Details

Time bar (total: 1.0m)

sample160.0ms

Algorithm
intervals
Results
37.0ms107×body80valid
37.0ms315×body80nan
36.0ms149×body160valid
32.0ms571×pre80true

simplify121.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
121.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize42.0ms

Local error

Found 4 expressions with local error:

29.9b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite168.0ms

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
83.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
67.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
9.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series474.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
140.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
115.0ms
(sqrt (- (* b b) (* (* c a) 4)))
60.0ms
(- (* b b) (* (* c a) 4))

simplify5.4s

Counts
49 → 88
Calls
49 calls:
Slowest
543.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
379.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
361.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
293.0ms
(/ (* (* (- (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)))
256.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 2) 2) (* (* a a) a)))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

localize11.0ms

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

prune76.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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
28.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series69.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
32.0ms
(/ (* a c) b)

simplify11.8s

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)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
929.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune619.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 8.9b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
120×add-exp-log
70×add-cbrt-cube
64×prod-exp
34×cbrt-unprod
32×div-exp
18×cbrt-undiv
13×associate-*r*
10×times-frac
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×rec-exp 1-exp
4×associate-*r/
3×pow-prod-down
2×un-div-inv insert-posit16 div-inv add-log-exp associate-/l/
1×clear-num associate-/r* frac-2neg associate-*l* *-commutative associate-/l*
Counts
2 → 87
Calls
2 calls:
Slowest
76.0ms
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))
38.0ms
(* (* a c) (/ 1 b))

series47.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
25.0ms
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))
22.0ms
(* (* a c) (/ 1 b))

simplify33.5s

Counts
69 → 93
Calls
69 calls:
Slowest
2.3s
(/ (* (* (* -2 -2) -2) (* (* (* (* a c) (* a c)) (* a c)) (/ (* (* 1 1) 1) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
2.2s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (/ (* (* 1 1) 1) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
2.2s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.9s
(/ (* (* (* -2 -2) -2) (* (* (* (* a c) (* a c)) (* a c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.9s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 2) 2) (* (* a a) a)))

prune765.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 8.9b

regimes621.0ms

Accuracy

44.3% (7.5b remaining)

Error of 16.5b against oracle of 9.0b and baseline of 22.4b

bsearch8.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.7s4518×body160valid
1.5s8848×body80nan
1.1s16848×pre80true
469.0ms3481×body80valid
0.0ms1×body320valid