Details

Time bar (total: 19.7s)

sample66.0ms

Algorithm
intervals
Results
12.0ms37×body2560valid
10.0ms185×body80valid
9.0ms33×body1280valid
5.0ms81×body80nan
4.0ms20×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite183.0ms

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:
17.0ms
(- (* b_2 b_2) (* a c))
114.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b_2 b_2) (* a c))
127.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
134.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
103 → 103
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01561821
13661727
210071611
327731595
done50001593

prune336.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.9b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite375.0ms

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:
87.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
171.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
96.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series848.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
247.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
351.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
115.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
139 → 139
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02373118
15822897
219162663
done50022625

prune518.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite179.0ms

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:
17.0ms
(- (* b_2 b_2) (* a c))
84.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* b_2 b_2) (* a c))
284.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
92.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.4s

Counts
95 → 95
Iterations

Useful iterations: 4 (2.6s)

IterNodesCost
01471588
13111491
27721393
318031389
445951375
done50011375

prune402.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.7b
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.1b
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite336.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
26×*-un-lft-identity
24×associate-*r*
22×times-frac
18×add-exp-log add-cube-cbrt add-cbrt-cube
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×flip3-- associate-*l* associate-/r* flip--
2×sqrt-div associate-*r/ associate-/r/ div-inv unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative associate-/l/ associate-/l*
Counts
4 → 97
Calls
4 calls:
77.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
150.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
72.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
28.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
288.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
231.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
106.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
109 → 109
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02031911
15081798
215671522
done50011486

prune334.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes345.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.3b

bsearch148.0ms

Steps
ItersRangePoint
8
1.538525478595148e+72
6.402915924844171e+74
4.19865099347443e+74
5
1.3461159678365104e-246
2.760780588216915e-246
1.3645292833571162e-246
6
-3.779251410483496e+105
-5.080294099506613e+104
-3.7277239731487426e+105

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03459
14155
done4155

end0.0ms

sample2.9s

Algorithm
intervals
Results
873.0ms1058×body2560valid
435.0ms5846×body80valid
386.0ms921×body1280valid
210.0ms2929×body80nan
196.0ms503×body640valid
117.0ms210×body320valid
54.0ms109×body5120valid
14.0ms109×body160valid