Details

Time bar (total: 4.9s)

sample39.0ms

Algorithm
intervals
Results
7.0ms36×body2560valid
6.0ms191×body80valid
3.0ms20×body1280valid
3.0ms77×body80nan
2.0ms17×body640valid
1.0ms10×body320valid
1.0ms3×body5120valid
0.0ms4×body160valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029
done1029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.0b
(- (* b b) (* (* 3.0 a) c))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite60.0ms

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:
17.0ms
(* (* 3.0 a) c)
8.0ms
(- (* b b) (* (* 3.0 a) c))
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
44.0ms
(- (* b b) (* (* 3.0 a) c))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Counts
72 → 72
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0307469
11303428
25001417
done5001417

prune186.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.7b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.5b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
86.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
60.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
149.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
193.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
75.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify109.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06472692
131142439
250012426
done50012426

prune448.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 3.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.1b
(/ (* 3.0 a) (* 3.0 (* a c)))
24.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div 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 → 70
Calls
4 calls:
8.0ms
(- (* b b) (* (* 3.0 a) c))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 3.0 a) c))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
12.0ms
(/ (* 3.0 a) (* 3.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify64.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0417636
12439522
25001492
done5001492

prune224.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
1.0b
(- (* b b) (* (* 3.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×div-exp
8×pow1
7×add-cube-cbrt
6×prod-exp
5×flip3-- associate-/r/ flip--
4×cbrt-undiv sqrt-prod
3×rec-exp times-frac diff-log 1-exp associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 82
Calls
4 calls:
55.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
8.0ms
(- (* b b) (* (* 3.0 a) c))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ 1 (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
50.0ms
(- (* b b) (* (* 3.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0432926
11830797
25003784
done5003784

prune203.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.1b

regimes467.0ms

Accuracy

94.6% (1.2b remaining)

Error of 8.9b against oracle of 7.7b and baseline of 30.1b

bsearch169.0ms

Steps
ItersRangePoint
10
3.439700743057548e+134
6.291895909276075e+152
6.167898436296758e+152
5
-2.053305062635759e-174
-8.786774377342885e-175
-8.887624764985495e-175
10
-9.407223570539366e+155
-5.3767202001825486e+144
-1.3292983864514407e+154

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04934
14934
done4934

end0.0ms

sample1.1s

Algorithm
intervals
Results
223.0ms1117×body2560valid
209.0ms5758×body80valid
143.0ms904×body1280valid
90.0ms2850×body80nan
59.0ms474×body640valid
34.0ms129×body5120valid
20.0ms216×body320valid
7.0ms107×body160valid