Details

Time bar (total: 23.2s)

sample84.0ms

Algorithm
intervals
Results
14.0ms174×body80valid
14.0ms30×body2560valid
11.0ms28×body1280valid
7.0ms97×body80nan
7.0ms23×body640valid
3.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010283
118283
232283
341283
444283
done44283

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
2.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite124.0ms

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:
68.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(- (* b_2 b_2) (* a c))
28.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms
(- (* b_2 b_2) (* a c))
107.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts
103 → 103
Iterations

Useful iterations: done (3.5s)

IterNodesCost
015839129
138335913
2103935553
3360835393
done500135352

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.5b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×associate-/l*
10×associate-/r/ sqrt-prod
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv 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 → 127
Calls
4 calls:
51.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
73.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
60.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series714.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
245.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
273.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
95.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.3s

Counts
139 → 139
Iterations

Useful iterations: 2 (845.0ms)

IterNodesCost
023759212
160854042
2210653081
done500253081

prune781.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.5b
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
26×*-un-lft-identity
24×associate-*r*
22×times-frac
18×add-cbrt-cube add-exp-log add-cube-cbrt
8×difference-of-squares
7×pow1 sqrt-prod
6×add-log-exp
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod distribute-lft-out--
3×associate-/r* flip3-- associate-*l* flip--
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 → 97
Calls
4 calls:
65.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
147.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
34.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series760.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
338.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
230.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts
109 → 109
Iterations

Useful iterations: done (2.5s)

IterNodesCost
020336308
153131960
2165931478
done500330760

prune654.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.5b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×associate-/l*
10×associate-/r/ sqrt-prod
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv 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 → 127
Calls
4 calls:
60.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
84.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
62.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series758.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
263.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
304.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts
139 → 139
Iterations

Useful iterations: 2 (904.0ms)

IterNodesCost
023759212
160854042
2210653081
done500253081

prune769.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.6b

regimes554.0ms

Accuracy

89.7% (2.7b remaining)

Error of 8.5b against oracle of 5.8b and baseline of 32.0b

bsearch274.0ms

Steps
ItersRangePoint
10
7.868349732386487e+96
4.727011775790926e+114
1.0928779650362586e+104
10
-7.955104670113648e-283
-3.206335945357617e-294
-3.264171759716638e-294
9
-1.5616592422619596e-10
-4.8623869860036984e-17
-5.2605709473303605e-14

simplify16.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0321079
1371079
done371079

end0.0ms

sample3.2s

Algorithm
intervals
Results
995.0ms5866×body80valid
901.0ms1040×body2560valid
447.0ms916×body1280valid
174.0ms2929×body80nan
119.0ms462×body640valid
101.0ms110×body5120valid
71.0ms220×body320valid
13.0ms113×body160valid