Details

Time bar (total: 57.3s)

sample112.0ms

Algorithm
intervals
Results
30.0ms237×body80nan
26.0ms167×body160valid
21.0ms493×pre80true
9.0ms38×body320valid
4.0ms51×body80valid

simplify121.0ms

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: 44.7b

localize23.0ms

Local error

Found 4 expressions with local error:

40.5b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(* (* 3 a) c)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.1b
(- (* b b) (* (* 3 a) c))

rewrite447.0ms

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
390.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
32.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
17.0ms
(* (* 3 a) c)
7.0ms
(- (* b b) (* (* 3 a) c))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
100.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
57.0ms
(- (* b b) (* (* 3 a) c))
23.0ms
(* (* 3 a) c)

simplify5.2s

Counts
50 → 91
Calls
50 calls:
Slowest
631.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
429.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
407.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
342.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
282.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.6b

localize6.0ms

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

prune81.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.6b

localize22.0ms

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)

rewrite41.0ms

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
17.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
15.0ms
(* -3/2 (/ (* a c) b))
8.0ms
(/ (* a c) b)

series75.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
32.0ms
(* -3/2 (/ (* a c) b))
22.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
21.0ms
(/ (* a c) b)

simplify12.7s

Counts
58 → 90
Calls
58 calls:
Slowest
1.4s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.2s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a 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)))
1.2s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
829.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune864.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* -3/2 (/ 1 (/ b (* a c)))) (* 3 a))
0.3b
(/ 1 (/ b (* a c)))
0.3b
(* -3/2 (/ 1 (/ b (* a c))))
0.3b
(/ b (* a c))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
161×add-exp-log
77×add-cbrt-cube
72×div-exp
69×times-frac
54×prod-exp
44×add-sqr-sqrt
38×*-un-lft-identity
37×add-cube-cbrt
32×cbrt-undiv
26×associate-*r*
22×cbrt-unprod
12×rec-exp 1-exp
11×div-inv
9×associate-/r*
7×pow1 associate-/l*
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l* unswap-sqr
2×associate-*r/ associate-/r/ un-div-inv associate-/l/
1×pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 185
Calls
4 calls:
Slowest
48.0ms
(/ (* -3/2 (/ 1 (/ b (* a c)))) (* 3 a))
32.0ms
(* -3/2 (/ 1 (/ b (* a c))))
21.0ms
(/ 1 (/ b (* a c)))
6.0ms
(/ b (* a c))

series127.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
41.0ms
(* -3/2 (/ 1 (/ b (* a c))))
33.0ms
(/ b (* a c))
27.0ms
(/ (* -3/2 (/ 1 (/ b (* a c)))) (* 3 a))
27.0ms
(/ 1 (/ b (* a c)))

simplify27.5s

Counts
172 → 197
Calls
172 calls:
Slowest
1.2s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* 1 1) 1) (/ (* (* b b) b) (* (* (* a a) a) (* (* c c) c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* 1 1) 1) (/ (* (* b b) b) (* (* (* a a) a) (* (* c c) c))))) (* (* (* 3 3) 3) (* (* a a) a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (/ 1 (/ b (* a c))) (/ 1 (/ b (* a c)))) (/ 1 (/ b (* a c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (/ 1 (/ b (* a c))) (/ 1 (/ b (* a c)))) (/ 1 (/ b (* a c))))) (* (* (* 3 3) 3) (* (* a a) a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* 1 1) 1) (* (* (/ b (* a c)) (/ b (* a c))) (/ b (* a c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune1.8s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 4.5b

regimes878.0ms

Accuracy

0% (6.9b remaining)

Error of 12.0b against oracle of 5.1b and baseline of 12.0b

bsearch1.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
1.6s8317×body80nan
1.3s4885×body160valid
1.1s16317×pre80true
582.0ms1340×body320valid
213.0ms1775×body80valid