Details

Time bar (total: 5.7s)

sample55.0ms

Algorithm
intervals
Results
9.0ms136×body160valid
9.0ms521×pre80true
8.0ms265×body80nan
7.0ms120×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059
done1059

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

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))
0.3b
(- (* b b) (* (* 4.0 a) c))
27.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite109.0ms

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)))
69.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25002674
done5002674

prune200.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(- (* b b) (* (* 4.0 a) c))
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:
85.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
193.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify116.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06422664
131752400
250032388
done50032388

prune428.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
15×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
9×pow1
7×add-cube-cbrt associate-*r*
6×prod-exp cbrt-unprod
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
72.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
159.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify128.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
05221156
13447949
25002944
done5002944

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-*r*
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×distribute-rgt-neg-out distribute-lft-out
4×associate-/r*
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
2×flip3-- sqrt-div associate-*r/ associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative neg-mul-1 sub-neg distribute-neg-out frac-2neg diff-log div-exp associate-*l* unsub-neg clear-num sum-log *-commutative div-inv
Counts
4 → 96
Calls
4 calls:
20.0ms
(+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
48.0ms
(* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
51.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series539.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
90.0ms
(* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
271.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify120.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
05851517
132201294
250021276
done50021276

prune314.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes132.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03416
14716
25516
35516
done5516

end0.0ms

sample1.4s

Algorithm
intervals
Results
291.0ms4446×body160valid
286.0ms16533×pre80true
275.0ms8533×body80nan
120.0ms3554×body80valid