Details

Time bar (total: 21.1s)

sample95.0ms

Algorithm
intervals
Results
20.0ms38×body2560valid
17.0ms178×body80valid
13.0ms29×body1280valid
7.0ms79×body80nan
4.0ms10×body640valid
2.0ms3×body5120valid
2.0ms6×body320valid
0.0ms2×body160valid

simplify139.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b
(- (* b b) (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite122.0ms

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:
25.0ms
(* (* 3.0 a) c)
46.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms
(- (* b b) (* (* 3.0 a) c))
30.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* 3.0 a) c)
110.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
101.0ms
(- (* b b) (* (* 3.0 a) c))
112.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.1s

Counts
72 → 72
Iterations

Useful iterations: done (4.1s)

IterNodesCost
01221001
1303907
21072805
34081795
done5000793

prune254.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.6b
(- (* b b) (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
32.0ms
(* (* 3.0 a) c)
59.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
9.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* 3.0 a) c)
111.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
72.0ms
(- (* b b) (* (* 3.0 a) c))
96.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.0s

Counts
72 → 72
Iterations

Useful iterations: done (4.0s)

IterNodesCost
01201001
1276903
2929825
33449821
done5000815

prune311.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 3.0 a) c))
0.6b
(- (* b b) (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite46.0ms

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) (* (* 3.0 a) c))
9.0ms
(- (* b b) (* (* 3.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (* b b) (* (* 3.0 a) c))
64.0ms
(- (* b b) (* (* 3.0 a) c))
92.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
105.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts
66 → 66
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune389.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 3.0 a) c))
9.8b
(- (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))) b)
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite110.0ms

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) (* (* 3.0 a) c))
77.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))) b)
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (* b b) (* (* 3.0 a) c))
119.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))) b)
129.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts
67 → 67
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0941323
1221961
2715895
32662890
done5001884

prune361.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 10.2b

regimes434.0ms

Accuracy

97.3% (0.6b remaining)

Error of 12.9b against oracle of 12.3b and baseline of 34.3b

bsearch320.0ms

Steps
ItersRangePoint
6
4.701299750517242e+134
2.9949035539067785e+135
9.437505947861472e+134
11
-2.650747406342512e-234
-3.579862835853504e-259
-2.0603322012078003e-258
8
-3.270149144775924e+135
-4.819399228408536e+132
-2.205465986680909e+135

simplify32.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03978
14777
25577
36377
46577
done6577

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.0s1087×body2560valid
922.0ms5807×body80valid
377.0ms931×body1280valid
286.0ms2994×body80nan
219.0ms447×body640valid
66.0ms117×body5120valid
46.0ms209×body320valid
16.0ms114×body160valid