Details

Time bar (total: 1.7m)

sample183.0ms

Algorithm
intervals
Results
45.0ms116×body320valid
44.0ms515×pre80true
31.0ms259×body80nan
26.0ms102×body160valid
5.0ms10×body640valid
3.0ms28×body80valid

simplify149.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
149.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize38.0ms

Local error

Found 4 expressions with local error:

28.3b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(* (* 3 a) c)
0.2b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.1b
(- (* b b) (* (* 3 a) c))

rewrite213.0ms

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
113.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
62.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
30.0ms
(* (* 3 a) c)
7.0ms
(- (* b b) (* (* 3 a) c))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
119.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
64.0ms
(- (* b b) (* (* 3 a) c))
21.0ms
(* (* 3 a) c)

simplify5.7s

Counts
50 → 91
Calls
50 calls:
Slowest
835.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
640.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
443.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
404.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
291.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.8b

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

prune49.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.8b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

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
29.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
19.0ms
(* -3/2 (/ (* a c) b))
8.0ms
(/ (* a c) b)

series113.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
49.0ms
(* -3/2 (/ (* a c) b))
37.0ms
(/ (* a c) b)
27.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

simplify13.1s

Counts
58 → 90
Calls
58 calls:
Slowest
1.4s
(/ (* (* (* -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 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)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
902.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune898.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 2.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ -27/8 (/ (* (* (* a (* a a)) 27) (* (/ b c) (* (/ b c) (/ b c)))) (* a (* a a)))))
0.6b
(* (/ b c) (/ b c))
0.4b
(* (* (* a (* a a)) 27) (* (/ b c) (* (/ b c) (/ b c))))
0.3b
(* (/ b c) (* (/ b c) (/ b c)))

rewrite441.0ms

Algorithm
rewrite-expression-head
Rules
335×add-cbrt-cube add-exp-log
204×prod-exp cbrt-unprod
79×pow1
69×cbrt-undiv div-exp
68×times-frac
63×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
46×pow-prod-down
27×associate-*l*
20×cbrt-prod
18×associate-*r/
15×associate-*r*
13×swap-sqr
11×frac-times
9×div-inv
7×associate-*l/
6×pow-prod-up unswap-sqr
4×insert-posit16 add-log-exp
3×*-commutative
2×pow2 pow-plus pow-sqr
1×cbrt-div pow1/3 cube-unmult associate-/r/
Counts
4 → 275
Calls
4 calls:
Slowest
204.0ms
(* (* (* a (* a a)) 27) (* (/ b c) (* (/ b c) (/ b c))))
190.0ms
(cbrt (/ -27/8 (/ (* (* (* a (* a a)) 27) (* (/ b c) (* (/ b c) (/ b c)))) (* a (* a a)))))
25.0ms
(* (/ b c) (* (/ b c) (/ b c)))
14.0ms
(* (/ b c) (/ b c))

series371.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(* (* (* a (* a a)) 27) (* (/ b c) (* (/ b c) (/ b c))))
88.0ms
(cbrt (/ -27/8 (/ (* (* (* a (* a a)) 27) (* (/ b c) (* (/ b c) (/ b c)))) (* a (* a a)))))
68.0ms
(* (/ b c) (* (/ b c) (/ b c)))
49.0ms
(* (/ b c) (/ b c))

simplify1.1m

Counts
268 → 287
Calls
268 calls:
Slowest
1.4s
(* (* (* (* (* a (* a a)) 27) (* (* a (* a a)) 27)) (* (* a (* a a)) 27)) (* (/ (* (* b b) b) (* (* c c) c)) (* (* (* (/ b c) (/ b c)) (/ b c)) (/ (* (* b b) b) (* (* c c) c)))))
1.2s
(* (* (* (* (* a a) a) (* (* (* a a) a) (* (* a a) a))) (* (* 27 27) 27)) (* (* (* (/ b c) (/ b c)) (/ b c)) (* (/ (* (* b b) b) (* (* c c) c)) (/ (* (* b b) b) (* (* c c) c)))))
1.1s
(* (* (* (* (* a (* a a)) 27) (* (* a (* a a)) 27)) (* (* a (* a a)) 27)) (* (/ (* (* b b) b) (* (* c c) c)) (* (/ (* (* b b) b) (* (* c c) c)) (* (* (/ b c) (/ b c)) (/ b c)))))
1.0s
(* (* (* (* (* a a) a) (* (* (* a a) a) (* (* a a) a))) (* (* 27 27) 27)) (* (/ (* (* b b) b) (* (* c c) c)) (* (/ (* (* b b) b) (* (* c c) c)) (* (* (/ b c) (/ b c)) (/ b c)))))
1.0s
(* (* (* (* (* a a) a) (* (* (* a a) a) (* (* a a) a))) (* (* 27 27) 27)) (* (/ (* (* b b) b) (* (* c c) c)) (* (/ (* (* b b) b) (* (* c c) c)) (/ (* (* b b) b) (* (* c c) c)))))

prune3.5s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 2.8b

regimes795.0ms

Accuracy

0% (3.5b remaining)

Error of 6.2b against oracle of 2.7b and baseline of 6.2b

bsearch2.0ms

end0.0ms

sample6.4s

Algorithm
intervals
Results
1.5s3626×body320valid
1.2s16289×pre80true
1.2s3001×body160valid
1.1s8289×body80nan
530.0ms904×body80valid
220.0ms469×body640valid