Details

Time bar (total: 40.9s)

sample182.0ms

Algorithm
intervals
Results
45.0ms148×body160valid
44.0ms512×pre80true
37.0ms256×body80nan
21.0ms48×body320valid
9.0ms60×body80valid

simplify163.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
162.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize46.0ms

Local error

Found 4 expressions with local error:

37.2b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(- (* b b) (* (* c a) 4))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite190.0ms

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
92.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
68.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(- (* b b) (* (* c a) 4))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
140.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
103.0ms
(sqrt (- (* b b) (* (* c a) 4)))
63.0ms
(- (* b b) (* (* c a) 4))

simplify5.4s

Counts
49 → 88
Calls
49 calls:
Slowest
595.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
400.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
397.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
280.0ms
(- b (* 2 (/ (* a c) b)))
279.0ms
(/ (* (* (- (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)))

prune979.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.1b

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

prune69.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.1b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite62.0ms

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
43.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series71.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
38.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
33.0ms
(/ (* a c) b)

simplify11.3s

Counts
37 → 59
Calls
37 calls:
Slowest
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)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
922.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune543.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
44×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
39×add-cbrt-cube add-exp-log
17×cbrt-undiv div-exp
14×associate-/r*
10×prod-exp cbrt-unprod
6×div-inv
4×associate-/l*
2×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×associate-*r/ associate-/r/ associate-/l/
Counts
2 → 102
Calls
2 calls:
Slowest
15.0ms
(/ (* -2 (/ a (/ b c))) (* 2 a))
6.0ms
(/ a (/ b c))

series69.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
42.0ms
(/ a (/ b c))
27.0ms
(/ (* -2 (/ a (/ b c))) (* 2 a))

simplify13.8s

Counts
122 → 108
Calls
122 calls:
Slowest
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* a a) a) (/ (* (* b b) b) (* (* c c) c)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.1s
(/ (* (* (* -2 (/ a (/ b c))) (* -2 (/ a (/ b c)))) (* -2 (/ a (/ b c)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.0s
(/ (* (* (* -2 -2) -2) (/ (* (* a a) a) (/ (* (* b b) b) (* (* c c) c)))) (* (* (* 2 2) 2) (* (* a a) a)))
933.0ms
(/ (* (* (* -2 -2) -2) (* (* (/ a (/ b c)) (/ a (/ b c))) (/ a (/ b c)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
831.0ms
(/ (* (* (* -2 -2) -2) (/ (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))) (* (* (* 2 2) 2) (* (* a a) a)))

prune919.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 5.1b

regimes688.0ms

Accuracy

9.3% (6.2b remaining)

Error of 11.3b against oracle of 5.1b and baseline of 11.9b

bsearch112.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.6s8371×body80nan
1.5s4872×body160valid
976.0ms1359×body320valid
935.0ms16371×pre80true
224.0ms1769×body80valid