Details

Time bar (total: 27.4s)

sample116.0ms

Algorithm
intervals
Results
23.0ms306×body80nan
22.0ms138×body160valid
19.0ms562×pre80true
9.0ms118×body80valid

simplify84.0ms

Counts
1 → 1
Iterations
IterNodes
done111
5111
4102
378
244
124
014

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* c a) 4.0)))
0.3b
(- (* b b) (* (* c a) 4.0))
0.3b
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
26.5b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 149
Calls
4 calls:
7.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
6.0ms
(- (* b b) (* (* c a) 4.0))
61.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
71.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

series397.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
65.0ms
(- (* b b) (* (* c a) 4.0))
116.0ms
(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
98.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)

simplify1.6s

Counts
161 → 161
Iterations
IterNodes
done5002
23057
1692
0280

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.6b

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune125.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.6b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac
380×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
88×associate-/l*
59×div-inv
37×add-cbrt-cube add-exp-log
21×cbrt-undiv div-exp
13×associate-/r/
11×associate-/r*
3×pow1 clear-num frac-2neg prod-exp cbrt-unprod add-log-exp
1×associate-/l/
Counts
3 → 421
Calls
3 calls:
6.0ms
(/ b (* c a))
10.0ms
(/ -2.0 (/ b (* c a)))
67.0ms
(/ (/ (/ -2.0 (/ b (* c a))) 2.0) a)

series120.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ b (* c a))
58.0ms
(/ -2.0 (/ b (* c a)))
24.0ms
(/ (/ (/ -2.0 (/ b (* c a))) 2.0) a)

simplify1.2s

Counts
430 → 430
Iterations
IterNodes
done5001
12284
0877

prune2.9s

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 9.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))) (/ (sqrt a) (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))))) (/ (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))) (sqrt a)))
0.7b
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))
0.7b
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))
0.7b
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
2145×times-frac
1235×cbrt-prod
960×add-sqr-sqrt
786×associate-*l*
716×*-un-lft-identity add-cube-cbrt
438×sqrt-prod
159×div-inv
158×associate-/r/
147×associate-*r/
70×associate-*r*
55×unswap-sqr
25×add-exp-log
16×add-cbrt-cube
14×cbrt-div
9×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod
4×add-log-exp
3×pow1/3
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 986
Calls
4 calls:
1.1s
(* (/ (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))) (/ (sqrt a) (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))))) (/ (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))) (sqrt a)))
8.0ms
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))
18.0ms
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))
18.0ms
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))

series683.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(* (/ (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))) (/ (sqrt a) (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))))) (/ (cbrt (/ -2.0 (* 2.0 (/ (/ b c) a)))) (sqrt a)))
135.0ms
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))
151.0ms
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))
184.0ms
(cbrt (/ -2.0 (* 2.0 (/ (/ b c) a))))

simplify2.8s

Counts
998 → 998
Iterations
IterNodes
done5000
13624
01048

prune9.1s

Pruning

42 alts after pruning (41 fresh and 1 done)

Merged error: 9.4b

regimes1.2s

Accuracy

46.1% (7.6b remaining)

Error of 16.6b against oracle of 9.0b and baseline of 23.1b

bsearch4.0ms

Steps
ItersRangePoint
0
700.5063928638829
720.2808939716874
710.3936434177851

simplify3.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.2s4419×body160valid
799.0ms3581×body80valid
754.0ms8508×body80nan
719.0ms16508×pre80true