Details

Time bar (total: 18.1s)

sample87.0ms

Algorithm
intervals
Results
18.0ms43×body2560valid
13.0ms175×body80valid
11.0ms31×body1280valid
8.0ms106×body80nan
5.0ms18×body640valid
2.0ms4×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify93.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite75.0ms

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:
22.0ms
(* (* 3.0 a) c)
10.0ms
(- (* b b) (* (* 3.0 a) c))
31.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 3.0 a) c)
72.0ms
(- (* b b) (* (* 3.0 a) c))
142.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
110.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.2s

Counts
72 → 72
Iterations

Useful iterations: done (4.2s)

IterNodesCost
01221001
1303907
21069805
34068795
done5000793

prune301.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.2b
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
32×add-sqr-sqrt
31×*-un-lft-identity
17×cbrt-undiv div-exp
14×associate-/l*
13×prod-exp cbrt-unprod
11×add-cube-cbrt
10×distribute-lft-out-- difference-of-squares
8×associate-/r* sqrt-prod add-log-exp
6×associate-/r/
5×pow1 flip3-- distribute-rgt-neg-in flip--
4×div-inv
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 120
Calls
4 calls:
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
133.0ms
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
88.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series623.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
176.0ms
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
261.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
99.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
132 → 132
Iterations

Useful iterations: 2 (554.0ms)

IterNodesCost
02243580
15913368
225382782
done50012782

prune505.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.9b
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
5.2b
(/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
57×add-exp-log add-cbrt-cube
33×add-sqr-sqrt
32×*-un-lft-identity
27×associate-*r*
23×prod-exp cbrt-unprod
22×times-frac
16×cbrt-undiv add-cube-cbrt div-exp
10×pow1
8×distribute-lft-out-- add-log-exp difference-of-squares
7×sqrt-prod
4×distribute-rgt-neg-in
3×flip3-- pow-prod-down flip--
2×sqrt-div diff-log associate-*r/ associate-/r/ div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*l* neg-log clear-num associate-/r* *-commutative associate-/l/ associate-/l*
Counts
4 → 114
Calls
4 calls:
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
134.0ms
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
82.0ms
(/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
294.0ms
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
179.0ms
(/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
113.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts
126 → 126
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02233204
16423041
231362125
done50002124

prune296.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 3.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0b
(/ (* (* 3.0 a) c) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log add-cbrt-cube
18×prod-exp cbrt-unprod
10×add-sqr-sqrt add-log-exp
9×cbrt-undiv *-un-lft-identity div-exp
5×pow1 add-cube-cbrt
4×flip3-- sqrt-prod flip--
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
8.0ms
(- (* b b) (* (* 3.0 a) c))
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
59.0ms
(/ (* (* 3.0 a) c) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (* b b) (* (* 3.0 a) c))
102.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
205.0ms
(/ (* (* 3.0 a) c) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
78.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts
90 → 90
Iterations

Useful iterations: 2 (514.0ms)

IterNodesCost
01762254
14931964
226961356
done50001356

prune198.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.6b

regimes427.0ms

Accuracy

89.9% (2.1b remaining)

Error of 10.1b against oracle of 8.0b and baseline of 29.1b

bsearch274.0ms

Steps
ItersRangePoint
8
1.9386293038794674e+155
5.973091654032696e+157
1.955976202061806e+155
9
-4.09118134758863e-163
-1.5699591568311042e-168
-1.5885810260222291e-168
6
-9.188861011096532e+114
-1.1922005359556833e+114
-7.949039921111462e+114

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03882
14680
done4680

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.6s1076×body2560valid
540.0ms5872×body80valid
428.0ms885×body1280valid
203.0ms3010×body80nan
130.0ms491×body640valid
51.0ms105×body5120valid
41.0ms218×body320valid
13.0ms95×body160valid