Details

Time bar (total: 11.5s)

sample99.0ms

Algorithm
intervals
Results
31.0ms534×pre80true
16.0ms152×body160valid
14.0ms278×body80nan
6.0ms39×body320valid
3.0ms65×body80valid

simplify78.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
36.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite180.0ms

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))
61.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series452.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
94.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.2s

Counts
118 → 118
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01952476
14802169
214441861
done50011789

prune421.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.5b

localize4.0ms

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

prune81.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

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:
10.0ms
(/ (* a c) b)
26.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series66.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ (* a c) b)
38.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify785.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (222.0ms)

IterNodesCost
0111818
1314787
21621559
done5001559

prune202.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 5.4b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite50.0ms

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:
49.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series38.0ms

Counts
1 → 3
Calls
1 calls:
38.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify2.7s

Counts
36 → 36
Iterations

Useful iterations: 2 (397.0ms)

IterNodesCost
088667
1280640
22036420
done5000420

prune44.0ms

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 5.4b

regimes391.0ms

Accuracy

14.4% (5.9b remaining)

Error of 10.9b against oracle of 5.0b and baseline of 11.9b

bsearch92.0ms

Steps
ItersRangePoint
5
2.7198827844106637e-05
8.755595256275303e-05
2.7592698756943847e-05

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02952
13952
done3952

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.0s8128×body80nan
937.0ms4874×body160valid
850.0ms16128×pre80true
780.0ms1334×body320valid
166.0ms1792×body80valid