Details

Time bar (total: 7.0s)

sample47.0ms

Algorithm
intervals
Results
11.0ms200×body80valid
8.0ms24×body2560valid
5.0ms256×pre80true
4.0ms15×body1280valid
2.0ms10×body640valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23317
33717
43917
54017
done4017

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.1b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.2b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
14.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series71.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify835.0ms

Counts
93 → 93
Iterations

Useful iterations: 3 (205.0ms)

IterNodesCost
01371776
12851603
27121526
318701484
done50001484

prune218.0ms

Filtered
72 candidates to 93 candidates (-29.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New831093
Fresh000
Picked101
Done000
Total841094

Merged error: 11.8b

Counts
94 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×sqrt-div associate-/r* add-log-exp
5×unswap-sqr
4×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip associate-*l* associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 122
Calls
4 calls:
9.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series41.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
10.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify934.0ms

Counts
134 → 134
Iterations

Useful iterations: 3 (408.0ms)

IterNodesCost
01582438
13752085
211051877
330741840
done50011840

prune233.0ms

Filtered
79 candidates to 134 candidates (-69.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1313134
Fresh279
Picked101
Done000
Total13410144

Merged error: 11.8b

Counts
144 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
0.2b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
23×add-sqr-sqrt
22×add-cube-cbrt
18×times-frac
16×sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log-pow
4×exp-prod sqrt-div
3×log-prod flip3-+ flip-+ associate-/l*
2×associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log div-inv distribute-lft-out
Counts
4 → 84
Calls
4 calls:
2.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
8.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
17.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series67.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
10.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts
96 → 96
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01511866
12951696
26811582
316681553
441221549
done50011548

prune259.0ms

Filtered
76 candidates to 96 candidates (-26.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New90696
Fresh459
Picked101
Done000
Total9511106

Merged error: 11.8b

Counts
106 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
23×*-un-lft-identity
22×times-frac
21×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×exp-prod sqrt-div prod-exp
3×log-prod flip3-+ associate-*l* flip-+
2×div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ rem-log-exp pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 91
Calls
4 calls:
16.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
35.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
13.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify923.0ms

Counts
103 → 103
Iterations

Useful iterations: 3 (373.0ms)

IterNodesCost
01741966
14051658
210731458
331811421
done50001421

prune201.0ms

Filtered
76 candidates to 103 candidates (-35.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1021103
Fresh2810
Picked101
Done000
Total1059114

Merged error: 11.8b

Counts
114 → 9

regimes330.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01821
12321
done2321

end0.0ms

sample1.3s

Algorithm
intervals
Results
348.0ms6092×body80valid
264.0ms783×body2560valid
159.0ms582×body1280valid
139.0ms8000×pre80true
68.0ms320×body640valid
24.0ms154×body320valid
7.0ms69×body160valid

Profiling

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