10
-1.6296067729935965e-307
7.986361683910152e-295
-2.08400593192104e-310

simplify14.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02640
13636
23836
done3836

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.3s1893×body1280valid
1.9s8022×body80valid
1.8s1414×body640valid
430.0ms663×body320valid
145.0ms294×body160valid