Details

Time bar (total: 6.5s)

sample56.0ms

Algorithm
intervals
Results
12.0ms305×body80nan
9.0ms561×pre80true
9.0ms141×body160valid
4.0ms115×body80valid

simplify71.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize11.0ms

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))
0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
27.2b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite174.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
53.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series311.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify950.0ms

Counts
118 → 118
Iterations

Useful iterations: done (946.0ms)

IterNodesCost
01952476
14802169
214441861
done50011789

prune304.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.5b

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

prune56.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.5b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

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:
23.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
10.0ms
(/ (* a c) b)

series45.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
23.0ms
(/ (* a c) b)

simplify646.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (198.0ms)

IterNodesCost
0111818
1314787
21661559
done5001559

prune154.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 9.4b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite39.0ms

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:
37.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series22.0ms

Counts
1 → 3
Calls
1 calls:
22.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify1.7s

Counts
36 → 36
Iterations

Useful iterations: 2 (239.0ms)

IterNodesCost
088667
1280640
22036420
done5000420

prune35.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 9.4b

regimes429.0ms

Accuracy

45% (7.8b remaining)

Error of 16.6b against oracle of 8.8b and baseline of 22.9b

bsearch11.0ms

Steps
ItersRangePoint
1
657.6396111444685
713.8183158130478
671.6842873116133

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02544
13344
done3344

end0.0ms

sample1.4s

Algorithm
intervals
Results
297.0ms4443×body160valid
266.0ms16443×pre80true
257.0ms8443×body80nan
117.0ms3557×body80valid