Details

Time bar (total: 53.8s)

sample151.0ms

Algorithm
intervals
Results
37.0ms238×body80nan
32.0ms142×body160valid
28.0ms494×pre80true
17.0ms49×body320valid
7.0ms65×body80valid

simplify120.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
120.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.4b

localize35.0ms

Local error

Found 4 expressions with local error:

37.8b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.2b
(* (* 3 a) c)
0.2b
(- (* b b) (* (* 3 a) c))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×add-cbrt-cube add-exp-log
13×*-un-lft-identity
9×pow1
8×add-log-exp
7×add-cube-cbrt
6×times-frac associate-/l* difference-of-squares
4×prod-exp cbrt-unprod insert-posit16
3×flip3-- associate-*r* pow-prod-down sqrt-prod flip-- distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×clear-num associate-/r* frac-2neg div-sub associate-*l* *-commutative div-inv
Counts
4 → 79
Calls
4 calls:
Slowest
67.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
45.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.0ms
(* (* 3 a) c)
14.0ms
(- (* b b) (* (* 3 a) c))

series375.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
116.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
75.0ms
(- (* b b) (* (* 3 a) c))
34.0ms
(* (* 3 a) c)

simplify5.7s

Counts
50 → 91
Calls
50 calls:
Slowest
533.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
488.0ms
(/ (exp (sqrt (- (* b b) (* (* 3 a) c)))) (exp b))
451.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
428.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
364.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune100.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
0.3b
(* -3/2 (/ (* a c) b))
0.2b
(/ (* a c) b)

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×times-frac associate-*r*
5×pow1
4×associate-/r*
3×associate-*l* insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r/ associate-/l*
1×pow-prod-down *-commutative unswap-sqr associate-/l/
Counts
3 → 81
Calls
3 calls:
Slowest
24.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
23.0ms
(* -3/2 (/ (* a c) b))
17.0ms
(/ (* a c) b)

series98.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
34.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
32.0ms
(/ (* a c) b)
32.0ms
(* -3/2 (/ (* a c) b))

simplify12.2s

Counts
58 → 90
Calls
58 calls:
Slowest
1.3s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.3s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
1.2s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
790.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune804.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 4.7b

localize34.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (* 3 a) (/ (* a c) b))
0.2b
(/ (* a c) b)
0.2b
(/ -3/2 (/ (* 3 a) (/ (* a c) b)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
92×times-frac
58×add-cbrt-cube add-exp-log
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
29×cbrt-undiv div-exp
22×associate-/r*
13×div-inv
11×prod-exp cbrt-unprod
6×associate-/r/
5×associate-/l*
3×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Counts
3 → 138
Calls
3 calls:
Slowest
20.0ms
(/ (* 3 a) (/ (* a c) b))
19.0ms
(/ -3/2 (/ (* 3 a) (/ (* a c) b)))
18.0ms
(/ (* a c) b)

series89.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
38.0ms
(/ (* 3 a) (/ (* a c) b))
31.0ms
(/ (* a c) b)
20.0ms
(/ -3/2 (/ (* 3 a) (/ (* a c) b)))

simplify24.5s

Counts
154 → 147
Calls
154 calls:
Slowest
1.1s
(/ (* (* -3/2 -3/2) -3/2) (/ (* (* (* 3 a) (* 3 a)) (* 3 a)) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))))
1.1s
(/ (* (* (* 3 a) (* 3 a)) (* 3 a)) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b)))
1.0s
(/ (* (* -3/2 -3/2) -3/2) (/ (* (* (* 3 a) (* 3 a)) (* 3 a)) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))))
1.0s
(/ (* (* -3/2 -3/2) -3/2) (/ (* (* (* 3 3) 3) (* (* a a) a)) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))))
938.0ms
(/ (* (* -3/2 -3/2) -3/2) (/ (* (* (* 3 3) 3) (* (* a a) a)) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))))

prune1.3s

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 4.7b

regimes861.0ms

Accuracy

14.8% (5.9b remaining)

Error of 10.9b against oracle of 5.0b and baseline of 11.9b

bsearch73.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
1.7s8296×body80nan
1.3s16296×pre80true
1.3s4789×body160valid
712.0ms1404×body320valid
249.0ms1807×body80valid