Details

Time bar (total: 54.1s)

sample717.0ms

Algorithm
intervals
Results
196.0ms84×body160valid
136.0ms125×body320valid
80.0ms259×body80nan
43.0ms515×pre80true
9.0ms12×body640valid
6.0ms35×body80valid

simplify196.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
195.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.7b

localize55.0ms

Local error

Found 4 expressions with local error:

25.2b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(- (* b b) (* (* c a) 4))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite187.0ms

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
101.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
60.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))
8.0ms
(- (* b b) (* (* c a) 4))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
129.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
106.0ms
(sqrt (- (* b b) (* (* c a) 4)))
57.0ms
(- (* b b) (* (* c a) 4))

simplify5.2s

Counts
49 → 88
Calls
49 calls:
Slowest
603.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
306.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
291.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
290.0ms
(/ (* (* (- (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)))
273.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

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

prune48.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

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
30.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
9.0ms
(/ (* a c) b)

series77.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
41.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
36.0ms
(/ (* 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 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 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)))
924.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune851.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 3.3b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
92×times-frac
58×add-cbrt-cube add-exp-log
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
29×cbrt-undiv div-exp
22×associate-/r*
13×div-inv
11×prod-exp cbrt-unprod
6×associate-/r/
5×associate-/l*
3×pow1 clear-num frac-2neg insert-posit16 add-log-exp
Counts
3 → 138
Calls
3 calls:
Slowest
23.0ms
(/ (* 2 a) (/ (* a c) b))
19.0ms
(/ -2 (/ (* 2 a) (/ (* a c) b)))
17.0ms
(/ (* a c) b)

series91.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
34.0ms
(/ (* a c) b)
31.0ms
(/ -2 (/ (* 2 a) (/ (* a c) b)))
26.0ms
(/ (* 2 a) (/ (* a c) b))

simplify25.7s

Counts
154 → 147
Calls
154 calls:
Slowest
1.2s
(/ (* (* -2 -2) -2) (/ (* (* (* 2 a) (* 2 a)) (* 2 a)) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))))
1.0s
(/ (* (* -2 -2) -2) (/ (* (* (* 2 2) 2) (* (* a a) a)) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))))
984.0ms
(/ (* (* -2 -2) -2) (/ (* (* (* 2 a) (* 2 a)) (* 2 a)) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))))
967.0ms
(/ -2 (/ a (/ (* a c) b)))
880.0ms
(/ (cbrt -2) (/ a (/ (* a c) b)))

prune1.0s

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 3.2b

regimes485.0ms

Accuracy

0% (3.6b remaining)

Error of 6.4b against oracle of 2.8b and baseline of 6.4b

bsearch2.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
1.7s3611×body320valid
1.4s2901×body160valid
1.3s8282×body80nan
1.1s16282×pre80true
337.0ms537×body640valid
129.0ms951×body80valid