Details

Time bar (total: 6.1s)

sample22.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms84×body80nan

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
068
188
done88

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
8.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series25.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
17.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify581.0ms

Counts
70 → 70
Iterations

Useful iterations: 2 (193.0ms)

IterNodesCost
01871150
14661087
216921037
done50011037

prune137.0ms

Filtered
55 candidates to 70 candidates (-27.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New67370
Fresh000
Picked011
Done000
Total67471

Merged error: 0b

Counts
71 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
232×sqrt-prod
192×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 317
Calls
4 calls:
6.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
9.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
25.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
11.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
38.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
23.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.1s

Counts
329 → 329
Iterations

Useful iterations: done (1.1s)

IterNodesCost
046810705
111479211
235368714
done50008712

prune607.0ms

Filtered
153 candidates to 329 candidates (-115.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New3290329
Fresh022
Picked011
Done011
Total3294333

Merged error: 0b

Counts
333 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cbrt x) (cbrt x))
2.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series100.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (cbrt x) (cbrt x))
23.0ms
(cbrt x)
27.0ms
(cbrt x)
23.0ms
(cbrt x)

simplify1.3s

Counts
85 → 85
Iterations

Useful iterations: 4 (625.0ms)

IterNodesCost
076590
1147521
2329462
3892382
42132374
done5000374

prune90.0ms

Filtered
56 candidates to 85 candidates (-51.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New85085
Fresh011
Picked011
Done022
Total85489

Merged error: 0b

Counts
89 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
21.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
9.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
17.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify1.1s

Counts
144 → 144
Iterations

Useful iterations: 2 (449.0ms)

IterNodesCost
03162787
18612520
235872362
done50002362

prune222.0ms

Filtered
94 candidates to 144 candidates (-53.2%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1440144
Fresh000
Picked011
Done033
Total1444148

Merged error: 0b

Counts
148 → 4

regimes69.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
done88

end0.0ms

sample481.0ms

Algorithm
intervals
Results
227.0ms7995×body80valid
74.0ms2671×body80nan
1.0ms5×body1280valid

Profiling

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