Details

Time bar (total: 6.4s)

sample424.0ms

Algorithm
intervals
Results
52.0ms54×body1280valid
24.0ms259×body80valid
16.0ms41×body640valid
5.0ms16×body320valid
1.0ms8×body160valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120
done500120

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize27.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.re)
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite50.0ms

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:
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
26.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
158.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify71.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0189422
1491385
21112381
32393381
45001381
done5001381

prune305.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

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))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite37.0ms

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:
8.0ms
(- (* (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)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
91.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify75.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0290540
1897500
22667491
35002491
done5002491

prune259.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize22.0ms

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)
1.9b
(* (atan2 x.im x.re) y.im)
30.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
41.8b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite38.0ms

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:
12.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series183.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify86.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0329609
11048548
23533542
35002542
done5002542

prune308.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
0.1b
(* (log x.re) y.re)
1.9b
(* (atan2 x.im x.re) y.im)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×pow1
7×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
6×associate-*r*
5×add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- diff-log log-pow flip--
Counts
3 → 49
Calls
3 calls:
7.0ms
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
8.0ms
(* (log x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)

series185.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(- (* (log x.re) y.re) (* (atan2 x.im x.re) y.im))
73.0ms
(* (log x.re) y.re)
18.0ms
(* (atan2 x.im x.re) y.im)

simplify69.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0208273
1698252
22248241
35002241
done5002241

prune130.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.1b

regimes290.0ms

Accuracy

74.8% (5.4b remaining)

Error of 8.9b against oracle of 3.5b and baseline of 25.1b

bsearch69.0ms

Steps
ItersRangePoint
6
-1.2071055562957725e-306
-2.9539567512785007e-307
-2.9822686677868795e-307

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03115
13515
23515
done3515

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s1948×body1280valid
676.0ms7994×body80valid
603.0ms1525×body640valid
193.0ms706×body320valid
45.0ms252×body160valid