Details

Time bar (total: 10.3s)

sample91.0ms

Algorithm
intervals
Results
22.0ms302×body80nan
17.0ms146×body160valid
14.0ms558×pre80true
6.0ms110×body80valid

simplify103.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize15.0ms

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))
28.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite266.0ms

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)))
19.0ms
(- (* b b) (* (* 4.0 a) c))
164.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
66.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series524.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms
(- (* b b) (* (* 4.0 a) c))
171.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
148.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.9s

Counts
118 → 118
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01952476
15182183
224661866
done50021794

prune456.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.4b

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

prune59.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.4b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

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:
29.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
11.0ms
(/ (* a c) b)

series45.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
22.0ms
(/ (* a c) b)

simplify1.3s

Counts
61 → 61
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0111818
1352787
22559605
done5001559

prune175.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.3b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite38.0ms

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:
36.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

series33.0ms

Counts
1 → 3
Calls
1 calls:
33.0ms
(/ (* -2.0 (* a c)) (* (* 2.0 a) b))

simplify1.3s

Counts
36 → 36
Iterations

Useful iterations: 2 (247.0ms)

IterNodesCost
088667
1309640
22459420
done5001420

prune58.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 9.3b

regimes429.0ms

Accuracy

47.9% (7.2b remaining)

Error of 16.3b against oracle of 9.1b and baseline of 22.9b

bsearch21.0ms

Steps
ItersRangePoint
2
3458.0513525580413
3728.980047040245
3559.6496129888674

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02646
13646
done3646

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.0s8805×body80nan
756.0ms4436×body160valid
607.0ms16805×pre80true
319.0ms3564×body80valid