Details

Time bar (total: 42.1s)

sample148.0ms

Algorithm
intervals
Results
33.0ms63×body80valid
29.0ms145×body160valid
25.0ms497×pre80true
22.0ms241×body80nan
14.0ms48×body320valid

simplify122.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
122.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.4b

localize19.0ms

Local error

Found 4 expressions with local error:

37.8b
(- (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))

rewrite174.0ms

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
97.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
51.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
17.0ms
(* (* 3 a) c)
7.0ms
(- (* b b) (* (* 3 a) c))

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
101.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
76.0ms
(- (* b b) (* (* 3 a) c))
34.0ms
(* (* 3 a) c)

simplify5.4s

Counts
50 → 91
Calls
50 calls:
Slowest
601.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
457.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
400.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
389.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
312.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.1b

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

prune62.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.1b

localize25.0ms

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)

rewrite66.0ms

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
31.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
24.0ms
(* -3/2 (/ (* a c) b))
10.0ms
(/ (* a c) b)

series96.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
46.0ms
(* -3/2 (/ (* a c) b))
29.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
21.0ms
(/ (* a c) b)

simplify12.8s

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 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)))
1.2s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
852.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 3) 3) (* (* a a) a)))

prune808.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.1b

localize16.0ms

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))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
21×prod-exp cbrt-unprod
17×add-sqr-sqrt
14×associate-*r*
12×cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
11×times-frac
10×pow1
6×associate-*l*
5×associate-*r/
4×pow-prod-down
3×insert-posit16 add-log-exp
2×*-commutative div-inv unswap-sqr
1×clear-num associate-/r* frac-2neg associate-/l* associate-/l/
Counts
3 → 86
Calls
3 calls:
Slowest
43.0ms
(/ (* -3/2 (* a (/ c b))) (* 3 a))
25.0ms
(* -3/2 (* a (/ c b)))
8.0ms
(* a (/ c b))

series94.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
35.0ms
(* a (/ c b))
31.0ms
(* -3/2 (* a (/ c b)))
28.0ms
(/ (* -3/2 (* a (/ c b))) (* 3 a))

simplify13.6s

Counts
63 → 95
Calls
63 calls:
Slowest
1.7s
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (* a a) a) (/ (* (* c c) c) (* (* b b) b)))) (* (* (* 3 3) 3) (* (* a a) a)))
1.3s
(/ (* (* (* -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 a) a) (/ (* (* c c) c) (* (* b b) b)))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.1s
(/ (* (* (* -3/2 (* a (/ c b))) (* -3/2 (* a (/ c b)))) (* -3/2 (* a (/ c b)))) (* (* (* 3 3) 3) (* (* a a) a)))
1.0s
(/ (* (* (* -3/2 -3/2) -3/2) (* (* (* a a) a) (* (* (/ c b) (/ c b)) (/ c b)))) (* (* (* 3 3) 3) (* (* a a) a)))

prune825.0ms

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 5.1b

regimes801.0ms

Accuracy

3.9% (6.5b remaining)

Error of 11.7b against oracle of 5.2b and baseline of 12.0b

bsearch168.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.6s4814×body160valid
1.0s16131×pre80true
1.0s8131×body80nan
581.0ms1372×body320valid
354.0ms1814×body80valid