Details

Time bar (total: 19.2s)

sample101.0ms

Algorithm
intervals
Results
29.0ms178×body80valid
22.0ms34×body2560valid
10.0ms19×body1280valid
10.0ms256×pre80true
5.0ms14×body640valid
4.0ms4×body5120valid
2.0ms4×body320valid
1.0ms3×body160valid

simplify6.9s

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: 15.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* p (* 4 p)))
0.0b
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
0.8b
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
12.6b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×sqrt-prod
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log associate-/r/ flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log distribute-lft1-in sqrt-pow1 distribute-rgt-out pow1/2 distribute-lft-out
Counts
4 → 62
Calls
4 calls:
8.0ms
(+ (* x x) (* p (* 4 p)))
43.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
43.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
10.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (* x x) (* p (* 4 p)))
265.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
106.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
65.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify945.0ms

Counts
74 → 74
Iterations
IterNodes
done2013
32013
2719
1236
0100

prune379.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ 0.5 (/ (* x 0.5) (sqrt (+ (* (* p 4) p) (* x x)))))
0.8b
(+ 0.5 (/ (* x 0.5) (sqrt (+ (* (* p 4) p) (* x x)))))
12.6b
(sqrt (+ (* (* p 4) p) (* x x)))
12.6b
(sqrt (+ (* (* p 4) p) (* x x)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 distribute-lft-out
Counts
4 → 58
Calls
4 calls:
37.0ms
(+ 0.5 (/ (* x 0.5) (sqrt (+ (* (* p 4) p) (* x x)))))
38.0ms
(+ 0.5 (/ (* x 0.5) (sqrt (+ (* (* p 4) p) (* x x)))))
17.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
22.0ms
(sqrt (+ (* (* p 4) p) (* x x)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ 0.5 (/ (* x 0.5) (sqrt (+ (* (* p 4) p) (* x x)))))
95.0ms
(+ 0.5 (/ (* x 0.5) (sqrt (+ (* (* p 4) p) (* x x)))))
52.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
46.0ms
(sqrt (+ (* (* p 4) p) (* x x)))

simplify1.0s

Counts
70 → 70
Iterations
IterNodes
done2001
42001
31380
2469
1171
069

prune394.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.6b

localize84.0ms

Local error

Found 4 expressions with local error:

12.6b
(sqrt (+ (* (* p 4) p) (* x x)))
12.6b
(sqrt (+ (* (* p 4) p) (* x x)))
12.6b
(sqrt (+ (* (* p 4) p) (* x x)))
12.6b
(sqrt (+ (* (* p 4) p) (* x x)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
18.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
22.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
29.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
19.0ms
(sqrt (+ (* (* p 4) p) (* x x)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
65.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
63.0ms
(sqrt (+ (* (* p 4) p) (* x x)))
57.0ms
(sqrt (+ (* (* p 4) p) (* x x)))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
done2011
52011
41799
3577
2237
196
042

prune744.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
0.6b
(log (exp (sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))))
0.8b
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
12.6b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
15×sqrt-prod
11×add-sqr-sqrt
10×log-pow
9×exp-prod add-cube-cbrt
7×pow1
6×associate-/r/ add-log-exp
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×log-prod distribute-lft1-in flip3-+ distribute-rgt-out flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log rem-log-exp
Counts
4 → 72
Calls
4 calls:
33.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
70.0ms
(log (exp (sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))))
34.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series603.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
243.0ms
(log (exp (sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))))
82.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
47.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.3s

Counts
84 → 84
Iterations
IterNodes
done2008
42008
31713
2566
1231
0118

prune456.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.6b

regimes181.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done40
140
030

end0.0ms

sample3.0s

Algorithm
intervals
Results
924.0ms781×body2560valid
781.0ms5919×body80valid
489.0ms671×body1280valid
344.0ms8000×pre80true
186.0ms327×body640valid
50.0ms157×body320valid
47.0ms55×body5120valid
20.0ms90×body160valid