Details

Time bar (total: 13.4s)

sample230.0ms

Algorithm
intervals
Results
61.0ms249×body80nan
27.0ms118×body320valid
20.0ms505×pre80true
17.0ms91×body160valid
7.0ms20×body640valid
3.0ms27×body80valid

simplify147.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
28.2b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×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:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(- (* b b) (* (* 4.0 a) c))
158.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
90.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series454.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
61.0ms
(- (* b b) (* (* 4.0 a) c))
139.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
133.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.7s

Counts
118 → 118
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01952476
14802169
214441861
done50011789

prune482.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.2b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune82.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.2b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 55
Calls
2 calls:
27.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
19.0ms
(/ (* a c) b)

series55.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
23.0ms
(/ (* a c) b)

simplify912.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (266.0ms)

IterNodesCost
0111818
1314787
21661559
done5001559

prune194.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 2.2b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
85×times-frac
76×add-exp-log add-cbrt-cube
60×add-cube-cbrt *-un-lft-identity
48×sqrt-prod
28×prod-exp cbrt-unprod
26×cbrt-undiv div-exp
22×associate-*r* associate-*l*
13×associate-/r*
9×unswap-sqr
7×associate-/l*
6×pow1
5×associate-*r/ div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
2×frac-times associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 199
Calls
4 calls:
14.0ms
(/ a (sqrt b))
6.0ms
(/ c (sqrt b))
79.0ms
(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
54.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ a (sqrt b))
52.0ms
(/ c (sqrt b))
40.0ms
(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
70.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify2.5s

Counts
211 → 211
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03113040
18752804
240902190
done50012182

prune638.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 2.2b

regimes426.0ms

Accuracy

0% (3.4b remaining)

Error of 6.1b against oracle of 2.6b and baseline of 6.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
165
done65

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.3s8051×body80nan
1.0s3634×body320valid
921.0ms2967×body160valid
701.0ms16051×pre80true
229.0ms500×body640valid
71.0ms899×body80valid