Details

Time bar (total: 11.8s)

sample169.0ms

Algorithm
intervals
Results
58.0ms304×body80nan
39.0ms156×body160valid
30.0ms560×pre80true
13.0ms100×body80valid

simplify130.0ms

Counts
1 → 1
Iterations
IterNodes
done98
798
697
595
487
370
243
124
014

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* c a) 4)))
0.2b
(- (* b b) (* (* c a) 4))
0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
30.7b
(- (sqrt (- (* b b) (* (* c a) 4))) b)

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
sqrt-prod add-log-exp
add-cbrt-cube add-exp-log associate-/l*
pow1 distribute-lft-out--
flip3-- insert-posit16 flip--
associate-/r*
sub-neg sqrt-div diff-log associate-/l/
cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))
15.0ms
(- (* b b) (* (* c a) 4))
101.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
61.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

series407.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(sqrt (- (* b b) (* (* c a) 4)))
55.0ms
(- (* b b) (* (* c a) 4))
134.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
122.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)

simplify1.1s

Counts
100 → 100
Iterations
IterNodes
done2005
32005
21103
1400
0161

prune551.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.8b

localize9.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune67.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.8b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
cbrt-undiv div-exp
add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
prod-exp cbrt-unprod
pow1 clear-num frac-2neg insert-posit16 div-inv associate-/l* add-log-exp
associate-*r/ associate-/l/
Counts
2 → 49
Calls
2 calls:
14.0ms
(/ (* a c) b)
27.0ms
(/ (* -2 (/ (* a c) b)) a)

series57.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ (* a c) b)
25.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify1.0s

Counts
55 → 55
Iterations
IterNodes
done2005
32005
21437
1278
099

prune307.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 8.7b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
121×add-sqr-sqrt
91×*-un-lft-identity add-cube-cbrt
72×sqrt-prod
52×add-cbrt-cube add-exp-log
46×associate-*r*
22×cbrt-undiv div-exp associate-*l*
18×div-inv
15×associate-/r*
12×prod-exp cbrt-unprod
11×associate-/l*
unswap-sqr
pow1
insert-posit16 add-log-exp
clear-num frac-2neg
frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 241
Calls
4 calls:
10.0ms
(/ (* a c) b)
4.0ms
(/ -2 (sqrt a))
32.0ms
(* (/ -2 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
20.0ms
(/ (/ (* a c) b) (sqrt a))

series223.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (* a c) b)
43.0ms
(/ -2 (sqrt a))
64.0ms
(* (/ -2 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
91.0ms
(/ (/ (* a c) b) (sqrt a))

simplify955.0ms

Counts
253 → 253
Iterations
IterNodes
done2003
22003
11032
0337

prune828.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 8.6b

regimes817.0ms

Accuracy

42.2% (8.0b remaining)

Error of 17.1b against oracle of 9.1b and baseline of 22.9b

bsearch29.0ms

Steps
ItersRangePoint
2
82.56954229495332
91.66372883969355
83.70631561304585

simplify6.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.5s8641×body80nan
1.3s4445×body160valid
1.1s16641×pre80true
481.0ms3555×body80valid