Details

Time bar (total: 16.9s)

sample79.0ms

Algorithm
intervals
Results
22.0ms36×body1280valid
14.0ms39×body2560valid
9.0ms166×body80valid
5.0ms89×body80nan
4.0ms18×body640valid
2.0ms10×body320valid
1.0ms4×body5120valid
0.0ms2×body160valid

simplify26.0ms

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: 36.2b

localize15.0ms

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))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite190.0ms

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:
106.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
104.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms
(- (* b_2 b_2) (* a c))
109.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify939.0ms

Counts
103 → 103
Iterations

Useful iterations: done (936.0ms)

IterNodesCost
01561821
13881727
215011611
done50001603

prune389.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
4.4b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.8b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 184
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
149.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
99.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series689.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (* b_2 b_2) (* a c))
243.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
299.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
196 → 196
Iterations

Useful iterations: 2 (783.0ms)

IterNodesCost
03025540
17704801
242364619
done50014619

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize39.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
7.3b
(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
64×add-sqr-sqrt
50×*-un-lft-identity
48×sqrt-prod
38×add-cube-cbrt
18×add-exp-log add-cbrt-cube
16×associate-/l*
14×sqrt-div
12×associate-/r* difference-of-squares
10×associate-/r/
7×cbrt-undiv flip3-- div-exp flip--
6×pow1 div-inv distribute-lft-out--
4×add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 145
Calls
4 calls:
137.0ms
(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
91.0ms
(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series1.6s

Counts
4 → 12
Calls
4 calls:
662.0ms
(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
702.0ms
(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
114.0ms
(sqrt (- (* b_2 b_2) (* a c)))
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts
157 → 157
Iterations

Useful iterations: 2 (566.0ms)

IterNodesCost
02603735
16703366
233313180
done50023180

prune658.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize34.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* (/ a (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ c (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
22.6b
(sqrt (- (* b_2 b_2) (* a c)))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
9×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp sqrt-prod
7×pow1
6×sqrt-div
4×prod-exp cbrt-unprod add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 times-frac pow1/2 associate-/r* flip-- associate-/l/
1×frac-times frac-2neg associate-*r/ associate-*l/ clear-num div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
71.0ms
(/ (* (/ a (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ c (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
457.0ms
(/ (* (/ a (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ c (sqrt (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))) a)
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))
93.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
87 → 87
Iterations

Useful iterations: 2 (390.0ms)

IterNodesCost
01542093
14581919
226261543
done50011543

prune429.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

regimes317.0ms

Accuracy

86.1% (3.7b remaining)

Error of 9.5b against oracle of 5.7b and baseline of 32.4b

bsearch286.0ms

Steps
ItersRangePoint
11
8.182113676652236e-12
2116652649.122401
2098867031.9345784
11
9.132164512921457e-291
8.018752023592085e-262
9.282718576312558e-291
8
-5.545092253462458e+82
-2.14594256023029e+80
-1.113821654949689e+81

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03886
14686
done4686

end0.0ms

sample2.6s

Algorithm
intervals
Results
728.0ms912×body1280valid
488.0ms1015×body2560valid
439.0ms5936×body80valid
173.0ms2930×body80nan
92.0ms438×body640valid
76.0ms232×body320valid
41.0ms100×body5120valid
17.0ms123×body160valid