Details

Time bar (total: 17.1s)

sample96.0ms

Algorithm
intervals
Results
36.0ms184×body80valid
12.0ms32×body2560valid
11.0ms30×body1280valid
6.0ms24×body640valid
6.0ms83×body80nan
1.0ms7×body320valid
0.0ms4×body160valid

simplify134.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
413017
513717
614117
done14117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
121.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms
(- (* b b) (* 4.0 (* a c)))
39.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
73.0ms
(- (* b b) (* 4.0 (* a c)))
142.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
100.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.1s

Counts
89 → 89
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01571750
14021650
213171474
349661459
done50001459

prune324.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
2.5b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.1b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite325.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
10.0ms
(- (* b b) (* 4.0 (* a c)))
154.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
146.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series752.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* 4.0 (* a c)))
274.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
300.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
107.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
150 → 150
Iterations

Useful iterations: 2 (631.0ms)

IterNodesCost
02524460
16153954
224613652
done50013652

prune732.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
2.6b
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.1b
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
19.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
51×add-exp-log
42×*-un-lft-identity
40×times-frac
28×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp
14×difference-of-squares
10×sqrt-prod
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r* distribute-lft-out--
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 136
Calls
4 calls:
21.0ms
(- (* b b) (* 4.0 (* a c)))
255.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
93.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series705.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* b b) (* 4.0 (* a c)))
226.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
287.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
133.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
148 → 148
Iterations

Useful iterations: 2 (656.0ms)

IterNodesCost
02574174
16743610
227093178
done50003178

prune413.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.6b
(- (* b b) (* 4.0 (* a c)))
11.9b
(/ (* (* 4.0 a) c) (* 2.0 a))
19.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
48.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms
(- (* b b) (* 4.0 (* a c)))
25.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series234.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
48.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(/ (* (* 4.0 a) c) (* 2.0 a))
85.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
79 → 79
Iterations

Useful iterations: 2 (325.0ms)

IterNodesCost
01501246
13931128
21995964
done5001964

prune342.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

regimes252.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.7b

bsearch264.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.7151811081882383e+78
9
3.6976431258031608e-267
1.8292500652683027e-260
7.061692521831336e-266
8
-6.990724105819741e+111
-2.6156774686163576e+108
-5.674469085146397e+110

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03257
13857
done3857

end0.0ms

sample3.3s

Algorithm
intervals
Results
959.0ms1081×body2560valid
501.0ms5913×body80valid
429.0ms891×body1280valid
308.0ms3009×body80nan
184.0ms107×body5120valid
138.0ms216×body320valid
133.0ms468×body640valid
17.0ms100×body160valid