Details

Time bar (total: 15.6s)

sample104.0ms

Algorithm
intervals
Results
34.0ms147×body160valid
19.0ms288×body80nan
16.0ms544×pre80true
8.0ms109×body80valid

simplify127.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
379
243
125
014

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* 4.0 (* c a))))
0.2b
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
0.3b
(- (* b b) (* 4.0 (* c a)))
29.2b
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 183
Calls
4 calls:
13.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
79.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
12.0ms
(- (* b b) (* 4.0 (* c a)))
56.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

series366.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (- (* b b) (* 4.0 (* c a))))
105.0ms
(/ (/ (- (sqrt (- (* b b) (* 4.0 (* c a)))) b) 2.0) a)
50.0ms
(- (* b b) (* 4.0 (* c a)))
121.0ms
(- (sqrt (- (* b b) (* 4.0 (* c a)))) b)

simplify1.8s

Counts
195 → 195
Iterations
IterNodes
done5001
22320
1798
0321

prune1.2s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.5b

localize10.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune200.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.5b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-cbrt-cube add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
7.0ms
(/ (* a c) b)
23.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series70.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(/ (* a c) b)
40.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify2.0s

Counts
83 → 83
Iterations
IterNodes
done5049
21836
1456
0171

prune769.0ms

Pruning

38 alts after pruning (38 fresh and 0 done)

Merged error: 9.4b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
106×add-sqr-sqrt
76×*-un-lft-identity add-cube-cbrt
53×add-cbrt-cube add-exp-log
48×sqrt-prod
23×cbrt-undiv div-exp
22×associate-*r* associate-*l*
15×associate-/r*
13×prod-exp cbrt-unprod associate-/l*
9×div-inv unswap-sqr
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 215
Calls
4 calls:
9.0ms
(/ a (sqrt b))
10.0ms
(/ c (sqrt b))
50.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
37.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ a (sqrt b))
75.0ms
(/ c (sqrt b))
70.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
70.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify2.5s

Counts
227 → 227
Iterations
IterNodes
done5189
24144
11054
0365

prune1.0s

Pruning

45 alts after pruning (45 fresh and 0 done)

Merged error: 9.3b

regimes1.2s

Accuracy

46.7% (7.5b remaining)

Error of 16.4b against oracle of 8.9b and baseline of 23.0b

bsearch28.0ms

Steps
ItersRangePoint
1
825.8857943049597
863.2800776740891
835.234365147242

simplify13.0ms

Iterations
IterNodes
done38
138
031

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s4406×body160valid
769.0ms8521×body80nan
569.0ms16521×pre80true
329.0ms3594×body80valid