Details

Time bar (total: 27.2s)

sample344.0ms

Algorithm
intervals
Results
88.0ms247×body80valid
71.0ms59×body1280valid
48.0ms47×body640valid
14.0ms25×body320valid
3.0ms8×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01937
13137
25336
38236
420136
582936
done500036

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize47.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.2b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite77.0ms

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)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (atan2 x.im x.re) y.im)
46.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
74.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
253.0ms
(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 (326.0ms)

IterNodesCost
095836
1193778
2437690
3816677
41651677
54087677
done5001677

prune477.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.2b

localize20.0ms

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)
1.2b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite84.0ms

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:
43.0ms
(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)
9.0ms
(* (atan2 x.im x.re) y.im)
15.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
122.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
64.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify3.6s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.8s)

IterNodesCost
01321042
1282985
2691871
31455860
44042859
done5000859

prune460.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
30.0b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
40.3b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite85.0ms

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:
38.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
16.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
12.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series283.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
71.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
70.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify2.0s

Counts
94 → 94
Iterations

Useful iterations: 3 (677.0ms)

IterNodesCost
01461404
13311042
2782958
32348944
done5001944

prune630.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize13.0ms

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))
1.2b
(* (atan2 x.im x.re) y.im)

rewrite27.0ms

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:
12.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
4.0ms
(exp (* (atan2 x.im x.re) y.im))
8.0ms
(* (atan2 x.im x.re) y.im)

series246.0ms

Counts
3 → 9
Calls
3 calls:
157.0ms
(/ (pow x.re y.re) (exp (* (atan2 x.im x.re) y.im)))
45.0ms
(exp (* (atan2 x.im x.re) y.im))
43.0ms
(* (atan2 x.im x.re) y.im)

simplify1.8s

Counts
82 → 82
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01401140
12581099
26741035
322511026
done50001024

prune266.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes570.0ms

Accuracy

68.3% (6.5b remaining)

Error of 10.4b against oracle of 3.9b and baseline of 24.5b

bsearch288.0ms

Steps
ItersRangePoint
12
-3.2120421718303128e-288
1.4555397631981125e-288
-3.5665767812761e-310

simplify13.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02755
13851
24051
done4051

end0.0ms

sample8.8s

Algorithm
intervals
Results
2.8s1963×body1280valid
2.8s7927×body80valid
1.7s1424×body640valid
454.0ms654×body320valid
167.0ms322×body160valid