Details

Time bar (total: 16.2s)

sample204.0ms

Algorithm
intervals
Results
25.0ms191×body80valid
21.0ms28×body2560valid
16.0ms26×body1280valid
9.0ms82×body80nan
8.0ms19×body640valid
3.0ms9×body320valid
2.0ms2×body5120valid
0.0ms2×body160valid

simplify58.0ms

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite157.0ms

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-- insert-posit16 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 → 95
Calls
4 calls:
90.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms
(- (* b_2 b_2) (* a c))
30.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
53.0ms
(- (* b_2 b_2) (* a c))
104.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
139.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
107 → 107
Iterations
IterNodes
done5001
21543
1397
0162

prune467.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×distribute-lft-out--
11×add-cbrt-cube add-exp-log
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp insert-posit16
3×associate-/l/
2×clear-num frac-2neg sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 191
Calls
4 calls:
42.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
97.0ms
(/ (/ (+ 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))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series712.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
263.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
288.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
203 → 203
Iterations
IterNodes
done5002
24136
1770
0308

prune942.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b
(- (* b_2 b_2) (* a c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×associate-*r* add-exp-log add-cube-cbrt
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp insert-posit16 distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div div-exp associate-*l/ cbrt-unprod
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 93
Calls
4 calls:
101.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
59.0ms
(- (* b_2 b_2) (* a c))
110.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
102.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
105 → 105
Iterations
IterNodes
done5001
22064
1467
0181

prune453.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 1 expressions with local error:

0.0b
(* -1/2 (/ c b_2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×associate-*r*
10×times-frac
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
3×pow1 associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative insert-posit16 div-inv add-log-exp
Counts
1 → 33
Calls
1 calls:
23.0ms
(* -1/2 (/ c b_2))

series21.0ms

Counts
1 → 3
Calls
1 calls:
21.0ms
(* -1/2 (/ c b_2))

simplify2.0s

Counts
36 → 36
Iterations
IterNodes
done5000
32451
2573
1179
069

prune108.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.7b

regimes385.0ms

Accuracy

88.8% (3.1b remaining)

Error of 8.4b against oracle of 5.3b and baseline of 32.7b

bsearch317.0ms

Steps
ItersRangePoint
10
1.0955696400612189e+91
1.0202913897586463e+104
2.026128983134594e+103
10
-3.7853197546515783e-110
-6.759455321393433e-120
-6.3209183644448e-115
9
-2.0190258033009663e+27
-4.429449841721669e+19
-3.234164035284793e+22

simplify7.0ms

Iterations
IterNodes
done43
243
142
035

end0.0ms

sample3.9s

Algorithm
intervals
Results
937.0ms1081×body2560valid
855.0ms5881×body80valid
802.0ms2917×body80nan
525.0ms892×body1280valid
217.0ms437×body640valid
125.0ms230×body320valid
93.0ms113×body5120valid
26.0ms127×body160valid