Details

Time bar (total: 12.5s)

sample85.0ms

Algorithm
intervals
Results
15.0ms198×body80valid
13.0ms27×body2560valid
10.0ms26×body1280valid
8.0ms101×body80nan
5.0ms15×body640valid
4.0ms14×body320valid
1.0ms9×body160valid
1.0ms2×body5120valid

simplify37.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize61.0ms

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))
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite148.0ms

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:
105.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(- (* b_2 b_2) (* a c))
21.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms
(- (* b_2 b_2) (* a c))
90.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
103 → 103
Iterations
IterNodes
done5000
21527
1392
0158

prune586.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
0.6b
(cbrt a)
2.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
8×add-log-exp
7×add-cube-cbrt
6×cbrt-prod
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod
2×flip3-- pow1/3 sqrt-div diff-log flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 55
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(cbrt a)
38.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series855.0ms

Counts
4 → 12
Calls
4 calls:
323.0ms
(cbrt a)
303.0ms
(cbrt a)
113.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
116.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify787.0ms

Counts
67 → 67
Iterations
IterNodes
done5001
2939
1247
0106

prune462.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
12.4b
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
9×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log flip--
3×diff-log
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log difference-of-squares
Counts
4 → 57
Calls
4 calls:
13.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* b_2 b_2) (* a c))
120.0ms
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify964.0ms

Counts
69 → 69
Iterations
IterNodes
done5000
21037
1252
096

prune462.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0 (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.6b
(- (* b_2 b_2) (* a c))
2.0b
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
25×add-sqr-sqrt
18×times-frac
16×add-cube-cbrt
8×distribute-lft-out-- add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out
4×difference-of-squares
3×associate-/r* flip3-- sqrt-prod flip--
2×sqrt-div associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log div-sub div-exp distribute-frac-neg flip-+ div-inv sub0-neg
Counts
4 → 82
Calls
4 calls:
165.0ms
(/ (- 0 (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
14.0ms
(- (* b_2 b_2) (* a c))
24.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- 0 (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
68.0ms
(- (* b_2 b_2) (* a c))
100.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
94 → 94
Iterations
IterNodes
done5002
21790
1417
0161

prune494.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.8b

regimes487.0ms

Accuracy

85.8% (4.0b remaining)

Error of 9.5b against oracle of 5.5b and baseline of 33.8b

bsearch200.0ms

Steps
ItersRangePoint
3
5.437233749566996e+22
6.419404774371196e+22
6.358019085320933e+22
7
-4.897053303415578e-149
-2.667940472730993e-151
-4.782406139136437e-149
7
-5.184880600629587e-130
-4.5773238538612075e-132
-4.652312659939379e-132
6
-0.042530208599811804
-0.005947574473424517
-0.03099989563658143

simplify11.0ms

Iterations
IterNodes
done50
250
143
036

end0.0ms

sample2.8s

Algorithm
intervals
Results
533.0ms237×body320valid
528.0ms5931×body80valid
447.0ms1024×body2560valid
355.0ms865×body1280valid
223.0ms2961×body80nan
160.0ms491×body640valid
55.0ms112×body5120valid
48.0ms116×body160valid