Details

Time bar (total: 15.7s)

sample445.0ms

Algorithm
intervals
Results
289.0ms199×body80valid
43.0ms19×body1280valid
18.0ms14×body2560valid
14.0ms14×body5120valid
3.0ms6×body640valid
2.0ms3×body160valid
0.0ms1×body320valid

simplify75.0ms

Counts
1 → 1
Iterations
IterNodes
535
435
330
224
117
012

prune47.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize51.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.9b
(- (sqrt (+ (* re re) (* im im))) re)
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1
6×*-un-lft-identity
5×sqrt-prod add-log-exp
4×sqrt-div add-cube-cbrt
3×sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16
2×flip3-- pow1/2 associate-*r/ flip-- difference-of-squares
1×rem-sqrt-square sub-neg flip3-+ diff-log pow-prod-down flip-+ distribute-lft-out--
Counts
3 → 46
Calls
3 calls:
21.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
48.0ms
(- (sqrt (+ (* re re) (* im im))) re)
22.0ms
(sqrt (+ (* re re) (* im im)))

series326.0ms

Counts
3 → 9
Calls
3 calls:
206.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
51.0ms
(- (sqrt (+ (* re re) (* im im))) re)
69.0ms
(sqrt (+ (* re re) (* im im)))

simplify705.0ms

Counts
55 → 55
Iterations
IterNodes
32259
2662
1230
0109

prune559.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.9b
(exp (log (sqrt (+ (* re re) (* im im)))))
13.8b
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×pow1 *-un-lft-identity
8×log-prod exp-sum add-cube-cbrt sqrt-prod
6×exp-prod sqrt-div add-log-exp
4×sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16
3×pow1/2 log-pow difference-of-squares
2×log-div flip3-+ flip3-- exp-diff associate-*r/ flip-+ flip--
1×rem-sqrt-square sub-neg diff-log pow-prod-down distribute-lft-out-- rem-exp-log
Counts
4 → 70
Calls
4 calls:
40.0ms
(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
8.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
58.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
10.0ms
(sqrt (+ (* re re) (* im im)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(sqrt (* 2.0 (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
45.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
70.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify719.0ms

Counts
82 → 82
Iterations
IterNodes
32409
2738
1285
0151

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.7b

localize53.0ms

Local error

Found 4 expressions with local error:

13.6b
(- (* (* (cbrt (exp (log (sqrt (+ (* re re) (* im im)))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×add-cbrt-cube add-exp-log insert-posit16
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sub-neg flip3-- diff-log flip--
Counts
4 → 61
Calls
4 calls:
180.0ms
(- (* (* (cbrt (exp (log (sqrt (+ (* re re) (* im im)))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
7.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))
17.0ms
(sqrt (+ (* re re) (* im im)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* (* (cbrt (exp (log (sqrt (+ (* re re) (* im im)))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) (cbrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
56.0ms
(sqrt (+ (* re re) (* im im)))
59.0ms
(sqrt (+ (* re re) (* im im)))
47.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts
73 → 73
Iterations
IterNodes
42670
3894
2351
1157
069

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.7b

localize128.0ms

Local error

Found 4 expressions with local error:

31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
9.0ms
(sqrt (+ (* re re) (* im im)))
11.0ms
(sqrt (+ (* re re) (* im im)))
12.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))

series206.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ (* re re) (* im im)))
70.0ms
(sqrt (+ (* re re) (* im im)))
51.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts
76 → 76
Iterations
IterNodes
52984
4989
3435
2194
190
039

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 15.7b

regimes356.0ms

Accuracy

40.6% (13.5b remaining)

Error of 30.9b against oracle of 17.4b and baseline of 40.1b

bsearch721.0ms

Steps
ItersRangePoint
10
9.062791147154517e+33
6.763790285975293e+44
1.859372996802564e+44
9
203.91479797368314
2267696953.837344
218.57910692591958
9
1.4051175593359627e-26
4.660166646174217e-21
8.029859693979724e-24
9
1.882335803414487e-155
3.768786011242832e-148
3.9853394263122405e-151
10
4.950543945967426e-264
1.0057073560265822e-251
5.029830627881142e-264
8
-8.380347169505624e-250
-1.6792198442350055e-252
-1.6983177429051942e-252
7
-1.7193558043547063e-157
-3.879349676624596e-159
-2.587387956107418e-158

simplify26.0ms

Iterations
IterNodes
262
162
051

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.4s5922×body80valid
566.0ms677×body2560valid
393.0ms521×body1280valid
349.0ms324×body5120valid
186.0ms317×body640valid
56.0ms160×body320valid
18.0ms79×body160valid