Details

Time bar (total: 18.3s)

sample69.0ms

Algorithm
intervals
Results
14.0ms37×body2560valid
11.0ms182×body80valid
9.0ms31×body1280valid
5.0ms22×body640valid
5.0ms89×body80nan
1.0ms9×body320valid
1.0ms1×body5120valid
0.0ms3×body160valid

simplify41.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

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-- 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 → 91
Calls
4 calls:
63.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
108.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms
(- (* b_2 b_2) (* a c))
80.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
103 → 103
Iterations
IterNodes
done5000
33629
21040
1384
0158

prune470.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
4.2b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.9b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
53×add-sqr-sqrt
40×*-un-lft-identity
28×add-cube-cbrt
18×add-cbrt-cube add-exp-log
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×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 124
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
97.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
63.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series691.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b_2 b_2) (* a c))
258.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
277.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
136 → 136
Iterations
IterNodes
done5000
22137
1608
0234

prune698.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
2.3b
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.2b
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
24×*-un-lft-identity associate-*r*
22×times-frac
18×add-cbrt-cube add-exp-log add-cube-cbrt
7×pow1
6×sqrt-prod add-log-exp difference-of-squares
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod
3×associate-/r* flip3-- associate-*l* flip-- distribute-lft-out--
2×sqrt-div associate-*r/ associate-/r/ div-inv unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative associate-/l* associate-/l/
Counts
4 → 94
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* a c))
147.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
53.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b_2 b_2) (* a c))
314.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
257.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts
106 → 106
Iterations
IterNodes
done5004
21681
1519
0196

prune615.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

localize121.0ms

Local error

Found 4 expressions with local error:

8.0b
(cbrt (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
1×cbrt-prod cbrt-div pow1/3 associate-*r/
Counts
4 → 55
Calls
4 calls:
43.0ms
(cbrt (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series1.3s

Counts
4 → 12
Calls
4 calls:
1.0s
(cbrt (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
113.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
67 → 67
Iterations
IterNodes
done5000
31417
2531
1207
093

prune501.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

regimes517.0ms

Accuracy

82.7% (4.5b remaining)

Error of 10.5b against oracle of 6.0b and baseline of 31.9b

bsearch100.0ms

Steps
ItersRangePoint
5
2.6243927093659187e+107
5.901159163981397e+107
3.038903409991338e+107
9
-1.0952546209266604e-55
-7.034794544076098e-65
-9.332433396832084e-58

simplify4.0ms

Iterations
IterNodes
done25
125
022

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.1s5889×body80valid
413.0ms1019×body2560valid
368.0ms891×body1280valid
259.0ms2880×body80nan
109.0ms461×body640valid
102.0ms98×body5120valid
41.0ms223×body320valid
14.0ms117×body160valid