Details

Time bar (total: 17.4s)

sample163.0ms

Algorithm
intervals
Results
43.0ms554×pre80true
40.0ms148×body160valid
40.0ms298×body80nan
14.0ms108×body80valid

simplify126.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize26.0ms

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)
29.2b
(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite148.0ms

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:
13.0ms
(sqrt (- (* b b) (* (* c a) 4)))
13.0ms
(- (* b b) (* (* c a) 4))
88.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
33.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

series433.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (- (* b b) (* (* c a) 4)))
80.0ms
(- (* b b) (* (* c a) 4))
140.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
101.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify1.6s

Counts
100 → 100
Iterations
IterNodes
33594
21093
1398
0161

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.9b

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

prune85.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.9b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite45.0ms

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:
10.0ms
(/ (* a c) b)
34.0ms
(/ (* -2 (/ (* a c) b)) a)

series59.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(/ (* a c) b)
30.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify3.0s

Counts
55 → 55
Iterations
IterNodes
36821
21066
1263
099

prune563.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 8.8b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

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:
6.0ms
(/ a (sqrt b))
5.0ms
(/ c (sqrt b))
34.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) a)
22.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ a (sqrt b))
74.0ms
(/ c (sqrt b))
63.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) a)
67.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.1s

Counts
199 → 199
Iterations
IterNodes
23002
1810
0289

prune2.1s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 8.8b

regimes829.0ms

Accuracy

47.9% (7.1b remaining)

Error of 16.1b against oracle of 8.9b and baseline of 22.7b

bsearch4.0ms

Steps
ItersRangePoint
0
622.2323332746612
633.6454832653068
627.9389082699839

simplify11.0ms

Iterations
IterNodes
235
135
026

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.6s8699×body80nan
1.2s4495×body160valid
1.0s3505×body80valid
1.0s16699×pre80true