Details

Time bar (total: 5.5s)

sample51.0ms

Algorithm
intervals
Results
10.0ms150×body160valid
10.0ms531×pre80true
9.0ms275×body80nan
4.0ms106×body80valid

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
29.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series297.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
79.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify743.0ms

Counts
161 → 161
Iterations

Useful iterations: done (737.0ms)

IterNodesCost
02804083
16653911
219753753
done50003752

prune456.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.2b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune61.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.2b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 frac-2neg clear-num add-log-exp
1×associate-/l/
Counts
2 → 73
Calls
2 calls:
10.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
3.0ms
(/ (* a c) b)

series42.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
18.0ms
(/ (* a c) b)

simplify560.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (175.0ms)

IterNodesCost
01671164
14401118
21797956
done5000956

prune227.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 9.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (/ (* -2.0 (* (* a c) (/ 1 b))) 2.0) a)
0.4b
(* (* a c) (/ 1 b))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
47×add-cbrt-cube
42×times-frac
33×prod-exp
29×div-exp
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×cbrt-undiv cbrt-unprod
13×associate-*r*
7×pow1 associate-/l*
6×div-inv
4×rec-exp 1-exp
3×pow-prod-down associate-/r*
2×add-log-exp
1×frac-2neg associate-*r/ associate-*l* clear-num un-div-inv *-commutative associate-/l/
Counts
2 → 98
Calls
2 calls:
26.0ms
(/ (/ (* -2.0 (* (* a c) (/ 1 b))) 2.0) a)
11.0ms
(* (* a c) (/ 1 b))

series43.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(/ (/ (* -2.0 (* (* a c) (/ 1 b))) 2.0) a)
19.0ms
(* (* a c) (/ 1 b))

simplify864.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (380.0ms)

IterNodesCost
02261724
16651405
225911143
done50001143

prune149.0ms

Pruning

37 alts after pruning (35 fresh and 2 done)

Merged error: 9.0b

regimes464.0ms

Accuracy

40.2% (8.2b remaining)

Error of 17.2b against oracle of 9.0b and baseline of 22.7b

bsearch4.0ms

Steps
ItersRangePoint
0
17.302597776335716
18.126688132261577
17.714642954298647

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02639
13239
done3239

end0.0ms

sample1.4s

Algorithm
intervals
Results
313.0ms4493×body160valid
303.0ms16612×pre80true
286.0ms8612×body80nan
123.0ms3507×body80valid