Details

Time bar (total: 19.9s)

sample207.0ms

Algorithm
intervals
Results
23.0ms40×body2560valid
15.0ms181×body80valid
11.0ms27×body1280valid
7.0ms92×body80nan
7.0ms7×body5120valid
4.0ms13×body640valid
1.0ms5×body320valid
0.0ms3×body160valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

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-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
105.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms
(- (* b_2 b_2) (* a c))
59.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
76.0ms
(- (* b_2 b_2) (* a c))
115.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
141.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
103 → 103
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01561821
13661727
210051611
327731595
done50011593

prune373.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize27.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.9b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.4b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×difference-of-squares
13×associate-/l*
10×sqrt-prod associate-/r/
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv add-log-exp
5×pow1
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 127
Calls
4 calls:
65.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
142.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
69.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series779.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
302.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
281.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
98.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
139 → 139
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02393118
15932899
219412569
done50002563

prune575.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite122.0ms

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-exp-log associate-/r* add-cbrt-cube
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 83
Calls
4 calls:
45.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms
(- (* b_2 b_2) (* a c))
52.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series632.0ms

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms
(- (* b_2 b_2) (* a c))
129.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
106.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts
95 → 95
Iterations

Useful iterations: 4 (2.5s)

IterNodesCost
01471588
13111491
27731393
318141389
445821375
done50001375

prune300.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
25×*-un-lft-identity
24×associate-*r*
20×times-frac
16×add-cube-cbrt
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp difference-of-squares
7×pow1 sqrt-prod
4×flip3-- prod-exp flip-- distribute-lft-out--
3×associate-*l* unswap-sqr
2×sub-neg sqrt-div diff-log div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
142.0ms
(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
16.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(* c (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
56.0ms
(- (* b_2 b_2) (* a c))
112.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
100.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
101 → 101
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01701564
13981354
29091212
320661208
done50001196

prune327.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

regimes204.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.3b against oracle of 5.2b and baseline of 29.5b

bsearch249.0ms

Steps
ItersRangePoint
10
4.61796087672408e+142
1.3206820209921783e+153
1.1043857160155008e+144
4
1.096458200021764e-161
2.1348066422084948e-161
1.123334719424155e-161
9
-6.354265220965125e+156
-1.769171722317776e+149
-2.4466612317601678e+151

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03357
14055
done4055

end0.0ms

sample3.6s

Algorithm
intervals
Results
706.0ms2913×body80nan
602.0ms1098×body2560valid
577.0ms119×body5120valid
529.0ms959×body1280valid
463.0ms5724×body80valid
125.0ms456×body640valid
98.0ms242×body320valid
74.0ms116×body160valid