Details

Time bar (total: 30.3s)

sample76.0ms

Algorithm
intervals
Results
25.0ms35×body2560valid
16.0ms190×body80valid
8.0ms256×pre80true
7.0ms17×body1280valid
3.0ms8×body640valid
1.0ms4×body160valid
1.0ms1×body5120valid
0.0ms1×body320valid

simplify19.8s

Counts
1 → 1
Iterations
IterNodes
done2000
1841992
1831984
1821956
1811950
1801924
1791917
1781894
1771888
1761867
1751861
1741841
1731835
1721818
1711812
1701797
1691790
1681774
1671768
1661752
1651746
1641730
1631724
1621709
1611703
1601688
1591682
1581669
1571663
1561650
1551644
1541631
1531625
1521612
1511606
1501593
1491587
1481574
1471568
1461555
1451549
1441536
1431530
1421517
1411511
1401498
1391492
1381479
1371473
1361460
1351454
1341441
1331435
1321422
1311416
1301403
1291397
1281384
1271378
1261365
1251359
1241346
1231340
1221327
1211321
1201308
1191302
1181289
1171283
1161270
1151264
1141251
1131245
1121232
1111226
1101213
1091207
1081194
1071188
1061175
1051169
1041156
1031150
1021137
1011131
1001118
991112
981099
971093
961080
951074
941061
931055
921042
911036
901023
891017
881004
87998
86985
85979
84966
83960
82947
81941
80928
79922
78909
77903
76890
75884
74871
73865
72852
71846
70833
69827
68814
67808
66795
65789
64776
63770
62757
61751
60738
59732
58719
57713
56700
55694
54681
53675
52662
51656
50643
49637
48624
47618
46605
45599
44586
43580
42567
41561
40548
39542
38529
37523
36510
35504
34491
33485
32472
31466
30453
29447
28434
27428
26415
25409
24396
23390
22377
21371
20358
19352
18339
17333
16320
15314
14301
13295
12282
11276
10263
9257
8244
7229
6217
5190
4147
395
258
130
014

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4 p) p) (* x x))
0.0b
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
0.9b
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
16.3b
(sqrt (+ (* (* 4 p) p) (* x x)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 *-un-lft-identity add-log-exp
7×add-sqr-sqrt
6×add-cube-cbrt
4×expm1-log1p-u fma-def flip3-+ add-cbrt-cube sqrt-div add-exp-log sqrt-prod flip-+ insert-posit16 log1p-expm1-u
3×sqrt-pow1
2×+-commutative sum-log pow1/2 associate-*r/
1×rem-sqrt-square pow-prod-down distribute-lft-out
Counts
4 → 67
Calls
4 calls:
15.0ms
(+ (* (* 4 p) p) (* x x))
52.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
61.0ms
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
29.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (* (* 4 p) p) (* x x))
238.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
102.0ms
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
62.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

simplify484.0ms

Counts
79 → 79
Iterations
IterNodes
done2000
2884
1260
0106

prune438.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))
8.7b
(+ 1 (/ x (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))))
16.3b
(sqrt (+ (* (* 4 p) p) (* x x)))
16.3b
(sqrt (+ (* (* 4 p) p) (* x x)))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
21×*-un-lft-identity
19×add-cube-cbrt
18×pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-cbrt-cube add-exp-log add-log-exp
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u
3×fma-def
2×rem-sqrt-square associate-*l/ associate-*r/
1×pow2 +-commutative sum-log rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 140
Calls
4 calls:
126.0ms
(* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))
88.0ms
(+ 1 (/ x (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))))
26.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
31.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))
101.0ms
(+ 1 (/ x (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))))
68.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
66.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

simplify667.0ms

Counts
152 → 152
Iterations
IterNodes
done2000
2962
1330
0146

prune636.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.5b

localize45.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (* (cbrt (+ (* (* 4 p) p) (* x x))) (cbrt (+ (* (* 4 p) p) (* x x)))))
17.1b
(cbrt (+ (* (* 4 p) p) (* x x)))
17.1b
(cbrt (+ (* (* 4 p) p) (* x x)))
17.1b
(cbrt (+ (* (* 4 p) p) (* x x)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u frac-times add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 78
Calls
4 calls:
36.0ms
(sqrt (* (cbrt (+ (* (* 4 p) p) (* x x))) (cbrt (+ (* (* 4 p) p) (* x x)))))
11.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
11.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(sqrt (* (cbrt (+ (* (* 4 p) p) (* x x))) (cbrt (+ (* (* 4 p) p) (* x x)))))
177.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
160.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
175.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))

simplify786.0ms

Counts
90 → 90
Iterations
IterNodes
done2000
31847
2533
1218
0112

prune652.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.5b

localize46.0ms

Local error

Found 4 expressions with local error:

16.3b
(sqrt (+ (* (* 4 p) p) (* x x)))
16.3b
(sqrt (+ (* (* 4 p) p) (* x x)))
16.3b
(sqrt (+ (* (* 4 p) p) (* x x)))
16.3b
(sqrt (+ (* (* 4 p) p) (* x x)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
29.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
18.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

series205.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
45.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
49.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
65.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

simplify887.0ms

Counts
84 → 84
Iterations
IterNodes
done2000
41682
3739
2294
1105
044

prune640.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.5b

regimes432.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done21
121
014

end0.0ms

sample2.3s

Algorithm
intervals
Results
751.0ms740×body2560valid
570.0ms5982×body80valid
330.0ms684×body1280valid
307.0ms8000×pre80true
121.0ms311×body640valid
54.0ms138×body320valid
36.0ms57×body5120valid
14.0ms88×body160valid