Details

Time bar (total: 16.5s)

sample103.0ms

Algorithm
intervals
Results
22.0ms153×body160valid
18.0ms286×body80nan
16.0ms542×pre80true
8.0ms41×body320valid
4.0ms62×body80valid

simplify112.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
410216
511116
done11116

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(- (* b b) (* (* 4.0 a) c))
199.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
117.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.0s

Counts
82 → 82
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01541565
14191461
219081245
done50001239

prune459.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-cbrt-cube add-exp-log
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×clear-num sub-neg frac-2neg prod-exp cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
37.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series631.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms
(- (* b b) (* (* 4.0 a) c))
187.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
231.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.8s

Counts
163 → 163
Iterations

Useful iterations: 2 (670.0ms)

IterNodesCost
02475048
16584512
238464174
done50024174

prune855.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
15×add-cbrt-cube add-exp-log
10×add-log-exp
8×add-cube-cbrt
7×associate-*r*
6×pow1
4×sub-neg flip3-- prod-exp associate-*r/ cbrt-unprod flip-- distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp associate-*l* associate-/l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in associate-*l/ associate-/r/ sqrt-prod associate-/l/
1×associate--l- neg-sub0 clear-num associate-/r* frac-2neg flip3-+ pow-prod-down neg-log *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
102.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
38.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(- (* b b) (* (* 4.0 a) c))
138.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series573.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
119.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(- (* b b) (* (* 4.0 a) c))
210.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify1.7s

Counts
97 → 97
Iterations

Useful iterations: 2 (514.0ms)

IterNodesCost
01832186
15431993
234891725
done50011725

prune529.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* a (- b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.1b
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (+ (* a (- b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*r*
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
8×add-log-exp
6×distribute-lft-neg-in pow1 distribute-rgt-neg-in sqrt-prod
5×distribute-rgt-neg-out
3×flip3-+ times-frac associate-*l* flip-+ associate-/l*
2×cbrt-undiv flip3-- sqrt-div div-exp associate-*l/ prod-exp associate-*r/ associate-/r/ cbrt-unprod flip-- distribute-neg-frac associate-/l/
1×+-commutative clear-num associate-/r* neg-mul-1 sum-log sub-neg frac-2neg diff-log unsub-neg pow-prod-down *-commutative div-inv distribute-neg-out distribute-lft-out unswap-sqr
Counts
4 → 86
Calls
4 calls:
14.0ms
(+ (* a (- b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
48.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (+ (* a (- b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))

series707.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(+ (* a (- b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
163.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
54.0ms
(- (* b b) (* (* 4.0 a) c))
338.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (+ (* a (- b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) 2.0))

simplify1.5s

Counts
98 → 98
Iterations

Useful iterations: 2 (510.0ms)

IterNodesCost
01912187
15581865
231501619
done50001619

prune640.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes248.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
01928
13026
24225
35225
46325
56925
67025
done7025

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.0s8376×body80nan
954.0ms4835×body160valid
593.0ms16376×pre80true
551.0ms1773×body80valid
339.0ms1392×body320valid