Details

Time bar (total: 51.2s)

sample157.0ms

Algorithm
intervals
Results
60.0ms248×body80nan
35.0ms140×body160valid
26.0ms504×pre80true
15.0ms116×body80valid

simplify169.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
169.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize44.0ms

Local error

Found 4 expressions with local error:

27.2b
(- (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)))

rewrite176.0ms

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
112.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
34.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(- (* b b) (* (* c a) 4))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
103.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
90.0ms
(sqrt (- (* b b) (* (* c a) 4)))
79.0ms
(- (* b b) (* (* c a) 4))

simplify5.2s

Counts
49 → 88
Calls
49 calls:
Slowest
520.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
368.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
347.0ms
(/ (* (* (- (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)))
287.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
250.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune885.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.5b

localize7.0ms

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

prune92.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

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
34.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
18.0ms
(/ (* a c) b)

series66.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
34.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
32.0ms
(/ (* a c) b)

simplify12.0s

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 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
873.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune576.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 9.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ b (* a c))
0.3b
(/ 1 (/ b (* a c)))
0.2b
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
128×add-exp-log
62×add-cbrt-cube
60×div-exp
41×prod-exp
37×times-frac
27×cbrt-undiv
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
17×cbrt-unprod
9×rec-exp associate-/r* 1-exp
7×div-inv associate-/l*
4×pow1
3×clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
1×associate-*r/ associate-/r/ un-div-inv pow-flip inv-pow
Counts
3 → 127
Calls
3 calls:
Slowest
36.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))
22.0ms
(/ 1 (/ b (* a c)))
13.0ms
(/ b (* a c))

series90.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
39.0ms
(/ 1 (/ b (* a c)))
34.0ms
(/ b (* a c))
18.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))

simplify23.9s

Counts
118 → 136
Calls
118 calls:
Slowest
1.5s
(/ (* (* (* -2 -2) -2) (/ (* (* 1 1) 1) (/ (* (* b b) b) (* (* (* a a) a) (* (* c c) c))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* 1 1) 1) (/ (* (* b b) b) (* (* (* a a) a) (* (* c c) c))))) (* (* (* 2 2) 2) (* (* a a) a)))
1.3s
(/ (* (* (* -2 -2) -2) (* (* (/ 1 (/ b (* a c))) (/ 1 (/ b (* a c)))) (/ 1 (/ b (* a c))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.1s
(/ (* (* (* -2 -2) -2) (* (* (/ 1 (/ b (* a c))) (/ 1 (/ b (* a c)))) (/ 1 (/ b (* a c))))) (* (* (* 2 2) 2) (* (* a a) a)))
1.1s
(/ (* (* (* -2 -2) -2) (/ (* (* 1 1) 1) (* (* (/ b (* a c)) (/ b (* a c))) (/ b (* a c))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune1.1s

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 9.4b

regimes836.0ms

Accuracy

44.1% (7.7b remaining)

Error of 16.8b against oracle of 9.1b and baseline of 22.8b

bsearch37.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.7s8570×body80nan
1.4s4408×body160valid
1.1s16570×pre80true
557.0ms3592×body80valid