Details

Time bar (total: 4.6s)

sample37.0ms

Algorithm
intervals
Results
8.0ms24×body2560valid
6.0ms192×body80valid
4.0ms25×body1280valid
3.0ms256×pre80true
1.0ms10×body640valid
0.0ms4×body320valid
0.0ms1×body160valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419
done419

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 add-cube-cbrt
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div sum-log
1×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
Counts
3 → 38
Calls
3 calls:
16.0ms
(+ (* (* 4.0 p) p) (* x x))
52.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series177.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ (* (* 4.0 p) p) (* x x))
81.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify83.0ms

Counts
47 → 47
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0203365
1753336
22672332
35002331
done5002331

prune141.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.8b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
20×*-un-lft-identity
18×add-cube-cbrt pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 125
Calls
4 calls:
117.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
65.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
80.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
02901356
110841258
250011216
done50011216

prune324.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.1b

localize23.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
133.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
135.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
134.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify67.0ms

Counts
66 → 66
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0170591
1527553
22131547
35001531
done5001531

prune393.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.1b

localize28.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.3b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
135.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
137.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify67.0ms

Counts
68 → 68
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0170562
1527530
22131526
35001514
done5001514

prune398.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.1b

regimes370.0ms

Accuracy

0% (0.2b remaining)

Error of 13.8b against oracle of 13.5b and baseline of 13.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0199
1199
done199

end0.0ms

sample873.0ms

Algorithm
intervals
Results
206.0ms5975×body80valid
180.0ms831×body2560valid
114.0ms632×body1280valid
100.0ms8000×pre80true
46.0ms344×body640valid
15.0ms150×body320valid
5.0ms68×body160valid