Details

Time bar (total: 12.1s)

sample34.0ms

Algorithm
intervals
Results
15.0ms286×body80valid
4.0ms79×body80nan

simplify93.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13838
27837
313637
415637
516537
616837
done16837

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize121.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
72 → 72
Iterations

Useful iterations: 3 (474.0ms)

IterNodesCost
0971211
12281091
27651009
33087998
done5001998

prune286.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize118.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.6b
(/ (* a c) b)
4.9b
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×*-un-lft-identity
14×add-exp-log add-cbrt-cube
9×add-cube-cbrt
8×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp sqrt-prod distribute-lft-out-- difference-of-squares
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 81
Calls
4 calls:
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(/ (* a c) b)
44.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (* a c) b)
67.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify513.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (148.0ms)

IterNodesCost
01831490
14431392
216641238
done50011238

prune346.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize121.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.9b
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
33×times-frac
30×add-exp-log *-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×unswap-sqr
5×associate-/r*
4×sqrt-prod distribute-lft-out-- difference-of-squares
3×flip3-- flip-- div-inv
2×sqrt-div diff-log associate-/r/
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 119
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
313.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
99.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify904.0ms

Counts
131 → 131
Iterations

Useful iterations: done (900.0ms)

IterNodesCost
02672588
17402457
228931963
done50001957

prune596.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize131.0ms

Local error

Found 4 expressions with local error:

1.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.9b
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
44×add-cbrt-cube
33×prod-exp cbrt-unprod
25×add-sqr-sqrt
24×cbrt-undiv div-exp
18×*-un-lft-identity
13×times-frac
10×add-cube-cbrt
8×add-log-exp
7×pow1 associate-*l*
5×associate-*r* associate-/r*
4×sqrt-prod distribute-lft-out-- difference-of-squares unswap-sqr
3×flip3-- flip-- div-inv
2×sqrt-div diff-log associate-/r/
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 118
Calls
4 calls:
36.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7s
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify992.0ms

Counts
130 → 130
Iterations

Useful iterations: done (987.0ms)

IterNodesCost
02853998
18473836
235543073
done50013072

prune607.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

regimes276.0ms

Accuracy

90.6% (1.4b remaining)

Error of 7.9b against oracle of 6.5b and baseline of 21.5b

bsearch197.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
9
-3.226264717511912e+140
-2.187052964502477e+134
-3.505198499083171e+136

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
058178
168178
done68178

end0.0ms

sample851.0ms

Algorithm
intervals
Results
453.0ms8739×body80valid
133.0ms2862×body80nan