Details

Time bar (total: 18.7s)

sample83.0ms

Algorithm
intervals
Results
37.0ms281×body80valid
10.0ms83×body80nan

simplify244.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize118.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
72 → 72
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0971211
12261091
27561009
32904998
done5001996

prune380.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

localize139.0ms

Local error

Found 4 expressions with local error:

12.6b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
16.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0901506
12251066
27261000
32540988
done5000984

prune495.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize111.0ms

Local error

Found 4 expressions with local error:

7.8b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log difference-of-squares
Counts
4 → 58
Calls
4 calls:
51.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series486.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
70 → 70
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune494.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize126.0ms

Local error

Found 4 expressions with local error:

19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
72 → 72
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0521140
11301008
2408928
31510928
done5000924

prune617.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 7.6b

regimes245.0ms

Accuracy

88.8% (1.4b remaining)

Error of 9.1b against oracle of 7.7b and baseline of 20.0b

bsearch190.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.822077811116171e+78
7
-2.95797388004145e+163
-3.6321213431321147e+161
-3.688468976067863e+161

simplify26.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
041130
147130
done47130

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.5s8776×body80valid
271.0ms3009×body80nan