Details

Time bar (total: 16.7s)

sample185.0ms

Algorithm
intervals
Results
52.0ms149×body160valid
42.0ms316×body80nan
35.0ms572×pre80true
19.0ms46×body320valid
9.0ms61×body80valid

simplify138.0ms

Counts
1 → 1
Iterations
IterNodes
898
798
697
595
487
370
243
124
014

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* c a) 4)))
0.2b
(- (* b b) (* (* c a) 4))
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
37.2b
(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
12.0ms
(sqrt (- (* b b) (* (* c a) 4)))
13.0ms
(- (* b b) (* (* c a) 4))
100.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
55.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

series402.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (- (* b b) (* (* c a) 4)))
50.0ms
(- (* b b) (* (* c a) 4))
130.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
130.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify1.5s

Counts
100 → 100
Iterations
IterNodes
33663
21093
1400
0161

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
10
00

prune88.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* -2 (/ (* a c) b)) a)
0.2b
(/ (* a c) b)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
8×cbrt-undiv div-exp
6×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
5×prod-exp cbrt-unprod
2×pow1 clear-num frac-2neg insert-posit16 div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 49
Calls
2 calls:
17.0ms
(/ (* -2 (/ (* a c) b)) a)
9.0ms
(/ (* a c) b)

series49.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(/ (* -2 (/ (* a c) b)) a)
25.0ms
(/ (* a c) b)

simplify2.3s

Counts
55 → 55
Iterations
IterNodes
36549
21058
1265
099

prune508.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 5.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ a (sqrt b))
0.2b
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) a)
0.3b
(/ c (sqrt b))
0.3b
(* (/ a (sqrt b)) (/ c (sqrt b)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
87×times-frac
62×*-un-lft-identity add-cube-cbrt
48×sqrt-prod
45×add-cbrt-cube add-exp-log
22×associate-*r* associate-*l*
16×cbrt-undiv div-exp
15×associate-/r*
13×prod-exp cbrt-unprod
9×unswap-sqr
7×associate-/l*
6×pow1
5×associate-*r/ div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l/
2×frac-times associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 187
Calls
4 calls:
8.0ms
(/ a (sqrt b))
48.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) a)
4.0ms
(/ c (sqrt b))
29.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ a (sqrt b))
55.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) a)
61.0ms
(/ c (sqrt b))
52.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify978.0ms

Counts
199 → 199
Iterations
IterNodes
22960
1811
0289

prune2.1s

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 5.4b

regimes682.0ms

Accuracy

12.3% (5.9b remaining)

Error of 10.9b against oracle of 5.0b and baseline of 11.7b

bsearch5.0ms

Steps
ItersRangePoint
0
2.6215348248553484e-05
2.6231519582090948e-05
2.6223433915322215e-05

simplify13.0ms

Iterations
IterNodes
235
135
026

end0.0ms

sample5.9s

Algorithm
intervals
Results
1.8s4847×body160valid
1.4s16358×pre80true
1.4s8358×body80nan
592.0ms1401×body320valid
254.0ms1752×body80valid