Details

Time bar (total: 19.7s)

sample100.0ms

Algorithm
intervals
Results
20.0ms45×body1280valid
18.0ms184×body80valid
14.0ms25×body2560valid
6.0ms17×body640valid
6.0ms69×body80nan
2.0ms8×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify156.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
32.0ms
(* (* 3.0 a) c)
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(- (* b b) (* (* 3.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* 3.0 a) c)
128.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms
(- (* b b) (* (* 3.0 a) c))
84.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.2s

Counts
72 → 72
Iterations

Useful iterations: done (4.2s)

IterNodesCost
01221001
1303907
21072805
34081795
done5000793

prune300.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.5b
(/ (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.2b
(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
28×add-sqr-sqrt
27×*-un-lft-identity
17×cbrt-undiv div-exp
14×associate-/l*
13×prod-exp cbrt-unprod
11×add-cube-cbrt
8×associate-/r* distribute-lft-out-- difference-of-squares
7×sqrt-prod
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×distribute-rgt-neg-in div-inv
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 114
Calls
4 calls:
15.0ms
(- (* b b) (* (* 3.0 a) c))
108.0ms
(/ (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
79.0ms
(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series662.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* b b) (* (* 3.0 a) c))
244.0ms
(/ (/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
277.0ms
(/ (* (* c 3.0) a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
89.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts
126 → 126
Iterations

Useful iterations: 2 (623.0ms)

IterNodesCost
02273379
16103193
229062607
done50002607

prune387.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize37.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
10×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
Counts
4 → 57
Calls
4 calls:
13.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* b b) (* (* 3.0 a) c))
113.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts
69 → 69
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0621075
1148969
2492881
31991881
done5000878

prune367.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize28.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

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:
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
89.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
97.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.0s

Counts
72 → 72
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0521140
11301008
2408928
31510928
done5000924

prune589.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.9b

regimes859.0ms

Accuracy

93.7% (1.3b remaining)

Error of 10.7b against oracle of 9.4b and baseline of 30.5b

bsearch313.0ms

Steps
ItersRangePoint
7
1.8931325595256007e+133
5.341589198600723e+134
5.137043888653352e+134
9
9.448397398655464e-278
1.4829972419072586e-270
2.1534153816661216e-275
10
-2.386196042261592e+160
-1.0923850232644114e+143
-1.0616560770096982e+154

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
047132
154132
done54132

end0.0ms

sample2.8s

Algorithm
intervals
Results
540.0ms480×body640valid
505.0ms1055×body2560valid
495.0ms5850×body80valid
312.0ms923×body1280valid
265.0ms2941×body80nan
124.0ms113×body5120valid
47.0ms108×body160valid
37.0ms206×body320valid