Details

Time bar (total: 9.8s)

sample110.0ms

Algorithm
intervals
Results
32.0ms258×body80nan
21.0ms154×body160valid
15.0ms514×pre80true
7.0ms102×body80valid

simplify64.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize12.0ms

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))
0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
29.2b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite219.0ms

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)))
14.0ms
(- (* b b) (* (* 4.0 a) c))
135.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
60.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series422.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms
(- (* b b) (* (* 4.0 a) c))
161.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
102.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: 2 (310.0ms)

IterNodesCost
01541592
14051496
217831332
done50021332

prune345.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.2b

localize6.0ms

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

prune51.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.2b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

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:
13.0ms
(/ (* a c) b)
28.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series43.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(/ (* a c) b)
23.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify942.0ms

Counts
57 → 57
Iterations

Useful iterations: done (940.0ms)

IterNodesCost
0107782
1345751
22490569
done5001543

prune196.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.1b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
16×prod-exp cbrt-unprod
15×add-sqr-sqrt
13×associate-*r*
11×cbrt-undiv times-frac div-exp
10×add-cube-cbrt *-un-lft-identity
pow1
associate-*r/ associate-*l*
div-inv add-log-exp unswap-sqr
frac-2neg pow-prod-down clear-num associate-/r* *-commutative associate-/l/ associate-/l*
Counts
2 → 62
Calls
2 calls:
24.0ms
(* a (/ c b))
33.0ms
(/ (* -2.0 (* a (/ c b))) (* 2.0 a))

series65.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(* a (/ c b))
33.0ms
(/ (* -2.0 (* a (/ c b))) (* 2.0 a))

simplify1.6s

Counts
68 → 68
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0128873
1407836
22758644
done5000632

prune139.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 9.1b

regimes582.0ms

Accuracy

45.2% (7.6b remaining)

Error of 16.6b against oracle of 9.0b and baseline of 22.9b

bsearch37.0ms

Steps
ItersRangePoint
2
226.92574334621128
255.61310276743285
230.51166327386397

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02139
12639
done2639

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s8791×body80nan
833.0ms4436×body160valid
697.0ms16791×pre80true
323.0ms3564×body80valid