Details

Time bar (total: 40.2s)

sample164.0ms

Algorithm
intervals
Results
40.0ms138×body160valid
40.0ms253×body80nan
36.0ms509×pre80true
18.0ms118×body80valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize34.0ms

Local error

Found 4 expressions with local error:

28.3b
(- (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))

rewrite203.0ms

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
114.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
45.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.0ms
(* (* 3 a) c)
15.0ms
(- (* b b) (* (* 3 a) c))

series360.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
124.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
62.0ms
(- (* b b) (* (* 3 a) c))
34.0ms
(* (* 3 a) c)

simplify5.3s

Counts
50 → 91
Calls
50 calls:
Slowest
532.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
459.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
458.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
361.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
338.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.9b

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

prune53.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.9b

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))
0.2b
(/ (* a c) b)

rewrite81.0ms

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
33.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
24.0ms
(* -3/2 (/ (* a c) b))
22.0ms
(/ (* a c) b)

series97.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
43.0ms
(* -3/2 (/ (* a c) b))
30.0ms
(/ (* a c) b)
25.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

simplify13.5s

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)))
1.3s
(/ (* (* (* -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 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
831.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune966.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 8.8b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube add-exp-log
20×associate-*r*
17×add-sqr-sqrt
15×sqrt-prod
14×prod-exp cbrt-unprod
13×*-un-lft-identity add-cube-cbrt
11×pow1
10×times-frac
9×sqrt-div
8×cbrt-undiv div-exp
7×associate-*r/
4×associate-/r* associate-*l* pow-prod-down insert-posit16 div-inv add-log-exp
3×associate-/l/
2×frac-times clear-num frac-2neg associate-*l/ *-commutative associate-/l* unswap-sqr
Counts
4 → 108
Calls
4 calls:
Slowest
82.0ms
(/ (* (* -3/2 (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))) (* 3 a))
53.0ms
(* (* -3/2 (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b)))
14.0ms
(* -3/2 (sqrt (/ (* a c) b)))
8.0ms
(/ (* a c) b)

series264.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(* (* -3/2 (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b)))
85.0ms
(* -3/2 (sqrt (/ (* a c) b)))
59.0ms
(/ (* (* -3/2 (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b))) (* 3 a))
22.0ms
(/ (* a c) b)

simplify10.6s

Counts
82 → 120
Calls
82 calls:
Slowest
1.4s
(/ (* (* (* (* -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)))
1.2s
(/ (* (* (* (* -3/2 (sqrt (/ (* a c) b))) (* -3/2 (sqrt (/ (* a c) b)))) (* -3/2 (sqrt (/ (* a c) b)))) (* (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b))) (sqrt (/ (* a c) b)))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
994.0ms
(/ (* (* (* (* -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)))
851.0ms
(/ (* (* (* (* -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)))
810.0ms
(/ (* (* (* (* -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)))

prune1.2s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 8.7b

regimes1.1s

Accuracy

47.9% (7.1b remaining)

Error of 16.1b against oracle of 9.0b and baseline of 22.6b

bsearch53.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.6s8530×body80nan
1.2s4480×body160valid
1.1s16530×pre80true
600.0ms3520×body80valid