Details

Time bar (total: 11.4s)

sample113.0ms

Algorithm
intervals
Results
23.0ms530×pre80true
22.0ms145×body160valid
19.0ms274×body80nan
8.0ms38×body320valid
5.0ms73×body80valid

simplify103.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize21.0ms

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))
38.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite244.0ms

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:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
57.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series407.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
63.0ms
(- (* b b) (* (* 4.0 a) c))
143.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
90.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify2.0s

Counts
118 → 118
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01952476
15182183
224661866
done50021794

prune360.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.1b

localize7.0ms

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

prune62.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

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:
34.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
18.0ms
(/ (* a c) b)

series58.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
23.0ms
(/ (* a c) b)

simplify1.3s

Counts
61 → 61
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0111818
1352787
22559605
done5001559

prune210.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite65.0ms

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:
63.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series23.0ms

Counts
1 → 3
Calls
1 calls:
23.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify1.5s

Counts
36 → 36
Iterations

Useful iterations: 2 (377.0ms)

IterNodesCost
088667
1309640
22459420
done5001420

prune60.0ms

Pruning

29 alts after pruning (27 fresh and 2 done)

Merged error: 5.1b

regimes412.0ms

Accuracy

8.9% (6.5b remaining)

Error of 11.5b against oracle of 5.1b and baseline of 12.2b

bsearch44.0ms

Steps
ItersRangePoint
4
0.12472275306628457
0.2162455449205228
0.12731425734469268

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02238
12738
done2738

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.1s16286×pre80true
900.0ms4863×body160valid
826.0ms8286×body80nan
629.0ms1285×body320valid
124.0ms1852×body80valid