Details

Time bar (total: 27.9s)

sample69.0ms

Algorithm
intervals
Results
18.0ms27×body2560valid
16.0ms192×body80valid
12.0ms26×body1280valid
8.0ms256×pre80true
1.0ms4×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify16.5s

Counts
1 → 1
Iterations
IterNodes
done2005
1932005
1921992
1911986
1901973
1891967
1881954
1871948
1861935
1851929
1841916
1831910
1821897
1811891
1801878
1791872
1781859
1771853
1761840
1751834
1741821
1731815
1721802
1711796
1701783
1691777
1681764
1671758
1661745
1651739
1641726
1631720
1621707
1611701
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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
0.0b
(+ (* (* 4 p) p) (* x x))
0.9b
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
17.1b
(sqrt (+ (* (* 4 p) p) (* x x)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u fma-def flip3-+ sqrt-div flip-+ insert-posit16 log1p-expm1-u
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv distribute-lft-out
Counts
4 → 95
Calls
4 calls:
21.0ms
(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
15.0ms
(+ (* (* 4 p) p) (* x x))
36.0ms
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
20.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ x (sqrt (+ (* (* 4 p) p) (* x x))))
35.0ms
(+ (* (* 4 p) p) (* x x))
65.0ms
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
43.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

simplify776.0ms

Counts
107 → 107
Iterations
IterNodes
done2000
32000
21164
1324
0136

prune770.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))
8.4b
(+ 1 (/ x (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))))
17.1b
(sqrt (+ (* (* 4 p) p) (* x x)))
17.1b
(sqrt (+ (* (* 4 p) p) (* x x)))

rewrite182.0ms

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:
87.0ms
(* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))
57.0ms
(+ 1 (/ x (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))))
19.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
17.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))
67.0ms
(+ 1 (/ x (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))))
42.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
45.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

simplify705.0ms

Counts
152 → 152
Iterations
IterNodes
done2000
32000
2962
1330
0146

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.0b

localize37.0ms

Local error

Found 4 expressions with local error:

9.1b
(+ 1 (/ x (* (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (sqrt (sqrt (+ (* (* 4 p) p) (* x x))))))))
17.1b
(sqrt (+ (* (* 4 p) p) (* x x)))
17.1b
(sqrt (+ (* (* 4 p) p) (* x x)))
17.1b
(sqrt (+ (* (* 4 p) p) (* x x)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u
3×rem-sqrt-square fma-def sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 72
Calls
4 calls:
147.0ms
(+ 1 (/ x (* (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (sqrt (sqrt (+ (* (* 4 p) p) (* x x))))))))
17.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
20.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
17.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

series200.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ 1 (/ x (* (* (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))) (sqrt (sqrt (sqrt (+ (* (* 4 p) p) (* x x)))))) (sqrt (sqrt (sqrt (+ (* (* 4 p) p) (* x x))))))))
43.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
46.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
43.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

simplify662.0ms

Counts
84 → 84
Iterations
IterNodes
done2001
32001
2713
1191
073

prune820.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.0b

localize57.0ms

Local error

Found 4 expressions with local error:

17.1b
(sqrt (+ (* (* 4 p) p) (* x x)))
17.9b
(cbrt (+ (* (* 4 p) p) (* x x)))
17.9b
(cbrt (+ (* (* 4 p) p) (* x x)))
17.9b
(cbrt (+ (* (* 4 p) p) (* x x)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 66
Calls
4 calls:
17.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
10.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
10.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))
129.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
129.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))
126.0ms
(cbrt (+ (* (* 4 p) p) (* x x)))

simplify1.2s

Counts
78 → 78
Iterations
IterNodes
done2014
42014
31996
2507
1181
083

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 14.0b

regimes163.0ms

Accuracy

0% (1.4b remaining)

Error of 14.2b against oracle of 12.8b and baseline of 14.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done27
127
018

end0.0ms

sample2.2s

Algorithm
intervals
Results
734.0ms743×body2560valid
629.0ms6068×body80valid
240.0ms586×body1280valid
239.0ms8000×pre80true
98.0ms306×body640valid
46.0ms49×body5120valid
40.0ms167×body320valid
13.0ms81×body160valid