Details

Time bar (total: 14.5s)

sample73.0ms

Algorithm
intervals
Results
16.0ms38×body2560valid
13.0ms178×body80valid
9.0ms28×body1280valid
5.0ms79×body80nan
3.0ms11×body640valid
1.0ms6×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify101.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
75.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
124.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune433.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
153.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
31.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
150.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
92 → 92
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01811881
14651671
216561400
done50001376

prune364.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

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:
24.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
66 → 66
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0621010
1148930
2492834
31991834
done5000832

prune345.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.6b
(/ (+ 0 (* (* 4.0 c) a)) (* a 2.0))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1
4×sqrt-prod
3×flip3-- times-frac diff-log flip-- associate-/l*
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp clear-num associate-/r* cbrt-unprod flip-+ div-inv
Counts
4 → 68
Calls
4 calls:
18.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(/ (+ 0 (* (* 4.0 c) a)) (* a 2.0))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(/ (+ 0 (* (* 4.0 c) a)) (* a 2.0))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
80 → 80
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
01531323
13721150
217691044
done50021044

prune402.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

regimes307.0ms

Accuracy

95.9% (1.2b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 34.4b

bsearch318.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.6082844052603056e+78
11
-1.0472779812871276e-269
-2.473343252086336e-295
-3.3534114850920523e-283
8
-6.990724105819741e+111
-2.6156774686163576e+108
-1.569310777886352e+111

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03562
14562
done4562

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.1s930×body1280valid
633.0ms5806×body80valid
507.0ms1087×body2560valid
307.0ms2994×body80nan
170.0ms446×body640valid
109.0ms117×body5120valid
43.0ms210×body320valid
17.0ms116×body160valid