Details

Time bar (total: 19.2s)

sample127.0ms

Algorithm
intervals
Results
11.0ms39×body2560valid
10.0ms188×body80valid
7.0ms31×body1280valid
5.0ms87×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify28.0ms

Counts
1 → 1
Iterations
IterNodes
done29
529
427
325
222
114
010

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite661.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×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:
122.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
16.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
452.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
49.0ms
(- (* b_2 b_2) (* a c))
96.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
112.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
100 → 100
Iterations
IterNodes
done5003
34058
21029
1378
0158

prune585.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp insert-posit16 difference-of-squares
3×unswap-sqr
2×frac-times sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
142.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
9.0ms
(- (* b_2 b_2) (* a c))
43.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
47.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
101 → 101
Iterations
IterNodes
done5002
34688
21305
1445
0178

prune484.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×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:
67.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms
(- (* b_2 b_2) (* a c))
54.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
56.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
100 → 100
Iterations
IterNodes
done5003
34058
21029
1378
0158

prune512.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.4b
(- (* b_2 b_2) (* a c))
8.1b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip-- distribute-lft-out--
3×associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
23.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
15.0ms
(- (* b_2 b_2) (* a c))
76.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
49.0ms
(- (* b_2 b_2) (* a c))
109.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
109 → 109
Iterations
IterNodes
done5007
33339
21033
1401
0179

prune396.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.4b

regimes332.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.5b

bsearch106.0ms

Steps
ItersRangePoint
8
1.287554927770862e-68
8.304725640954512e-66
1.9573510501313932e-67
9
-5.599802959155633e+154
-4.186518194588193e+147
-6.037409549902714e+148

simplify4.0ms

Iterations
IterNodes
done26
126
023

end0.0ms

sample2.9s

Algorithm
intervals
Results
612.0ms1065×body2560valid
567.0ms95×body5120valid
496.0ms5888×body80valid
403.0ms902×body1280valid
282.0ms2851×body80nan
147.0ms450×body640valid
95.0ms201×body320valid
23.0ms137×body160valid