Details

Time bar (total: 21.4s)

sample141.0ms

Algorithm
intervals
Results
48.0ms192×body80valid
29.0ms27×body2560valid
22.0ms26×body1280valid
14.0ms256×pre80true
3.0ms4×body640valid
3.0ms5×body320valid
1.0ms2×body160valid

simplify7.9s

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize48.0ms

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 x) (* p (* 4 p)))
0.9b
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
17.1b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite138.0ms

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:
60.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
11.0ms
(+ (* x x) (* p (* 4 p)))
53.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
57.0ms
(+ (* x x) (* p (* 4 p)))
114.0ms
(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
55.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.2s

Counts
74 → 74
Iterations
IterNodes
done2036
32036
2721
1236
0100

prune750.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:
16.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
11.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
10.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
47.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
58.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
70.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.1s

Counts
76 → 76
Iterations
IterNodes
done2000
42000
3638
2253
197
042

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.0b

localize83.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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:
8.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
63.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
58.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
50.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

simplify934.0ms

Counts
76 → 76
Iterations
IterNodes
done2000
42000
3638
2253
197
042

prune1.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 13.9b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 93
Calls
4 calls:
48.0ms
(sqrt (* (* (cbrt (+ (* x x) (* p (* 4 p)))) (cbrt (+ (* x x) (* p (* 4 p))))) (cbrt (+ (* x x) (* p (* 4 p))))))
4.0ms
(cbrt (+ (* x x) (* p (* 4 p))))
4.0ms
(cbrt (+ (* x x) (* p (* 4 p))))
4.0ms
(cbrt (+ (* x x) (* p (* 4 p))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(sqrt (* (* (cbrt (+ (* x x) (* p (* 4 p)))) (cbrt (+ (* x x) (* p (* 4 p))))) (cbrt (+ (* x x) (* p (* 4 p))))))
109.0ms
(cbrt (+ (* x x) (* p (* 4 p))))
110.0ms
(cbrt (+ (* x x) (* p (* 4 p))))
110.0ms
(cbrt (+ (* x x) (* p (* 4 p))))

simplify1.0s

Counts
105 → 105
Iterations
IterNodes
done2011
42011
31638
2572
1307
0174

prune1.1s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 13.9b

regimes208.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done30
130
021

end0.0ms

sample2.4s

Algorithm
intervals
Results
889.0ms6068×body80valid
534.0ms743×body2560valid
325.0ms586×body1280valid
297.0ms8000×pre80true
106.0ms306×body640valid
67.0ms167×body320valid
32.0ms49×body5120valid
14.0ms81×body160valid