Details

Time bar (total: 13.3s)

sample253.0ms

Algorithm
intervals
Results
63.0ms517×pre80true
31.0ms120×body320valid
23.0ms261×body80nan
16.0ms94×body160valid
5.0ms14×body640valid
2.0ms28×body80valid

simplify122.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
25.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
add-exp-log add-cbrt-cube
add-log-exp
fma-neg
times-frac associate-/l* difference-of-squares
pow1
expm1-log1p-u flip3-- flip-- log1p-expm1-u
distribute-lft-out--
cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
131.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
79.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series505.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms
(- (* b b) (* (* 4.0 a) c))
174.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
160.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.6s

Counts
118 → 118
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01952476
14802169
214441861
done50011789

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.5b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune56.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.5b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
0.3b
(/ (* a c) b)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv associate-/l* add-log-exp
associate-*r/ associate-/l/
Counts
2 → 55
Calls
2 calls:
46.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
21.0ms
(/ (* a c) b)

series65.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
31.0ms
(/ (* a c) b)

simplify1.2s

Counts
61 → 61
Iterations

Useful iterations: 2 (434.0ms)

IterNodesCost
0111818
1314787
21661559
done5001559

prune236.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 2.5b

localize16.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
18×prod-exp cbrt-unprod
cbrt-undiv div-exp
pow1 add-sqr-sqrt expm1-log1p-u add-cube-cbrt frac-2neg *-un-lft-identity times-frac clear-num associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
Counts
1 → 33
Calls
1 calls:
65.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series29.0ms

Counts
1 → 3
Calls
1 calls:
29.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify2.8s

Counts
36 → 36
Iterations

Useful iterations: 2 (379.0ms)

IterNodesCost
088667
1280640
22036420
done5000420

prune43.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.5b

regimes354.0ms

Accuracy

4.4% (3.5b remaining)

Error of 6.1b against oracle of 2.7b and baseline of 6.3b

bsearch138.0ms

Steps
ItersRangePoint
8
3.0026527018200954e-17
2.4173674189391156e-14
3.0547987684067384e-17

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02438
13138
done3138

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.2s8269×body80nan
1.2s16269×pre80true
1.1s3625×body320valid
520.0ms2929×body160valid
154.0ms528×body640valid
68.0ms918×body80valid