Details

Time bar (total: 29.6s)

sample126.0ms

Algorithm
intervals
Results
36.0ms178×body80valid
29.0ms34×body2560valid
15.0ms19×body1280valid
12.0ms256×pre80true
8.0ms14×body640valid
4.0ms4×body5120valid
2.0ms4×body320valid
1.0ms3×body160valid

simplify20.4s

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.7b

localize23.0ms

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)))))))
0.8b
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
12.6b
(sqrt (+ (* (* 4 p) p) (* x x)))

rewrite108.0ms

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:
14.0ms
(+ (* (* 4 p) p) (* x x))
37.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
39.0ms
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
17.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (* (* 4 p) p) (* x x))
167.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
65.0ms
(+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))
46.0ms
(sqrt (+ (* (* 4 p) p) (* x x)))

simplify878.0ms

Counts
79 → 79
Iterations
IterNodes
done2000
32000
2884
1260
0106

prune315.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.6b

localize44.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* x x) (fma 4 (* p p) (* x x)))
12.6b
(sqrt (fma 4 (* p p) (* x x)))
12.6b
(sqrt (fma 4 (* p p) (* x x)))
12.6b
(sqrt (fma 4 (* p p) (* x x)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
7×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square associate-/r* sqrt-pow1 times-frac pow1/2
2×cbrt-undiv div-exp
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
8.0ms
(/ (* x x) (fma 4 (* p p) (* x x)))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))

series192.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (* x x) (fma 4 (* p p) (* x x)))
47.0ms
(sqrt (fma 4 (* p p) (* x x)))
45.0ms
(sqrt (fma 4 (* p p) (* x x)))
48.0ms
(sqrt (fma 4 (* p p) (* x x)))

simplify730.0ms

Counts
84 → 84
Iterations
IterNodes
done2000
32000
2601
1152
067

prune453.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.6b

localize53.0ms

Local error

Found 4 expressions with local error:

5.2b
(exp (log (sqrt (fma 4 (* p p) (* x x)))))
12.6b
(sqrt (fma 4 (* p p) (* x x)))
12.6b
(sqrt (fma 4 (* p p) (* x x)))
12.6b
(sqrt (fma 4 (* p p) (* x x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sqrt-prod
10×*-un-lft-identity add-cube-cbrt
9×pow1
6×log-prod exp-prod exp-sum
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square log-pow
1×rem-exp-log
Counts
4 → 71
Calls
4 calls:
4.0ms
(exp (log (sqrt (fma 4 (* p p) (* x x)))))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))

series186.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(exp (log (sqrt (fma 4 (* p p) (* x x)))))
48.0ms
(sqrt (fma 4 (* p p) (* x x)))
44.0ms
(sqrt (fma 4 (* p p) (* x x)))
50.0ms
(sqrt (fma 4 (* p p) (* x x)))

simplify861.0ms

Counts
83 → 83
Iterations
IterNodes
done2001
82001
71686
6835
5416
4236
3171
2112
182
062

prune517.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.6b

localize52.0ms

Local error

Found 4 expressions with local error:

5.6b
(pow E (log (sqrt (fma 4 (* p p) (* x x)))))
12.6b
(sqrt (fma 4 (* p p) (* x x)))
12.6b
(sqrt (fma 4 (* p p) (* x x)))
12.6b
(sqrt (fma 4 (* p p) (* x x)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×sqrt-prod
11×*-un-lft-identity add-cube-cbrt
10×pow1
6×unpow-prod-up pow-unpow log-prod
5×add-exp-log
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square unpow-prod-down log-pow
2×pow-exp
1×pow-to-exp e-exp-1 pow-pow sqr-pow
Counts
4 → 78
Calls
4 calls:
3.0ms
(pow E (log (sqrt (fma 4 (* p p) (* x x)))))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))
1.0ms
(sqrt (fma 4 (* p p) (* x x)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(pow E (log (sqrt (fma 4 (* p p) (* x x)))))
47.0ms
(sqrt (fma 4 (* p p) (* x x)))
43.0ms
(sqrt (fma 4 (* p p) (* x x)))
49.0ms
(sqrt (fma 4 (* p p) (* x x)))

simplify707.0ms

Counts
90 → 90
Iterations
IterNodes
done2000
42000
3813
2318
1174
085

prune621.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.6b

regimes259.0ms

Accuracy

0% (0.3b remaining)

Error of 14.0b against oracle of 13.7b and baseline of 14.0b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample2.4s

Algorithm
intervals
Results
865.0ms5919×body80valid
521.0ms781×body2560valid
369.0ms671×body1280valid
251.0ms8000×pre80true
130.0ms327×body640valid
54.0ms55×body5120valid
41.0ms157×body320valid
34.0ms90×body160valid