Details

Time bar (total: 11.2s)

sample244.0ms

Algorithm
intervals
Results
33.0ms190×body80valid
22.0ms21×body2560valid
14.0ms19×body1280valid
12.0ms10×body5120valid
5.0ms7×body640valid
2.0ms6×body160valid
1.0ms3×body320valid

simplify50.0ms

Counts
1 → 1
Iterations
IterNodes
done35
435
330
224
117
012

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize46.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (sqrt (+ (* re re) (* im im))) re)
32.4b
(sqrt (+ (* re re) (* im im)))

rewrite532.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×*-un-lft-identity
4×sqrt-prod add-log-exp
3×pow1 add-cube-cbrt
2×add-cbrt-cube sqrt-div add-exp-log insert-posit16 difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out--
Counts
2 → 32
Calls
2 calls:
57.0ms
(- (sqrt (+ (* re re) (* im im))) re)
14.0ms
(sqrt (+ (* re re) (* im im)))

series129.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(- (sqrt (+ (* re re) (* im im))) re)
59.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts
38 → 38
Iterations
IterNodes
done2000
52000
41983
3761
2328
1139
066

prune189.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 20.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (sqrt (+ (* re re) (* im im))) re)
7.0b
(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
22.8b
(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
32.4b
(sqrt (+ (* re re) (* im im)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt pow1
7×add-cube-cbrt
6×add-log-exp
4×associate-/r* times-frac sqrt-prod insert-posit16
3×sqrt-pow1 flip3-+ sqrt-div flip-+ distribute-lft-out
2×cbrt-undiv pow1/2 div-exp associate-/r/
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg pow-prod-down prod-exp associate-*r/ cbrt-unprod div-inv associate-/l*
Counts
4 → 68
Calls
4 calls:
25.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
20.0ms
(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
40.0ms
(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
16.0ms
(sqrt (+ (* re re) (* im im)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
244.0ms
(sqrt (* 2.0 (/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))))
123.0ms
(/ (* im im) (+ (sqrt (+ (* re re) (* im im))) re))
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts
80 → 80
Iterations
IterNodes
done2313
32313
21423
1405
0149

prune503.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize26.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune34.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.5b
(+ (sqrt (+ (* re re) (* im im))) re)
30.4b
(sqrt (* 2.0 (* im im)))
32.4b
(sqrt (+ (* re re) (* im im)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
32×sqrt-prod
28×times-frac
24×add-sqr-sqrt
23×add-cube-cbrt
11×pow1
7×associate-/r*
6×add-cbrt-cube add-exp-log distribute-lft-out add-log-exp
4×sqrt-pow1 sqrt-div insert-posit16 associate-/l*
3×flip3-+ pow-prod-down flip-+
2×pow1/2 associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv clear-num sum-log frac-2neg div-exp div-inv
Counts
4 → 97
Calls
4 calls:
45.0ms
(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
37.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms
(sqrt (* 2.0 (* im im)))
10.0ms
(sqrt (+ (* re re) (* im im)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(/ (sqrt (* 2.0 (* im im))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
73.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
53.0ms
(sqrt (* 2.0 (* im im)))
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
109 → 109
Iterations
IterNodes
done2001
32001
21069
1401
0184

prune497.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes283.0ms

Accuracy

47.7% (21.7b remaining)

Error of 24.1b against oracle of 2.4b and baseline of 43.9b

bsearch716.0ms

Steps
ItersRangePoint
8
2.401794819672077e+140
2.626676984913581e+143
1.1910552598904152e+142
6
232.09055164250086
2750.7292470041752
1523.943947555021
8
2.124739062182176e-34
6.217821280309226e-31
6.1294351368168115e-31
5
6.752685187424894e-204
1.6657514273570165e-203
1.6408918126130706e-203
7
-7.534446558861262e-308
4.867548318358949e-308
2.9021426245006e-309
6
-2.3353827726901156e-261
-3.1581098487864757e-262
-1.330280636298453e-261
7
-1.3046992663425911e-179
-6.34209636622517e-182
-3.3981436272511237e-181
5
-1.0107859835148207e+106
-4.1302838583952404e+105
-4.3633837281117996e+105

simplify67.0ms

Iterations
IterNodes
done96
396
292
184
060

end0.0ms

sample2.9s

Algorithm
intervals
Results
906.0ms6107×body80valid
659.0ms297×body5120valid
546.0ms664×body2560valid
362.0ms459×body1280valid
151.0ms251×body640valid
49.0ms135×body320valid
44.0ms87×body160valid