Details

Time bar (total: 19.6s)

sample89.0ms

Algorithm
intervals
Results
23.0ms154×body160valid
21.0ms296×body80nan
20.0ms552×pre80true
8.0ms102×body80valid

simplify81.0ms

Counts
1 → 1
Iterations
IterNodes
done93
793
692
590
482
366
240
121
012

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3 a) c)
0.3b
(- (* b b) (* (* 3 a) c))
0.4b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
30.6b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×add-cbrt-cube add-exp-log
13×*-un-lft-identity
9×pow1
8×add-log-exp
7×add-cube-cbrt
6×times-frac associate-/l* difference-of-squares
4×prod-exp cbrt-unprod insert-posit16
3×flip3-- associate-*r* pow-prod-down sqrt-prod flip-- distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×clear-num associate-/r* frac-2neg div-sub associate-*l* *-commutative div-inv
Counts
4 → 79
Calls
4 calls:
25.0ms
(* (* 3 a) c)
13.0ms
(- (* b b) (* (* 3 a) c))
112.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
56.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)

series383.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (* 3 a) c)
71.0ms
(- (* b b) (* (* 3 a) c))
172.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
117.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)

simplify1.5s

Counts
91 → 91
Iterations
IterNodes
done2037
32037
21442
1422
0158

prune662.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.7b

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune74.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.7b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(* -3/2 (/ (* a c) b))
0.4b
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×times-frac associate-*r*
5×pow1
4×associate-/r*
3×associate-*l* insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r/ associate-/l*
1×pow-prod-down *-commutative unswap-sqr associate-/l/
Counts
3 → 81
Calls
3 calls:
18.0ms
(/ (* a c) b)
30.0ms
(* -3/2 (/ (* a c) b))
36.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

series124.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(/ (* a c) b)
48.0ms
(* -3/2 (/ (* a c) b))
35.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

simplify933.0ms

Counts
90 → 90
Iterations
IterNodes
done2001
22001
1382
0126

prune433.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 8.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* 9/4 (/ a (/ b c))) (/ a (/ b c)))
0.4b
(* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c)))
0.4b
(/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a)))
0.6b
(cbrt (/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
1534×add-cbrt-cube add-exp-log
678×cbrt-undiv div-exp
675×prod-exp cbrt-unprod
155×times-frac
88×associate-*r*
81×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×pow1
13×div-inv
11×cbrt-prod
10×associate-*r/
9×pow-prod-down
7×associate-/l*
6×frac-times associate-*l/
4×insert-posit16 add-log-exp
2×associate-*l* associate-/r/ *-commutative
1×cbrt-div clear-num associate-/r* frac-2neg pow1/3 associate-/l/
Counts
4 → 525
Calls
4 calls:
59.0ms
(* (* 9/4 (/ a (/ b c))) (/ a (/ b c)))
176.0ms
(* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c)))
682.0ms
(/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a)))
603.0ms
(cbrt (/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (* 9/4 (/ a (/ b c))) (/ a (/ b c)))
175.0ms
(* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c)))
100.0ms
(/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a)))
94.0ms
(cbrt (/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a))))

simplify2.5s

Counts
537 → 537
Iterations
IterNodes
done2000
12000
0858

prune3.5s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 8.6b

regimes1.3s

Accuracy

41.8% (7.8b remaining)

Error of 17.1b against oracle of 9.2b and baseline of 22.7b

bsearch45.0ms

Steps
ItersRangePoint
2
82.56954229495332
91.66372883969355
83.70631561304585

simplify10.0ms

Iterations
IterNodes
done35
135
025

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.6s8548×body80nan
1.4s4472×body160valid
1.3s16548×pre80true
593.0ms3528×body80valid