Details

Time bar (total: 43.4s)

sample199.0ms

Algorithm
intervals
Results
68.0ms159×body160valid
35.0ms484×pre80true
34.0ms228×body80nan
21.0ms47×body320valid
7.0ms50×body80valid

simplify129.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
129.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.2b

localize44.0ms

Local error

Found 4 expressions with local error:

40.5b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.2b
(* (* 3 a) c)
0.1b
(- (* b b) (* (* 3 a) c))

rewrite186.0ms

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
84.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
61.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
26.0ms
(* (* 3 a) c)
14.0ms
(- (* b b) (* (* 3 a) c))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
112.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
51.0ms
(- (* b b) (* (* 3 a) c))
22.0ms
(* (* 3 a) c)

simplify5.6s

Counts
50 → 91
Calls
50 calls:
Slowest
676.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
510.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
479.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
419.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
325.0ms
(/ (* (* (- (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

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

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

prune94.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.2b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

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
34.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
32.0ms
(* -3/2 (/ (* a c) b))
16.0ms
(/ (* a c) b)

series99.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
43.0ms
(* -3/2 (/ (* a c) b))
33.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
24.0ms
(/ (* a c) b)

simplify13.0s

Counts
58 → 90
Calls
58 calls:
Slowest
1.5s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
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 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)))
824.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune819.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 4.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
0.3b
(/ (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 3 a))
0.3b
(* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))
0.3b
(/ (* a c) b)

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube add-exp-log
34×sqrt-prod
32×add-sqr-sqrt
24×pow1
19×*-un-lft-identity add-cube-cbrt
16×times-frac
14×prod-exp cbrt-unprod
13×associate-*l*
12×sqrt-div swap-sqr
11×associate-*r*
9×associate-*r/
8×cbrt-undiv sqrt-pow1 pow1/2 div-exp
6×pow-prod-down div-inv
5×pow-prod-up unswap-sqr
4×associate-/r* insert-posit16 add-log-exp
3×frac-times associate-*l/ pow-sqr associate-/l/
2×clear-num frac-2neg *-commutative associate-/l*
1×pow2 rem-square-sqrt pow-plus sqrt-unprod
Counts
4 → 139
Calls
4 calls:
Slowest
69.0ms
(* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))
69.0ms
(/ (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 3 a))
33.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
8.0ms
(/ (* a c) b)

series263.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))
79.0ms
(* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))
74.0ms
(/ (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* 3 a))
22.0ms
(/ (* a c) b)

simplify12.6s

Counts
135 → 151
Calls
135 calls:
Slowest
1.2s
(/ (* (* (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.0s
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.0s
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))) (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.0s
(/ (* (* (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* -3/2 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 3 3) 3) (* (* a a) a)))
831.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))))) (* (* (* 3 3) 3) (* (* a a) a)))

prune1.6s

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 4.1b

regimes999.0ms

Accuracy

14.7% (5.6b remaining)

Error of 10.6b against oracle of 5.1b and baseline of 11.6b

bsearch114.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
1.5s8293×body80nan
1.3s4903×body160valid
1.1s16293×pre80true
921.0ms1391×body320valid
285.0ms1706×body80valid