Details

Time bar (total: 50.0s)

sample172.0ms

Algorithm
intervals
Results
52.0ms597×pre80true
40.0ms341×body80nan
34.0ms145×body160valid
13.0ms111×body80valid

simplify143.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
143.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize38.0ms

Local error

Found 4 expressions with local error:

29.4b
(- (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))

rewrite184.0ms

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
92.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
52.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.0ms
(* (* 3 a) c)
14.0ms
(- (* b b) (* (* 3 a) c))

series312.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
110.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
48.0ms
(- (* b b) (* (* 3 a) c))
21.0ms
(* (* 3 a) c)

simplify5.5s

Counts
50 → 91
Calls
50 calls:
Slowest
663.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
432.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
413.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
393.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
298.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.6b

localize12.0ms

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

prune83.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.6b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

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))
12.0ms
(* -3/2 (/ (* a c) b))
8.0ms
(/ (* a c) b)

series124.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
46.0ms
(* -3/2 (/ (* a c) b))
42.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
36.0ms
(/ (* a c) b)

simplify12.9s

Counts
58 → 90
Calls
58 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)))
1.3s
(/ (* (* (* -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 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
844.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune823.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 9.5b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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)
12.0ms
(* -3/2 (/ (* a c) b))
11.0ms
(/ (* a c) b)

series141.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(* -3/2 (/ (* a c) b))
38.0ms
(/ (/ (* -3/2 (/ (* a c) b)) 3) a)
29.0ms
(/ (* -3/2 (/ (* a c) b)) 3)
24.0ms
(/ (* a c) b)

simplify20.5s

Counts
120 → 142
Calls
120 calls:
Slowest
903.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* 3 3) 3)) (* (* a a) a))
826.0ms
(- (- (+ (log -3/2) (- (+ (log a) (log c)) (log b))) (log 3)) (log a))
633.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* 3 3) 3))
613.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* 3 3) 3)) (* (* a a) a))
558.0ms
(/ (/ (/ (* a c) b) 3) a)

prune1.2s

Pruning

37 alts after pruning (36 fresh and 1 done)

Merged error: 9.4b

regimes1.3s

Accuracy

47.9% (7.2b remaining)

Error of 16.2b against oracle of 8.9b and baseline of 22.8b

bsearch14.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.7s16516×pre80true
1.2s4428×body160valid
1.0s8516×body80nan
836.0ms3572×body80valid