Details

Time bar (total: 12.4s)

sample89.0ms

Algorithm
intervals
Results
20.0ms268×body80nan
18.0ms146×body160valid
14.0ms524×pre80true
7.0ms110×body80valid

simplify106.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize23.0ms

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)

rewrite231.0ms

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:
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
75.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series440.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms
(- (* b b) (* (* 4.0 a) c))
150.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
107.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.5s

Counts
118 → 118
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01952476
14802169
214441861
done50011789

prune372.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.8b

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

prune48.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.8b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

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:
17.0ms
(/ (* a c) b)
34.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series50.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(/ (* a c) b)
25.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify868.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (277.0ms)

IterNodesCost
0111818
1314787
21621559
done5001559

prune241.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

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:
52.0ms
(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
15.0ms
(/ a (sqrt b))
7.0ms
(/ c (sqrt b))
51.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2.0 a))
54.0ms
(/ a (sqrt b))
63.0ms
(/ c (sqrt b))
59.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify2.4s

Counts
211 → 211
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03113040
18752804
241012190
done50022182

prune637.0ms

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 9.7b

regimes869.0ms

Accuracy

43.8% (7.9b remaining)

Error of 16.7b against oracle of 8.9b and baseline of 22.9b

bsearch12.0ms

Steps
ItersRangePoint
1
172.19531990517868
188.1359396834071
176.18047484973576

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02544
13344
done3344

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.3s4450×body160valid
1.0s16620×pre80true
680.0ms8620×body80nan
321.0ms3550×body80valid