Details

Time bar (total: 47.0s)

sample179.0ms

Algorithm
intervals
Results
46.0ms141×body160valid
39.0ms252×body80nan
37.0ms508×pre80true
29.0ms115×body80valid

simplify176.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
175.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize39.0ms

Local error

Found 4 expressions with local error:

29.5b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(- (* b b) (* (* c a) 4))
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
68.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
41.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
20.0ms
(- (* b b) (* (* c a) 4))
10.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
102.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
85.0ms
(sqrt (- (* b b) (* (* c a) 4)))
51.0ms
(- (* b b) (* (* c a) 4))

simplify5.4s

Counts
49 → 88
Calls
49 calls:
Slowest
591.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
462.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
325.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
274.0ms
(- b (* 2 (/ (* a c) b)))
265.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune1.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.7b

localize5.0ms

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

prune115.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.7b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
2×pow1 clear-num frac-2neg insert-posit16 div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
Slowest
39.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series47.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
26.0ms
(/ (* a c) b)
21.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.9s

Counts
37 → 59
Calls
37 calls:
Slowest
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
957.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune611.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 8.7b

localize34.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))
0.3b
(/ (* a c) b)

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
125×add-exp-log
69×prod-exp
61×add-cbrt-cube
32×div-exp
29×cbrt-unprod
16×cbrt-undiv
8×rec-exp 1-exp
7×pow1 associate-*r*
6×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* pow-prod-down associate-*r/
2×insert-posit16 div-inv add-log-exp
1×frac-times clear-num frac-2neg associate-*l* associate-*l/ un-div-inv *-commutative associate-/l*
Counts
2 → 85
Calls
2 calls:
Slowest
98.0ms
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))
9.0ms
(/ (* a c) b)

series67.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
35.0ms
(/ (* a c) b)
31.0ms
(* (* -2 (/ (* a c) b)) (/ 1 (* 2 a)))

simplify19.8s

Counts
72 → 91
Calls
72 calls:
Slowest
1.1s
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* a a) a))))
990.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 a) (* 2 a)) (* 2 a))))
818.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (/ (* (* 1 1) 1) (* (* (* 2 2) 2) (* (* a a) a))))
765.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (/ 1 (* 2 a)) (/ 1 (* 2 a))) (/ 1 (* 2 a))))
736.0ms
(* (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (/ 1 (* 2 a)) (/ 1 (* 2 a))) (/ 1 (* 2 a))))

prune706.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 8.6b

regimes815.0ms

Accuracy

45.4% (7.6b remaining)

Error of 16.6b against oracle of 9.1b and baseline of 22.9b

bsearch17.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.7s8693×body80nan
1.5s4405×body160valid
1.1s16693×pre80true
534.0ms3595×body80valid