Details

Time bar (total: 19.1s)

sample82.0ms

Algorithm
intervals
Results
17.0ms35×body2560valid
14.0ms185×body80valid
9.0ms23×body1280valid
7.0ms103×body80nan
5.0ms19×body640valid
1.0ms7×body160valid
1.0ms4×body320valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11913
23313
34613
44913
done4913

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 171
Calls
4 calls:
87.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (* b_2 b_2) (* a c))
25.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
58.0ms
(- (* b_2 b_2) (* a c))
93.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
183 → 183
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02445995
15834338
221523550
done50003004

prune755.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
0.6b
(- (pow b_2 2) (* c a))
1.8b
(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
22.7b
(sqrt (- (pow b_2 2) (* c a)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
174×*-un-lft-identity
165×times-frac
122×add-cube-cbrt
68×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×fma-neg
15×add-exp-log
10×add-log-exp
9×add-cbrt-cube associate-/r/
7×neg-mul-1 flip3-- div-exp flip--
6×pow1 unpow-prod-down
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log associate-/l*
2×rec-exp sub-neg sqrt-div 1-exp unpow2 sqr-pow
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log pow-flip inv-pow
Counts
4 → 271
Calls
4 calls:
58.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
28.0ms
(- (pow b_2 2) (* c a))
74.0ms
(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
15.0ms
(sqrt (- (pow b_2 2) (* c a)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
36.0ms
(- (pow b_2 2) (* c a))
91.0ms
(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
78.0ms
(sqrt (- (pow b_2 2) (* c a)))

simplify2.3s

Counts
283 → 283
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03668832
19026686
241915856
done50005855

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b
(- (* b_2 b_2) (* a c))
5.6b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
1339×times-frac
946×add-sqr-sqrt
940×*-un-lft-identity
926×add-cube-cbrt
749×prod-diff
323×sqrt-prod
210×distribute-rgt-neg-in
207×distribute-lft-neg-in
69×neg-mul-1
60×div-inv
35×fma-neg
8×add-log-exp
7×distribute-lft-out--
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div log1p-expm1-u flip--
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-sub div-exp frac-sub sub-div
Counts
4 → 889
Calls
4 calls:
27.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
13.0ms
(- (* b_2 b_2) (* a c))
139.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
25.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
55.0ms
(- (* b_2 b_2) (* a c))
128.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
108.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
901 → 901
Iterations

Useful iterations: done (992.0ms)

IterNodesCost
090368622
1201359567
done500046463

prune3.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
14.3b
(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
48×add-sqr-sqrt
46×*-un-lft-identity add-cube-cbrt
35×fma-neg prod-diff
18×distribute-lft-neg-in distribute-rgt-neg-in
12×sqrt-div
8×add-log-exp
6×pow1 neg-mul-1 flip3-- sqrt-prod flip--
5×frac-sub
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
2×frac-times rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-*l/ associate-*r/ div-inv
1×associate--l- neg-sub0 div-sub sub-div
Counts
4 → 139
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
48.0ms
(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b_2 b_2) (* a c))
151.0ms
(- (/ (- b_2) a) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
151 → 151
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02425074
16033210
220493050
done50003008

prune950.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes601.0ms

Accuracy

87.7% (3.6b remaining)

Error of 9.0b against oracle of 5.4b and baseline of 34.5b

bsearch301.0ms

Steps
ItersRangePoint
9
6.258218916731328e+93
1.8883840965187804e+99
6.637037935235253e+98
7
-1.9525004674970017e-146
-8.640740768077714e-148
-1.571246895950166e-147
10
-6.172175216823688e+56
-1.1198862992811701e+41
-1.532647813487865e+52

simplify8.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03764
14562
25062
35262
done5262

end0.0ms

sample3.0s

Algorithm
intervals
Results
973.0ms5778×body80valid
516.0ms1115×body2560valid
356.0ms885×body1280valid
280.0ms2929×body80nan
112.0ms463×body640valid
112.0ms111×body5120valid
71.0ms254×body320valid
15.0ms124×body160valid