Details

Time bar (total: 14.6s)

sample122.0ms

Algorithm
intervals
Results
28.0ms268×body80nan
25.0ms146×body160valid
18.0ms524×pre80true
10.0ms110×body80valid

simplify134.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
28.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×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:
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
50.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series458.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(- (* b b) (* (* 4.0 a) c))
161.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
144.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify3.1s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01541592
13861488
212341332
346461324
done50001324

prune418.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.9b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune49.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.9b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.2b
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
2×pow1 frac-2neg clear-num div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 51
Calls
2 calls:
21.0ms
(/ (* a c) b)
54.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series78.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (* a c) b)
40.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify1.2s

Counts
57 → 57
Iterations

Useful iterations: 2 (359.0ms)

IterNodesCost
0107782
1310751
21631523
done5000523

prune200.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 9.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
0.3b
(/ a (sqrt b))
0.3b
(/ c (sqrt b))
0.3b
(* (/ a (sqrt b)) (/ c (sqrt b)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
85×times-frac
76×add-exp-log add-cbrt-cube
60×add-cube-cbrt *-un-lft-identity
48×sqrt-prod
28×prod-exp cbrt-unprod
26×cbrt-undiv div-exp
22×associate-*r* associate-*l*
13×associate-/r*
9×unswap-sqr
7×associate-/l*
6×pow1
5×associate-*r/ div-inv
4×add-log-exp
3×frac-2neg clear-num associate-/l/
2×frac-times associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 191
Calls
4 calls:
77.0ms
(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
11.0ms
(/ a (sqrt b))
11.0ms
(/ c (sqrt b))
68.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
57.0ms
(/ a (sqrt b))
68.0ms
(/ c (sqrt b))
62.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify2.3s

Counts
203 → 203
Iterations

Useful iterations: 2 (948.0ms)

IterNodesCost
03032968
18532732
240502134
done50002134

prune675.0ms

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 9.7b

regimes802.0ms

Accuracy

44.7% (7.7b remaining)

Error of 16.6b against oracle of 8.9b and baseline of 22.9b

bsearch22.0ms

Steps
ItersRangePoint
1
172.19531990517868
188.1359396834071
176.18047484973576

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02445
13245
done3245

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.1s16620×pre80true
1.1s4450×body160valid
992.0ms8620×body80nan
314.0ms3550×body80valid