Details

Time bar (total: 15.9s)

sample121.0ms

Algorithm
intervals
Results
39.0ms25×body2560valid
28.0ms194×body80valid
15.0ms19×body1280valid
12.0ms256×pre80true
6.0ms10×body640valid
3.0ms7×body320valid
1.0ms1×body5120valid

simplify7.3s

Counts
1 → 1
Iterations
IterNodes
done2004
592004
581998
571980
561947
551929
541896
531878
521845
511827
501794
491776
481743
471725
461692
451674
441641
431623
421590
411572
401539
391521
381488
371470
361437
351419
341386
331368
321335
311317
301284
291266
281233
271215
261182
251164
241131
231113
221080
211062
201029
191011
18978
17960
16927
15909
14876
13858
12825
11786
10745
9598
8441
7301
6200
5145
4104
376
251
129
014

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
0.0b
(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
0.2b
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
87×*-un-lft-identity
83×add-sqr-sqrt
81×add-cube-cbrt
45×sqrt-prod
22×associate-/r*
9×add-cbrt-cube add-exp-log
6×pow1 add-log-exp
5×associate-/r/ div-inv
4×sqrt-div insert-posit16
3×cbrt-undiv flip3-+ div-exp flip-+ associate-/l*
2×rem-sqrt-square distribute-lft1-in sqrt-pow1 distribute-rgt-out pow1/2 distribute-lft-out
1×+-commutative clear-num sum-log frac-2neg
Counts
4 → 157
Calls
4 calls:
31.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
10.0ms
(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
39.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
11.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
79.0ms
(/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))
90.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
48.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.2s

Counts
169 → 169
Iterations
IterNodes
done2001
32001
21781
1641
0261

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 13.0b

localize39.0ms

Local error

Found 4 expressions with local error:

17.0b
(sqrt (+ (* x x) (* p (* 4 p))))
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))
19.6b
(cbrt (* (* (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 cbrt-div *-un-lft-identity add-cube-cbrt
6×sqrt-div
5×frac-times associate-*l/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 66
Calls
4 calls:
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
88.0ms
(cbrt (* (* (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
55.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
53.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
129.0ms
(cbrt (* (* (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))) (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5))))

simplify1.1s

Counts
78 → 78
Iterations
IterNodes
done2016
42016
31419
2397
1157
080

prune935.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 13.0b

regimes54.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done17
117
013

end0.0ms

sample2.6s

Algorithm
intervals
Results
640.0ms6023×body80valid
603.0ms760×body2560valid
538.0ms8000×pre80true
355.0ms622×body1280valid
137.0ms312×body640valid
48.0ms64×body5120valid
46.0ms150×body320valid
12.0ms69×body160valid