Details

Time bar (total: 42.7s)

sample152.0ms

Algorithm
intervals
Results
37.0ms164×body160valid
27.0ms480×pre80true
25.0ms224×body80nan
9.0ms31×body320valid
7.0ms61×body80valid

simplify477.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
477.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize39.0ms

Local error

Found 4 expressions with local error:

38.1b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.3b
(* (* 3 a) c)
0.2b
(- (* b b) (* (* 3 a) c))

rewrite238.0ms

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
122.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
73.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
26.0ms
(* (* 3 a) c)
15.0ms
(- (* b b) (* (* 3 a) c))

series359.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
131.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
65.0ms
(- (* b b) (* (* 3 a) c))
21.0ms
(* (* 3 a) c)

simplify5.6s

Counts
50 → 91
Calls
50 calls:
Slowest
589.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
528.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
480.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
382.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
290.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.4b

localize13.0ms

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: 6.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
0.3b
(* -3/2 (/ (* a c) b))
0.2b
(/ (* a c) b)

rewrite65.0ms

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
25.0ms
(* -3/2 (/ (* a c) b))
22.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
17.0ms
(/ (* a c) b)

series104.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
51.0ms
(* -3/2 (/ (* a c) b))
28.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
25.0ms
(/ (* a c) b)

simplify12.4s

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 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)))
983.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
836.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune885.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 6.3b

localize34.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (/ (* -3/2 (* a c)) b) (* 3 a))
0.3b
(* -3/2 (* a c))
0.3b
(/ (* -3/2 (* a c)) b)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
17×cbrt-undiv div-exp
16×times-frac prod-exp cbrt-unprod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 associate-/l*
4×associate-/r* div-inv
3×associate-*l* pow-prod-down insert-posit16 add-log-exp
2×clear-num frac-2neg
1×associate-*r* *-commutative associate-/l/
Counts
3 → 86
Calls
3 calls:
Slowest
35.0ms
(/ (/ (* -3/2 (* a c)) b) (* 3 a))
34.0ms
(/ (* -3/2 (* a c)) b)
27.0ms
(* -3/2 (* a c))

series97.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
44.0ms
(/ (* -3/2 (* a c)) b)
29.0ms
(/ (/ (* -3/2 (* a c)) b) (* 3 a))
23.0ms
(* -3/2 (* a c))

simplify14.1s

Counts
68 → 95
Calls
68 calls:
Slowest
1.5s
(/ (/ (* (* (* -3/2 -3/2) -3/2) (* (* (* a a) a) (* (* c c) c))) (* (* b b) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.0s
(/ (/ (* (* (* -3/2 -3/2) -3/2) (* (* (* a a) a) (* (* c c) c))) (* (* b b) b)) (* (* (* 3 3) 3) (* (* a a) a)))
944.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (* (* (* a c) (* a c)) (* a c))) (* (* b b) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
942.0ms
(/ (/ (* (* (* -3/2 (* a c)) (* -3/2 (* a c))) (* -3/2 (* a c))) (* (* b b) b)) (* (* (* 3 3) 3) (* (* a a) a)))
899.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (* (* (* a c) (* a c)) (* a c))) (* (* b b) b)) (* (* (* 3 3) 3) (* (* a a) a)))

prune787.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 6.2b

regimes783.0ms

Accuracy

0% (6.9b remaining)

Error of 12.1b against oracle of 5.2b and baseline of 12.1b

bsearch1.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.8s4862×body160valid
1.2s16105×pre80true
1.0s8105×body80nan
531.0ms1364×body320valid
236.0ms1774×body80valid