Details

Time bar (total: 50.0s)

sample152.0ms

Algorithm
intervals
Results
49.0ms256×body80nan
39.0ms165×body160valid
24.0ms512×pre80true
13.0ms43×body320valid
6.0ms48×body80valid

simplify189.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
188.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.6b

localize50.0ms

Local error

Found 4 expressions with local error:

40.8b
(- (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))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite170.0ms

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
90.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
63.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series439.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
140.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
86.0ms
(sqrt (- (* b b) (* (* c a) 4)))
68.0ms
(- (* b b) (* (* c a) 4))

simplify5.6s

Counts
49 → 88
Calls
49 calls:
Slowest
557.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
376.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
358.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
331.0ms
(/ (* (* (- (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)))
279.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune949.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.1b

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

prune48.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.1b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite57.0ms

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))
21.0ms
(/ (* a c) b)

series53.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
32.0ms
(/ (* a c) b)
21.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.2s

Counts
37 → 59
Calls
37 calls:
Slowest
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
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 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)))
886.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune543.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 4.0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ 1 (/ b (* a c)))
0.3b
(/ b (* a c))
0.2b
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))

rewrite75.0ms

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
43.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))
20.0ms
(/ 1 (/ b (* a c)))
11.0ms
(/ b (* a c))

series91.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
37.0ms
(/ b (* a c))
28.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) (* 2 a))
26.0ms
(/ 1 (/ b (* a c)))

simplify23.8s

Counts
118 → 136
Calls
118 calls:
Slowest
1.6s
(/ (* (* (* -2 -2) -2) (* (* (/ 1 (/ b (* a c))) (/ 1 (/ b (* a c)))) (/ 1 (/ b (* a 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 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* 1 1) 1) (/ (* (* b b) b) (* (* (* a a) a) (* (* c c) c))))) (* (* (* 2 a) (* 2 a)) (* 2 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

32 alts after pruning (31 fresh and 1 done)

Merged error: 4.0b

regimes560.0ms

Accuracy

12.1% (6.0b remaining)

Error of 11.0b against oracle of 5.0b and baseline of 11.8b

bsearch117.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.4s8342×body80nan
1.2s4846×body160valid
796.0ms16342×pre80true
671.0ms1383×body320valid
252.0ms1771×body80valid