Details

Time bar (total: 9.4s)

sample81.0ms

Algorithm
intervals
Results
22.0msbody640valid
16.0ms194×body80valid
11.0ms24×body2560valid
6.0ms11×body5120valid
5.0ms13×body1280valid
1.0msbody320valid
0.0msbody160valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01215
12215
22415
done2415

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
30.1b
(sqrt (+ (* re re) (* im im)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
pow1
*-un-lft-identity
add-sqr-sqrt add-log-exp
sqrt-div add-cube-cbrt sqrt-prod
sqrt-pow1 flip3-+ add-cbrt-cube add-exp-log flip-+
pow1/2 associate-*r/
+-commutative rem-sqrt-square sum-log pow-prod-down distribute-lft-out
Counts
3 → 40
Calls
3 calls:
45.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
68.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
15.0ms
(sqrt (+ (* re re) (* im im)))

series535.0ms

Counts
3 → 9
Calls
3 calls:
362.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
103.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
71.0ms
(sqrt (+ (* re re) (* im im)))

simplify862.0ms

Counts
49 → 49
Iterations

Useful iterations: done (860.0ms)

IterNodesCost
099722
1254621
2955571
done5001547

prune323.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.5b
(- (sqrt (+ (* re re) (* im im))) re)
28.9b
(sqrt (* 2.0 (+ (* im im) 0)))
30.1b
(sqrt (+ (* re re) (* im im)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt sqrt-prod
37×*-un-lft-identity
36×times-frac
25×add-cube-cbrt
12×difference-of-squares
associate-/r*
pow1 sqrt-div
add-cbrt-cube add-exp-log distribute-lft-out-- add-log-exp
associate-*r/ associate-/l*
sqrt-pow1 flip3-+ flip-+
flip3-- pow1/2 associate-/r/ flip-- associate-/l/
cbrt-undiv rem-sqrt-square sqrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down div-inv
Counts
4 → 109
Calls
4 calls:
104.0ms
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
76.0ms
(- (sqrt (+ (* re re) (* im im))) re)
19.0ms
(sqrt (* 2.0 (+ (* im im) 0)))
25.0ms
(sqrt (+ (* re re) (* im im)))

series1.2s

Counts
4 → 12
Calls
4 calls:
382.0ms
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
694.0ms
(- (sqrt (+ (* re re) (* im im))) re)
73.0ms
(sqrt (* 2.0 (+ (* im im) 0)))
76.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.8s

Counts
121 → 121
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02112952
14702509
222202366
done50012346

prune708.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

regimes858.0ms

Accuracy

70.2% (8.5b remaining)

Error of 18.6b against oracle of 10.2b and baseline of 38.6b

bsearch276.0ms

Steps
ItersRangePoint
7
8.899619087721241e+126
1.7133257233628994e+129
4.9447949615143554e+128
6
-2.5756920490778766e-295
-3.47690487203495e-296
-3.532234512109791e-296
8
-5.460036253378982e+137
-9.352743772962526e+133
-5.369633668174499e+137

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
04269
15467
25567
done5567

end0.0ms

sample2.4s

Algorithm
intervals
Results
560.0ms5976×body80valid
538.0ms668×body2560valid
309.0ms322×body5120valid
263.0ms482×body1280valid
122.0ms316×body640valid
91.0ms157×body320valid
68.0ms79×body160valid