Details

Time bar (total: 3.9s)

sample28.0ms

Algorithm
intervals
Results
6.0ms185×body80valid
5.0ms29×body2560valid
3.0ms14×body5120valid
2.0ms16×body1280valid
1.0ms6×body640valid
0.0ms4×body320valid
0.0ms2×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0178
1248
2308
3358
4358
done358

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.4b
(- (sqrt (+ (* re re) (* im im))) re)
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1
6×*-un-lft-identity
5×sqrt-prod add-log-exp
4×add-cube-cbrt sqrt-div
3×add-exp-log sqrt-pow1 add-cbrt-cube
2×flip3-- pow1/2 associate-*r/ flip-- difference-of-squares
1×sub-neg rem-sqrt-square flip3-+ diff-log pow-prod-down flip-+ distribute-lft-out--
Counts
3 → 43
Calls
3 calls:
26.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
41.0ms
(- (sqrt (+ (* re re) (* im im))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))

series259.0ms

Counts
3 → 9
Calls
3 calls:
171.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
47.0ms
(- (sqrt (+ (* re re) (* im im))) re)
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Counts
52 → 52
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0232382
1768356
22506346
35001344
done5001344

prune143.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.7b
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.7b
(sqrt (+ (* re re) (* im im)))
31.7b
(sqrt (+ (* re re) (* im im)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×flip3-+ flip-+
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 126
Calls
4 calls:
53.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
39.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
50.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
36.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify45.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02611112
1935975
25001951
done5001951

prune280.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.3b

localize25.0ms

Local error

Found 4 expressions with local error:

31.7b
(sqrt (+ (* re re) (* im im)))
32.8b
(cbrt (+ (* re re) (* im im)))
32.8b
(cbrt (+ (* re re) (* im im)))
32.8b
(cbrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
7.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ (* re re) (* im im)))
97.0ms
(cbrt (+ (* re re) (* im im)))
96.0ms
(cbrt (+ (* re re) (* im im)))
99.0ms
(cbrt (+ (* re re) (* im im)))

simplify49.0ms

Counts
66 → 66
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0141466
1440436
21469430
35002429
done5002429

prune353.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 20.3b

localize28.0ms

Local error

Found 4 expressions with local error:

31.7b
(sqrt (+ (* re re) (* im im)))
32.8b
(cbrt (+ (* re re) (* im im)))
32.8b
(cbrt (+ (* re re) (* im im)))
34.8b
(pow (+ (* re re) (* im im)) 1/3)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod
5×add-exp-log
4×cbrt-div add-cbrt-cube add-log-exp
3×unpow-prod-down pow-unpow flip3-+ sqrt-prod flip-+
2×pow1/3 sqrt-div
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow1/3 pow-exp sqr-pow
Counts
4 → 59
Calls
4 calls:
10.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
10.0ms
(pow (+ (* re re) (* im im)) 1/3)

series330.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(sqrt (+ (* re re) (* im im)))
97.0ms
(cbrt (+ (* re re) (* im im)))
98.0ms
(cbrt (+ (* re re) (* im im)))
98.0ms
(pow (+ (* re re) (* im im)) 1/3)

simplify82.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0189451
1662396
22534389
35002389
done5002389

prune354.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.3b

regimes245.0ms

Accuracy

57% (9.2b remaining)

Error of 27.1b against oracle of 18.0b and baseline of 39.3b

bsearch126.0ms

Steps
ItersRangePoint
10
2.7636474607770915e-218
1.3181567757377188e-202
2.8212693804736227e-218
7
-1.1247036883386809e-263
-5.3645173288875583e-266
-6.851668065765394e-264
11
-6.794613467217019e+116
-3.315834628005633e+95
-6.754060706975556e+99

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05033
15033
done5033

end0.0ms

sample710.0ms

Algorithm
intervals
Results
199.0ms5947×body80valid
136.0ms726×body2560valid
84.0ms528×body1280valid
69.0ms294×body5120valid
33.0ms284×body640valid
12.0ms136×body320valid
5.0ms85×body160valid