Details

Time bar (total: 15.9s)

sample82.0ms

Algorithm
intervals
Results
39.0ms289×body80valid
10.0ms104×body80nan

simplify207.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02038
13838
27837
313637
416337
517537
617937
done17937

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize152.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
153.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.2s

Counts
66 → 66
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
0621010
1165930
2739834
34972834
done5001834

prune483.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.8b

localize136.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
4.1b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
6.8b
(/ (* a c) b)
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac
7×associate-/l*
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp associate-/r* distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/ difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 78
Calls
4 calls:
14.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
11.0ms
(/ (* a c) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
29.0ms
(/ (* a c) b)
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
90 → 90
Iterations

Useful iterations: 2 (422.0ms)

IterNodesCost
01661417
14591349
224551183
done50001183

prune532.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.6b

localize125.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac associate-/r* sqrt-prod difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
56.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
79.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series567.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
109.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
80.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
83 → 83
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01451551
13741453
217491297
done50001289

prune548.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

localize151.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
10.3b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
1×difference-of-squares
Counts
4 → 55
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
112.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify884.0ms

Counts
67 → 67
Iterations

Useful iterations: done (882.0ms)

IterNodesCost
0941323
1243973
21100895
done5001893

prune466.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.5b

regimes447.0ms

Accuracy

92.3% (1.1b remaining)

Error of 7.5b against oracle of 6.4b and baseline of 20.6b

bsearch239.0ms

Steps
ItersRangePoint
8
1.051086597250448e+104
1.8086281629461872e+108
2.750597423682243e+107
9
-5.388960530500634e+155
-8.097032161796104e+150
-1.3613714418567412e+154

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
047137
155137
done55137

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.5s8766×body80valid
341.0ms2950×body80nan