Details

Time bar (total: 50.1s)

sample144.0ms

Algorithm
intervals
Results
37.0ms162×body160valid
36.0ms237×body80nan
28.0ms493×pre80true
12.0ms35×body320valid
7.0ms59×body80valid

simplify133.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
133.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize47.0ms

Local error

Found 4 expressions with local error:

39.2b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.3b
(* (* 3 a) c)
0.1b
(- (* b b) (* (* 3 a) c))

rewrite122.0ms

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))
33.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
14.0ms
(* (* 3 a) c)
8.0ms
(- (* b b) (* (* 3 a) c))

series326.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
106.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
51.0ms
(- (* b b) (* (* 3 a) c))
34.0ms
(* (* 3 a) c)

simplify5.5s

Counts
50 → 91
Calls
50 calls:
Slowest
631.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
415.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
374.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
373.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
332.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.2b

localize7.0ms

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

prune78.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 6.2b

localize15.0ms

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)

rewrite43.0ms

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))
16.0ms
(* -3/2 (/ (* a c) b))
9.0ms
(/ (* a c) b)

series79.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
31.0ms
(* -3/2 (/ (* a c) b))
25.0ms
(/ (* a c) b)
23.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

simplify12.9s

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 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) 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)))
1.0s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))

prune906.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 6.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
52×add-cbrt-cube add-exp-log
42×times-frac
29×add-sqr-sqrt
27×*-un-lft-identity add-cube-cbrt
21×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-/r* associate-/l*
8×div-inv
7×associate-*r*
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l*
2×associate-*r/ associate-/l/
1×pow-prod-down *-commutative unswap-sqr
Counts
4 → 130
Calls
4 calls:
Slowest
23.0ms
(/ (/ (* -3/2 (/ (* a c) b)) 3) a)
16.0ms
(/ (* -3/2 (/ (* a c) b)) 3)
15.0ms
(* -3/2 (/ (* a c) b))
9.0ms
(/ (* a c) b)

series135.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
47.0ms
(* -3/2 (/ (* a c) b))
33.0ms
(/ (* -3/2 (/ (* a c) b)) 3)
33.0ms
(/ (/ (* -3/2 (/ (* a c) b)) 3) a)
22.0ms
(/ (* a c) b)

simplify20.5s

Counts
120 → 142
Calls
120 calls:
Slowest
900.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* 3 3) 3)) (* (* a a) a))
851.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* 3 3) 3)) (* (* a a) a))
552.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* 3 3) 3))
525.0ms
(/ (/ (/ (* a c) b) 3) a)
477.0ms
(- (- (+ (log -3/2) (- (+ (log a) (log c)) (log b))) (log 3)) (log a))

prune1.2s

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 6.1b

regimes962.0ms

Accuracy

11.5% (6.2b remaining)

Error of 11.2b against oracle of 5.0b and baseline of 12.0b

bsearch87.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.7s4797×body160valid
1.6s16145×pre80true
1.0s8145×body80nan
582.0ms1386×body320valid
282.0ms1817×body80valid