Details

Time bar (total: 18.5s)

sample93.0ms

Algorithm
intervals
Results
10.0ms178×body80valid
10.0ms38×body2560valid
7.0ms29×body1280valid
4.0ms79×body80nan
2.0ms11×body640valid
1.0ms3×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
91.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
111.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
52.0ms
(- (* b_2 b_2) (* a c))
109.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
92 → 92
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01511534
13551440
210011266
327841252
done50011249

prune335.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.5b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
13×add-exp-log add-cube-cbrt associate-*r*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1
5×associate-*l*
4×prod-exp distribute-lft-out
3×flip3-+ sqrt-prod flip-+ unswap-sqr
2×frac-times flip3-- distribute-rgt-neg-in sqrt-div div-exp associate-*l/ sum-log flip-- cbrt-unprod
1×cbrt-undiv +-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp sqrt-pow1 pow1/2 diff-log 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 84
Calls
4 calls:
113.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
40.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
109.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms
(- (* b_2 b_2) (* a c))
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts
96 → 96
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01751643
14381441
213351224
340831198
done50001198

prune359.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.6b
(/ (+ (* a c) 0) a)
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×*-un-lft-identity
13×add-cube-cbrt
10×add-log-exp
9×times-frac
6×add-exp-log add-cbrt-cube
5×pow1
4×sqrt-prod
3×flip3-- diff-log associate-/r* flip-- associate-/l*
2×sub-neg sqrt-div associate-/l/ distribute-lft-out-- difference-of-squares
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 74
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
33.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms
(/ (+ (* a c) 0) a)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (* b_2 b_2) (* a c))
129.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(/ (+ (* a c) 0) a)
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts
86 → 86
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
01481154
1323982
21060904
33700866
done5000866

prune383.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.6b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite140.0ms

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-/r*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/l*
2×sub-neg sqrt-div associate-/r/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp neg-log clear-num div-inv
Counts
4 → 90
Calls
4 calls:
50.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms
(- (* b_2 b_2) (* a c))
58.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series477.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
48.0ms
(- (* b_2 b_2) (* a c))
99.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
102 → 102
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01511775
13251672
28691558
322541540
done50011534

prune322.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.1b

regimes433.0ms

Accuracy

96.1% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 34.3b

bsearch203.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.6082844052603056e+78
11
-1.0472779812871276e-269
-2.473343252086336e-295
-3.1400906193105714e-291
8
-6.990724105819741e+111
-2.6156774686163576e+108
-1.569310777886352e+111

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03054
13554
done3554

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.2s1087×body2560valid
476.0ms936×body1280valid
441.0ms5805×body80valid
247.0ms2994×body80nan
152.0ms443×body640valid
69.0ms211×body320valid
60.0ms117×body5120valid
15.0ms113×body160valid