Details

Time bar (total: 12.0s)

sample125.0ms

Algorithm
intervals
Results
26.0ms142×body160valid
24.0ms262×body80nan
20.0ms518×pre80true
11.0ms114×body80valid

simplify167.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
28.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite205.0ms

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:
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
86.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series387.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
55.0ms
(- (* b b) (* (* 4.0 a) c))
151.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
89.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.2s

Counts
118 → 118
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01952476
14802169
214441861
done50011789

prune442.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.8b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune67.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.8b

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)

rewrite60.0ms

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:
39.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
17.0ms
(/ (* a c) b)

series57.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
34.0ms
(/ (* a c) b)

simplify890.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (267.0ms)

IterNodesCost
0111818
1314787
21661559
done5001559

prune174.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 8.7b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite56.0ms

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:
52.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify2.8s

Counts
36 → 36
Iterations

Useful iterations: 2 (415.0ms)

IterNodesCost
088667
1280640
22036420
done5000420

prune43.0ms

Pruning

30 alts after pruning (28 fresh and 2 done)

Merged error: 8.7b

regimes1.1s

Accuracy

46.2% (7.4b remaining)

Error of 16.3b against oracle of 9.0b and baseline of 22.7b

bsearch21.0ms

Steps
ItersRangePoint
2
1430.9534847553177
1659.0567802753424
1459.4663966953208

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02438
13138
done3138

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.3s4462×body160valid
821.0ms8741×body80nan
749.0ms16741×pre80true
335.0ms3538×body80valid