Details

Time bar (total: 19.1s)

sample122.0ms

Algorithm
intervals
Results
43.0ms198×body80valid
9.0ms34×body1280valid
8.0ms29×body2560valid
4.0ms92×body80nan
2.0ms12×body640valid
1.0ms5×body320valid
0.0ms4×body160valid
0.0ms1×body5120valid

simplify28.0ms

Counts
1 → 1
Iterations
IterNodes
done44
444
341
232
118
010

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.2b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 91
Calls
4 calls:
61.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
96.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
103 → 103
Iterations
IterNodes
done5000
33629
21040
1384
0158

prune580.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.2b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div div-exp associate-*l/ cbrt-unprod
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
106.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
36.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
101.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms
(- (* b_2 b_2) (* a c))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
101 → 101
Iterations
IterNodes
done5000
34270
21315
1451
0177

prune696.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
2.2b
(- (* b_2 b_2) (* a c))
5.2b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
37×times-frac
24×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
7×distribute-lft-out--
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div flip--
3×associate-/r* distribute-rgt-neg-in div-inv
2×sub-neg diff-log associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-sub div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
16.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
12.0ms
(- (* b_2 b_2) (* a c))
89.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
48.0ms
(- (* b_2 b_2) (* a c))
106.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
109 → 109
Iterations
IterNodes
done5001
33558
21088
1410
0178

prune619.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize43.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (* b_2 b_2) (* a c))
2.6b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.6b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
53×add-sqr-sqrt
40×*-un-lft-identity
28×add-cube-cbrt
18×add-cbrt-cube add-exp-log
13×associate-/l*
12×difference-of-squares
10×associate-/r/
9×associate-/r* sqrt-prod
7×cbrt-undiv flip3-- div-exp flip--
6×div-inv distribute-lft-out-- add-log-exp
5×pow1
2×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 124
Calls
4 calls:
12.0ms
(- (* b_2 b_2) (* a c))
87.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
65.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series660.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b_2 b_2) (* a c))
218.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
283.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
116.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
136 → 136
Iterations
IterNodes
done5000
22137
1608
0234

prune723.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes534.0ms

Accuracy

90.1% (2.6b remaining)

Error of 8.3b against oracle of 5.7b and baseline of 32.3b

bsearch233.0ms

Steps
ItersRangePoint
5
6.972240796235003e+85
2.4695855038465726e+86
2.433359793914947e+86
10
-4.6078091521834716e-184
-2.457648077762901e-195
-1.608116455888013e-192
5
-2.2871888563215003e+52
-1.1365470274565651e+52
-1.3597436970592748e+52

simplify32.0ms

Iterations
IterNodes
done38
138
032

end0.0ms

sample2.9s

Algorithm
intervals
Results
658.0ms5857×body80valid
613.0ms1086×body2560valid
472.0ms187×body320valid
298.0ms902×body1280valid
239.0ms2952×body80nan
118.0ms484×body640valid
47.0ms98×body5120valid
14.0ms112×body160valid