Details

Time bar (total: 10.3s)

sample85.0ms

Algorithm
intervals
Results
17.0ms530×pre80true
16.0ms145×body160valid
13.0ms274×body80nan
6.0ms38×body320valid
4.0ms73×body80valid

simplify81.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
38.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
add-exp-log add-cbrt-cube
add-log-exp
add-cube-cbrt
times-frac sqrt-prod associate-/l* difference-of-squares
pow1
flip3-- flip--
distribute-lft-out--
cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(- (* b b) (* (* 4.0 a) c))
100.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
51.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series383.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
98.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: 2 (252.0ms)

IterNodesCost
01541592
14051496
217831332
done50021332

prune310.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune41.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
0.3b
(/ (* a c) b)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
pow1 frac-2neg clear-num div-inv associate-/l* add-log-exp
associate-*r/ associate-/l/
Counts
2 → 51
Calls
2 calls:
28.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
10.0ms
(/ (* a c) b)

series46.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
23.0ms
(/ (* a c) b)

simplify1.2s

Counts
57 → 57
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0107782
1346751
22499551
done5001523

prune149.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 5.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
18×prod-exp cbrt-unprod
cbrt-undiv div-exp
pow1 add-sqr-sqrt add-cube-cbrt frac-2neg *-un-lft-identity times-frac clear-num associate-/r* div-inv associate-/l* add-log-exp
Counts
1 → 31
Calls
1 calls:
38.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series23.0ms

Counts
1 → 3
Calls
1 calls:
23.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify1.6s

Counts
34 → 34
Iterations

Useful iterations: 2 (269.0ms)

IterNodesCost
086643
1309616
22437396
done5000396

prune40.0ms

Pruning

24 alts after pruning (22 fresh and 2 done)

Merged error: 5.2b

regimes392.0ms

Accuracy

9% (6.4b remaining)

Error of 11.5b against oracle of 5.1b and baseline of 12.2b

bsearch53.0ms

Steps
ItersRangePoint
4
0.12472275306628457
0.2162455449205228
0.12731425734469268

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02139
12639
done2639

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.5s4863×body160valid
1.2s8286×body80nan
638.0ms16286×pre80true
383.0ms1285×body320valid
139.0ms1852×body80valid