Details

Time bar (total: 40.9s)

sample173.0ms

Algorithm
intervals
Results
60.0ms148×body160valid
32.0ms242×body80nan
30.0ms498×pre80true
18.0ms44×body320valid
8.0ms64×body80valid

simplify149.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
149.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize43.0ms

Local error

Found 4 expressions with local error:

37.0b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite150.0ms

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))
36.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(- (* b b) (* (* c a) 4))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
114.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
100.0ms
(sqrt (- (* b b) (* (* c a) 4)))
52.0ms
(- (* b b) (* (* c a) 4))

simplify5.7s

Counts
49 → 88
Calls
49 calls:
Slowest
983.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
394.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
339.0ms
(/ (* (* (- (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)))
301.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
263.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.4b

localize9.0ms

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

prune57.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.4b

localize28.0ms

Local error

Found 2 expressions with local error:

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

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))
8.0ms
(/ (* a c) b)

series66.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(/ (* a c) b)
29.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.3s

Counts
37 → 59
Calls
37 calls:
Slowest
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 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 c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
918.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune611.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 5.3b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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
14.0ms
(/ (* -2 (/ a (/ b c))) (* 2 a))
9.0ms
(/ a (/ b c))

series50.0ms

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

simplify14.0s

Counts
122 → 108
Calls
122 calls:
Slowest
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* a a) a) (/ (* (* b b) b) (* (* c c) c)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 (/ a (/ b c))) (* -2 (/ a (/ b c)))) (* -2 (/ a (/ b c)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.1s
(/ (* (* (* -2 -2) -2) (/ (* (* a a) a) (/ (* (* b b) b) (* (* c c) c)))) (* (* (* 2 2) 2) (* (* a a) a)))
892.0ms
(/ (* (* (* -2 -2) -2) (/ (* (* a a) a) (* (* (/ b c) (/ b c)) (/ b c)))) (* (* (* 2 2) 2) (* (* a a) a)))

prune910.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 5.3b

regimes730.0ms

Accuracy

9.3% (6.2b remaining)

Error of 11.3b against oracle of 5.2b and baseline of 12.0b

bsearch62.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.7s8300×body80nan
1.4s4806×body160valid
1.0s16300×pre80true
570.0ms1415×body320valid
284.0ms1779×body80valid