Details

Time bar (total: 24.7s)

sample135.0ms

Algorithm
intervals
Results
26.0ms182×body80valid
24.0ms33×body1280valid
22.0ms25×body2560valid
21.0ms77×body80nan
10.0ms17×body640valid
5.0ms12×body320valid
4.0ms4×body5120valid
1.0ms5×body160valid

simplify43.0ms

Counts
1 → 1
Iterations
IterNodes
544
444
341
232
118
010

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (* b_2 b_2) (* a c))
1.6b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite129.0ms

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:
68.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms
(- (* b_2 b_2) (* a c))
29.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
53.0ms
(- (* b_2 b_2) (* a c))
102.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts
107 → 107
Iterations
IterNodes
32584
21011
1386
0162

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize38.0ms

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)
8.8b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite208.0ms

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-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 → 188
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
69.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series544.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b_2 b_2) (* a c))
162.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
252.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify998.0ms

Counts
200 → 200
Iterations
IterNodes
22201
1732
0306

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize52.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
4.4b
(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
4.5b
(* (/ a (cbrt a)) (/ c (cbrt a)))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
300×times-frac
243×add-sqr-sqrt
176×*-un-lft-identity
170×associate-*r*
140×add-cube-cbrt
131×add-exp-log
96×cbrt-prod
59×add-cbrt-cube
54×div-exp
49×prod-exp
36×difference-of-squares
31×cbrt-undiv cbrt-unprod
23×associate-*l*
21×sqrt-prod
18×distribute-lft-out--
12×pow1 associate-/r/
9×div-inv unswap-sqr
8×flip3-- flip--
6×frac-times associate-*l/ add-log-exp
5×rec-exp 1-exp
4×pow-prod-down associate-*r/ insert-posit16
2×sqrt-div *-commutative
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 310
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
135.0ms
(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
20.0ms
(* (/ a (cbrt a)) (/ c (cbrt a)))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series579.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b_2 b_2) (* a c))
309.0ms
(* (* (/ a (cbrt a)) (/ c (cbrt a))) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
139.0ms
(* (/ a (cbrt a)) (/ c (cbrt a)))
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts
322 → 322
Iterations
IterNodes
26382
11787
0529

prune4.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize60.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b
(- (* b_2 b_2) (* a c))
4.4b
(* (* (cbrt a) c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
22.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
191×add-sqr-sqrt
152×*-un-lft-identity
148×associate-*r*
114×add-cube-cbrt
72×cbrt-prod
39×add-exp-log
38×difference-of-squares
22×sqrt-prod
19×distribute-lft-out--
18×add-cbrt-cube
15×prod-exp
12×div-exp associate-/r/
10×pow1
9×flip3-- cbrt-unprod flip--
8×add-log-exp
7×div-inv
6×cbrt-undiv
4×insert-posit16
3×pow-prod-down
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-*r/ *-commutative
Counts
4 → 222
Calls
4 calls:
55.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(- (* b_2 b_2) (* a c))
162.0ms
(* (* (cbrt a) c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms
(- (* b_2 b_2) (* a c))
233.0ms
(* (* (cbrt a) c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts
234 → 234
Iterations
IterNodes
23500
11320
0400

prune2.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

regimes457.0ms

Accuracy

93.2% (1.7b remaining)

Error of 7.2b against oracle of 5.5b and baseline of 30.2b

bsearch276.0ms

Steps
ItersRangePoint
7
1.602087361235081e+82
9.448026055101687e+83
9.336288915836175e+83
7
-3.701119893670698e-252
-1.0592482103697749e-253
-5.587449545143923e-253
6
-2.694901367577156e+142
-2.6421566329593826e+141
-6.565090470125855e+141

simplify13.0ms

Iterations
IterNodes
243
143
036

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.4s958×body1280valid
804.0ms5859×body80valid
747.0ms1035×body2560valid
354.0ms2918×body80nan
244.0ms461×body640valid
93.0ms225×body320valid
82.0ms106×body5120valid
23.0ms113×body160valid