Details

Time bar (total: 19.8s)

sample79.0ms

Algorithm
intervals
Results
17.0ms38×body2560valid
14.0ms178×body80valid
10.0ms29×body1280valid
5.0ms79×body80nan
3.0ms10×body640valid
1.0ms6×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify96.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.3b

localize13.0ms

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)))

rewrite90.0ms

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:
33.0ms
(* (* 3.0 a) c)
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(- (* b b) (* (* 3.0 a) c))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* 3.0 a) c)
128.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
53.0ms
(- (* b b) (* (* 3.0 a) c))
112.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.3s

Counts
72 → 72
Iterations

Useful iterations: done (4.3s)

IterNodesCost
01221001
1303907
21072805
34081795
done5000793

prune251.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.2b

localize24.0ms

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)))

rewrite112.0ms

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:
24.0ms
(* (* 3.0 a) c)
59.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (* 3.0 a) c)
143.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
87.0ms
(- (* b b) (* (* 3.0 a) c))
106.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.7s

Counts
72 → 72
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01201001
1276903
2929825
33449821
done5000815

prune250.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.2b

localize22.0ms

Local error

Found 4 expressions with local error:

14.3b
(cbrt (* (* 3.0 a) c))
14.3b
(cbrt (* (* 3.0 a) c))
14.3b
(cbrt (* (* 3.0 a) c))
20.2b
(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 42
Calls
4 calls:
25.0ms
(cbrt (* (* 3.0 a) c))
31.0ms
(cbrt (* (* 3.0 a) c))
25.0ms
(cbrt (* (* 3.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

series595.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(cbrt (* (* 3.0 a) c))
144.0ms
(cbrt (* (* 3.0 a) c))
127.0ms
(cbrt (* (* 3.0 a) c))
180.0ms
(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

simplify1.5s

Counts
54 → 54
Iterations

Useful iterations: done (1.5s)

IterNodesCost
088981
1206897
2492529
31528514
done5001489

prune276.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.2b

localize28.0ms

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)))

rewrite67.0ms

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:
14.0ms
(- (* b b) (* (* 3.0 a) c))
24.0ms
(- (* b b) (* (* 3.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* (* 3.0 a) c))
87.0ms
(- (* b b) (* (* 3.0 a) c))
113.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
87.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts
66 → 66
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune291.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 10.2b

regimes355.0ms

Accuracy

97.3% (0.6b remaining)

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

bsearch277.0ms

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

simplify15.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03979
14778
25578
36378
46578
done6578

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.1s1087×body2560valid
855.0ms931×body1280valid
576.0ms5807×body80valid
237.0ms2994×body80nan
123.0ms447×body640valid
63.0ms117×body5120valid
54.0ms114×body160valid
43.0ms209×body320valid