Details

Time bar (total: 16.7s)

sample53.0ms

Algorithm
intervals
Results
26.0ms283×body80valid
6.0ms96×body80nan

simplify168.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13838
27837
313537
415537
516537
616937
done16937

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize112.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×*-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--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log difference-of-squares
1×distribute-lft-out--
Counts
4 → 57
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
89.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
69 → 69
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0911129
12071001
2651935
32361930
done5000924

prune396.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.4b

localize162.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.2b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.6b
(/ (* a c) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
9×add-cube-cbrt times-frac
7×associate-/l*
6×add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv div-exp associate-/r* sqrt-prod difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 81
Calls
4 calls:
44.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
58.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
10.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
68.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
25.0ms
(/ (* a c) b)
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
93 → 93
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01831536
14621432
216911274
done50001243

prune641.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize129.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite191.0ms

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:
67.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
9.0ms
(- (* b b) (* (* 4.0 a) c))
96.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
81.0ms
(- (* b b) (* (* 4.0 a) c))
101.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
83 → 83
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01451551
13461445
211411291
344741287
done50001287

prune474.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

localize143.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 c))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite214.0ms

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 sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
101.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 c))
14.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 c))
64.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
88.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01541592
13851488
212451332
347451322
done50011322

prune401.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.7b

regimes370.0ms

Accuracy

91.5% (1.3b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 21.3b

bsearch304.0ms

Steps
ItersRangePoint
9
1.2073698495971617e+61
8.75865749938149e+67
4.620002785864607e+67
10
-2.3639790504379266e+162
-1.7004475472942417e+152
-1.333835582926585e+154

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
045125
154125
done54125

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.4s8706×body80valid
263.0ms2844×body80nan