Details

Time bar (total: 5.6s)

sample55.0ms

Algorithm
intervals
Results
9.0ms142×body160valid
9.0ms509×pre80true
8.0ms253×body80nan
4.0ms45×body320valid
2.0ms69×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059
done1059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
35.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
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×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405779
11563685
25002674
done5002674

prune196.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

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-exp-log add-cbrt-cube
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×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
155.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
193.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify116.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06422664
131752400
250032388
done50032388

prune421.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
14×*-un-lft-identity
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv add-cube-cbrt div-exp
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 85
Calls
4 calls:
78.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
158.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify89.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
05121105
13243867
25001860
done5001860

prune249.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(+ (* -1 (* a b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b
(/ (* 4.0 (* a c)) (+ (* -1 (* a b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*r*
15×add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
8×add-log-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×prod-exp distribute-rgt-neg-out cbrt-unprod
3×cbrt-undiv times-frac div-exp associate-*l* associate-/r*
2×flip3-- flip3-+ sqrt-div associate-*r/ associate-/r/ flip-- flip-+ distribute-neg-frac
1×+-commutative neg-mul-1 sub-neg distribute-neg-out frac-2neg mul-1-neg diff-log unsub-neg pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 85
Calls
4 calls:
44.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(+ (* -1 (* a b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
39.0ms
(/ (* 4.0 (* a c)) (+ (* -1 (* a b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(+ (* -1 (* a b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
242.0ms
(/ (* 4.0 (* a c)) (+ (* -1 (* a b)) (* a (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify81.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05151118
12637926
25001907
done5001907

prune272.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03213
13813
23813
done3813

end0.0ms

sample1.6s

Algorithm
intervals
Results
339.0ms4823×body160valid
286.0ms16463×pre80true
280.0ms8463×body80nan
135.0ms1346×body320valid
64.0ms1831×body80valid