Details

Time bar (total: 44.5s)

sample101.0ms

Algorithm
intervals
Results
22.0ms18×body640valid
18.0ms193×body80valid
17.0ms31×body2560valid
8.0ms97×body80nan
8.0ms18×body1280valid
4.0ms6×body5120valid
1.0ms4×body320valid
1.0ms3×body160valid

simplify42.0ms

Counts
1 → 1
Iterations
IterNodes
done44
444
341
232
118
010

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- insert-posit16 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 → 95
Calls
4 calls:
102.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
48.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
39.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
107 → 107
Iterations
IterNodes
done5005
33743
21046
1388
0162

prune567.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b
(- (* b_2 b_2) (* a c))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×add-cbrt-cube associate-/r/
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
3×cbrt-undiv diff-log associate-/l*
2×rec-exp sub-neg sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log pow-flip inv-pow
Counts
4 → 181
Calls
4 calls:
68.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms
(- (* b_2 b_2) (* a c))
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
57.0ms
(- (* b_2 b_2) (* a c))
118.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
193 → 193
Iterations
IterNodes
done5001
21730
1655
0270

prune875.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b
(- (* b_2 b_2) (* a c))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
528×add-sqr-sqrt
527×*-un-lft-identity
355×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
46×sqrt-prod
44×add-exp-log
43×distribute-rgt-neg-in div-inv
32×div-exp
29×associate-/r/
27×associate-/r*
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/l*
10×add-log-exp
8×cbrt-undiv rec-exp 1-exp
5×pow1
4×insert-posit16
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 472
Calls
4 calls:
81.0ms
(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms
(- (* b_2 b_2) (* a c))
37.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
56.0ms
(- (* b_2 b_2) (* a c))
103.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify30.7s

Counts
484 → 484
Iterations
IterNodes
done5017
24926
11827
0599

prune858.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1 a))
0.6b
(cbrt (/ 1 a))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-prod
24×add-sqr-sqrt
23×*-un-lft-identity
19×add-cube-cbrt
18×times-frac
8×add-log-exp
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod insert-posit16
2×cbrt-div flip3-- pow1/3 sqrt-div diff-log div-inv flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 81
Calls
4 calls:
2.0ms
(cbrt (/ 1 a))
2.0ms
(cbrt (/ 1 a))
25.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series614.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(cbrt (/ 1 a))
228.0ms
(cbrt (/ 1 a))
96.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts
93 → 93
Iterations
IterNodes
done5000
32284
2739
1287
0143

prune383.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.3b

regimes335.0ms

Accuracy

86.7% (3.7b remaining)

Error of 9.2b against oracle of 5.5b and baseline of 33.1b

bsearch189.0ms

Steps
ItersRangePoint
8
2.5230591910300896e+45
6.095379443414697e+48
2.35488256262753e+48
8
-1.2685277833442503e-121
-9.432483994551924e-125
-6.029020104220027e-124
9
-1.4862902811470342e+56
-5.980481707988314e+50
-1.5244621186076104e+55

simplify7.0ms

Iterations
IterNodes
done39
139
033

end0.0ms

sample2.5s

Algorithm
intervals
Results
830.0ms5847×body80valid
434.0ms1069×body2560valid
387.0ms903×body1280valid
238.0ms3066×body80nan
141.0ms465×body640valid
105.0ms122×body5120valid
37.0ms215×body320valid
13.0ms115×body160valid