Details

Time bar (total: 14.7s)

sample88.0ms

Algorithm
intervals
Results
24.0ms189×body80valid
20.0ms26×body2560valid
13.0ms13×body5120valid
10.0ms14×body1280valid
5.0ms8×body640valid
1.0ms3×body320valid
1.0ms3×body160valid

simplify29.0ms

Counts
1 → 1
Iterations
IterNodes
356
256
146
012

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b
(+ (sqrt (+ (* re re) (* im im))) re)
29.3b
(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×sqrt-div add-cube-cbrt sqrt-prod
3×sqrt-pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square sum-log pow-prod-down distribute-lft-out
Counts
3 → 43
Calls
3 calls:
40.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
28.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms
(sqrt (+ (* re re) (* im im)))

series385.0ms

Counts
3 → 9
Calls
3 calls:
252.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
75.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
57.0ms
(sqrt (+ (* re re) (* im im)))

simplify554.0ms

Counts
52 → 52
Iterations
IterNodes
32003
2891
1431
0102

prune535.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.5b

localize58.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
30.2b
(cbrt (+ (* re re) (* im im)))
30.2b
(cbrt (+ (* re re) (* im im)))
30.2b
(cbrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 70
Calls
4 calls:
28.0ms
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
14.0ms
(cbrt (+ (* re re) (* im im)))
7.0ms
(cbrt (+ (* re re) (* im im)))
7.0ms
(cbrt (+ (* re re) (* im im)))

series494.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
111.0ms
(cbrt (+ (* re re) (* im im)))
148.0ms
(cbrt (+ (* re re) (* im im)))
118.0ms
(cbrt (+ (* re re) (* im im)))

simplify1.9s

Counts
82 → 82
Iterations
IterNodes
54676
41842
31006
2574
1362
098

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize77.0ms

Local error

Found 4 expressions with local error:

30.2b
(cbrt (+ (* re re) (* im im)))
30.2b
(cbrt (+ (* re re) (* im im)))
30.2b
(cbrt (+ (* re re) (* im im)))
30.2b
(cbrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube pow1/3 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 56
Calls
4 calls:
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(cbrt (+ (* re re) (* im im)))
122.0ms
(cbrt (+ (* re re) (* im im)))
105.0ms
(cbrt (+ (* re re) (* im im)))
103.0ms
(cbrt (+ (* re re) (* im im)))

simplify1.6s

Counts
68 → 68
Iterations
IterNodes
54426
41684
3855
2428
1223
052

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.9b
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.3b
(sqrt (+ (* re re) (* im im)))
29.3b
(sqrt (+ (* re re) (* im im)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-cbrt-cube add-exp-log add-log-exp
5×pow-prod-down pow-sqr
4×frac-times insert-posit16
2×rem-sqrt-square associate-*l/ associate-*r/
1×pow2 +-commutative sum-log rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
62.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
21.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
69.0ms
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
52.0ms
(sqrt (+ (* re re) (* im im)))
44.0ms
(sqrt (+ (* re re) (* im im)))

simplify792.0ms

Counts
140 → 140
Iterations
IterNodes
32120
2969
1503
0136

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.6b

regimes571.0ms

Accuracy

57.8% (8.4b remaining)

Error of 25.7b against oracle of 17.3b and baseline of 37.2b

bsearch108.0ms

Steps
ItersRangePoint
4
1.6614623208655807e+111
2.310891359266851e+111
2.1282394422164936e+111
4
1.0526647032619268e-288
1.7669848660662517e-288
1.0730314248253915e-288
8
-9.687258947367738e-245
-1.5584770251340243e-249
-1.940844341770915e-249

simplify7.0ms

Iterations
IterNodes
248
148
036

end0.0ms

sample2.6s

Algorithm
intervals
Results
825.0ms677×body2560valid
764.0ms6059×body80valid
379.0ms494×body1280valid
232.0ms301×body5120valid
149.0ms281×body640valid
40.0ms131×body320valid
13.0ms57×body160valid