Details

Time bar (total: 13.2s)

sample145.0ms

Algorithm
intervals
Results
13.0ms198×body80valid
8.0ms23×body2560valid
5.0ms16×body1280valid
2.0ms7×body5120valid
1.0ms6×body320valid
1.0ms5×body640valid
0.0ms1×body160valid

simplify493.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.9b
(- (sqrt (+ (* re re) (* im im))) re)
31.3b
(sqrt (+ (* re re) (* im im)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-log-exp
6×*-un-lft-identity
4×pow1 add-cube-cbrt sqrt-prod
3×add-cbrt-cube add-exp-log
2×flip3-+ sqrt-div flip-+ difference-of-squares
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
3 → 41
Calls
3 calls:
27.0ms
(+ (* re re) (* im im))
63.0ms
(- (sqrt (+ (* re re) (* im im))) re)
16.0ms
(sqrt (+ (* re re) (* im im)))

series195.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ (* re re) (* im im))
83.0ms
(- (sqrt (+ (* re re) (* im im))) re)
81.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.0s

Counts
50 → 50
Iterations
IterNodes
done5001
32011
2493
1174
074

prune296.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (sqrt (+ (* re re) (* im im))) re)
5.3b
(sqrt (* 2.0 (/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) re))))
23.1b
(/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) re))
31.3b
(sqrt (+ (* re re) (* im im)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
8×pow1
6×add-cbrt-cube add-exp-log add-log-exp
5×distribute-lft-out
4×associate-/r* flip3-+ sqrt-prod flip-+
3×sqrt-pow1 sqrt-div associate-/l*
2×pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp pow-prod-down associate-*r/ div-inv
Counts
4 → 74
Calls
4 calls:
31.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
45.0ms
(sqrt (* 2.0 (/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) re))))
69.0ms
(/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) re))
13.0ms
(sqrt (+ (* re re) (* im im)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
268.0ms
(sqrt (* 2.0 (/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) re))))
122.0ms
(/ (+ (* im im) 0) (+ (sqrt (+ (* re re) (* im im))) re))
58.0ms
(sqrt (+ (* re re) (* im im)))

simplify2.9s

Counts
86 → 86
Iterations
IterNodes
done5044
34168
21110
1391
0162

prune548.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune54.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
0.5b
(+ (sqrt (+ (* re re) (* im im))) re)
5.3b
(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
31.3b
(sqrt (+ (* re re) (* im im)))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt
18×associate-*r*
14×add-cube-cbrt
13×pow1 times-frac
9×add-cbrt-cube add-exp-log
6×add-log-exp
4×sqrt-pow1 pow-prod-down sqrt-prod distribute-lft-out
3×flip3-+ sqrt-div associate-*l* associate-*r/ flip-+
2×pow1/2 prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative rem-sqrt-square sum-log div-exp *-commutative div-inv
Counts
4 → 77
Calls
4 calls:
100.0ms
(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
32.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
96.0ms
(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
7.0ms
(sqrt (+ (* re re) (* im im)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))
82.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
209.0ms
(sqrt (* 2.0 (* (fabs im) (/ (fabs im) (+ (sqrt (+ (* re re) (* im im))) re)))))
48.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts
89 → 89
Iterations
IterNodes
done5001
21674
1480
0179

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

regimes345.0ms

Accuracy

50.9% (19.3b remaining)

Error of 25.0b against oracle of 5.6b and baseline of 45.1b

bsearch603.0ms

Steps
ItersRangePoint
9
3.9952915796079135e+93
1.8874507556058633e+102
8.312232129912929e+97
9
2.5431457216642727e+36
1.1392637045427953e+45
2.580378641751245e+36
7
1.8546558419492603e+18
7.015438422230291e+19
6.939159969879892e+19
8
1.7368421141129907e-168
1.054098417937684e-163
1.0325561614582738e-163
8
-1.4343846815141505e-92
-3.201997325218648e-96
-9.390513393497782e-96
8
-1.2418282342479434e+117
-1.3893569940611192e+114
-1.2297103312292532e+117
7
-1.8254437613711665e+160
-1.8020288129482739e+158
-1.83059393992081e+158

simplify78.0ms

Iterations
IterNodes
done107
3107
2106
1101
073

end0.0ms

sample2.0s

Algorithm
intervals
Results
809.0ms6033×body80valid
256.0ms677×body2560valid
255.0ms313×body5120valid
247.0ms479×body1280valid
158.0ms274×body640valid
24.0ms142×body320valid
14.0ms82×body160valid