Details

Time bar (total: 7.2s)

sample52.0ms

Algorithm
intervals
Results
10.0ms314×body80nan
10.0ms570×pre80true
9.0ms137×body160valid
4.0ms119×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: 27.5b

localize11.0ms

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))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
27.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite68.0ms

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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
20.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series307.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify788.0ms

Counts
161 → 161
Iterations

Useful iterations: done (782.0ms)

IterNodesCost
02804083
16653911
221763753
done50003752

prune471.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.8b

localize4.0ms

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

prune72.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 9.8b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

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)

series45.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
20.0ms
(/ (* a c) b)

simplify601.0ms

Counts
79 → 79
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
01671164
14401118
21944956
done5001956

prune241.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 9.8b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
762×times-frac
318×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
312×sqrt-prod
59×div-inv
55×add-exp-log add-cbrt-cube
54×associate-/l*
30×cbrt-undiv div-exp
15×associate-/r*
9×prod-exp cbrt-unprod
3×pow1 frac-2neg clear-num add-log-exp
2×associate-/l/
Counts
3 → 448
Calls
3 calls:
3.0ms
(/ (* a c) b)
27.0ms
(/ (/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a)) (sqrt a))
11.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a))

series151.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(/ (* a c) b)
49.0ms
(/ (/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a)) (sqrt a))
78.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) (sqrt a))

simplify1.7s

Counts
457 → 457
Iterations

Useful iterations: 2 (846.0ms)

IterNodesCost
059412092
1145210911
2495510168
done500010168

prune633.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 9.7b

regimes532.0ms

Accuracy

47.8% (7.2b remaining)

Error of 16.2b against oracle of 9.1b and baseline of 22.8b

bsearch4.0ms

Steps
ItersRangePoint
0
3187.1734153117472
3187.188536646724
3187.1809759792354

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02639
13239
done3239

end0.0ms

sample1.4s

Algorithm
intervals
Results
306.0ms4461×body160valid
296.0ms16802×pre80true
284.0ms8802×body80nan
127.0ms3538×body80valid
0.0ms1×body320valid