Details

Time bar (total: 22.5s)

sample175.0ms

Algorithm
intervals
Results
53.0ms35×body2560valid
34.0ms184×body80valid
25.0ms28×body1280valid
15.0ms86×body80nan
12.0ms15×body640valid
5.0ms4×body5120valid
4.0ms8×body320valid
2.0ms5×body160valid

simplify97.0ms

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: 34.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
0.6b
(- (* b b) (* (* c a) 4))
1.7b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
24.6b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite184.0ms

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:
89.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
17.0ms
(- (* b b) (* (* c a) 4))
62.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
65.0ms
(- (* b b) (* (* c a) 4))
100.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
100.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.4s

Counts
100 → 100
Iterations
IterNodes
33565
21088
1398
0161

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
0.6b
(- (* b b) (* (* c a) 4))
8.4b
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
24.6b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip-- distribute-lft-out--
3×associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
15.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
9.0ms
(- (* b b) (* (* c a) 4))
58.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (sqrt (- (* b b) (* (* c a) 4))) a)
58.0ms
(- (* b b) (* (* c a) 4))
132.0ms
(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
87.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.6s

Counts
109 → 109
Iterations
IterNodes
33577
21188
1411
0179

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
0.6b
(- (* b b) (* (* c a) 4))
12.6b
(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
24.6b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac associate-*r* add-exp-log
10×sqrt-div
9×add-cbrt-cube sqrt-prod
8×add-log-exp
7×pow1 flip3-- flip--
6×associate-*l* frac-sub unswap-sqr
4×frac-times associate-*l/ prod-exp insert-posit16
3×associate-*r/ un-div-inv
2×sub-neg diff-log div-exp cbrt-unprod div-inv sub-div
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 distribute-rgt-out-- pow1/2 1-exp pow-prod-down *-commutative
Counts
4 → 98
Calls
4 calls:
57.0ms
(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
17.0ms
(- (* b b) (* (* c a) 4))
49.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a))
54.0ms
(- (* b b) (* (* c a) 4))
136.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (/ 1 a)) (/ b a))
120.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify4.6s

Counts
110 → 110
Iterations
IterNodes
34164
21495
1523
0199

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* c a) 4))
16.0b
(- (* (sqrt (sqrt (- (* b b) (* (* c a) 4)))) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
24.6b
(sqrt (- (* b b) (* (* c a) 4)))
24.6b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-div
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity flip3-- add-cube-cbrt sqrt-prod flip--
5×frac-sub
4×add-cbrt-cube add-exp-log insert-posit16
2×frac-times rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-*l/ associate-*r/
1×sub-div
Counts
4 → 64
Calls
4 calls:
16.0ms
(- (* b b) (* (* c a) 4))
38.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* c a) 4)))) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
10.0ms
(sqrt (- (* b b) (* (* c a) 4)))
17.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (* b b) (* (* c a) 4))
143.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* c a) 4)))) (/ (sqrt (sqrt (- (* b b) (* (* c a) 4)))) a)) (/ b a))
90.0ms
(sqrt (- (* b b) (* (* c a) 4)))
119.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
32999
21009
1342
0131

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

regimes270.0ms

Accuracy

84.7% (4.4b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 34.1b

bsearch206.0ms

Steps
ItersRangePoint
10
8.296670056881522e-85
2.5972983117194536e-74
2.326372645943808e-74
7
-1.8217288728729631e+111
-6.606823090402082e+109
-5.148407540792454e+110

simplify7.0ms

Iterations
IterNodes
234
134
029

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.1s1126×body2560valid
1.1s915×body1280valid
1.0s5836×body80valid
663.0ms417×body640valid
416.0ms2976×body80nan
160.0ms119×body5120valid
154.0ms236×body320valid
33.0ms115×body160valid