Details

Time bar (total: 20.5s)

sample88.0ms

Algorithm
intervals
Results
11.0ms42×body2560valid
9.0ms173×body80valid
5.0ms25×body1280valid
3.0ms69×body80nan
3.0ms18×body640valid
1.0ms11×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify69.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite273.0ms

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:
209.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (- 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)))

series630.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
271.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms
(- (* b_2 b_2) (* a c))
139.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
103 → 103
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01561821
13661727
210051611
327701595
done50011593

prune447.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
2.4b
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.8b
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
53×add-sqr-sqrt
40×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
13×associate-/l*
12×difference-of-squares
10×associate-/r/
9×associate-/r* sqrt-prod
7×cbrt-undiv flip3-- div-exp flip--
6×div-inv distribute-lft-out-- 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 → 124
Calls
4 calls:
20.0ms
(- (* b_2 b_2) (* a c))
144.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
58.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series1.1s

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* b_2 b_2) (* a c))
719.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
250.0ms
(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts
136 → 136
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02372999
15862794
219382466
done50012460

prune504.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

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:
80.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
55.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
102.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms
(- (* b_2 b_2) (* a c))
111.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.3s

Counts
95 → 95
Iterations

Useful iterations: 4 (2.5s)

IterNodesCost
01471588
13111491
27741393
318101389
445681375
done50011375

prune338.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite159.0ms

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×associate-/r/ add-cbrt-cube
7×flip3-- div-exp flip--
6×pow1
5×div-inv
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 177
Calls
4 calls:
80.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
27.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
78.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms
(- (* b_2 b_2) (* a c))
122.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts
189 → 189
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
02664484
15773936
213803617
338543507
done50003507

prune524.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.2b

regimes274.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.6b

bsearch269.0ms

Steps
ItersRangePoint
5
1.7897742140858872e+53
5.1194650287633095e+53
5.031608061939103e+53
9
9.448397398655464e-278
1.4829972419072586e-270
8.216265756828381e-276
9
-1.4642911230069481e+159
-8.435593739772907e+149
-3.5132588248780117e+152

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03357
14055
done4055

end0.0ms

sample3.2s

Algorithm
intervals
Results
710.0ms2938×body80nan
595.0ms5843×body80valid
545.0ms1104×body2560valid
381.0ms860×body1280valid
206.0ms492×body640valid
75.0ms226×body320valid
53.0ms107×body5120valid
13.0ms106×body160valid