Details

Time bar (total: 5.5s)

sample58.0ms

Algorithm
intervals
Results
13.0ms314×body80nan
10.0ms150×body160valid
9.0ms570×pre80true
4.0ms106×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: 28.5b

localize11.0ms

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))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite108.0ms

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)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms
(+ (- 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)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405779
11563685
25002674
done5002674

prune190.0ms

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
(- (- 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)))))

rewrite184.0ms

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))
86.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
156.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
194.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify115.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06422664
131752400
250032388
done50032388

prune414.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

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:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
56.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
118.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
156.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify123.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
05221156
13447949
25002944
done5002944

prune256.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ 1 (* (/ 2.0 4.0) (/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))))
0.3b
(/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
71×add-cbrt-cube
65×div-exp
59×prod-exp
28×cbrt-undiv
23×cbrt-unprod
14×add-sqr-sqrt
12×*-un-lft-identity
11×rec-exp 1-exp
9×pow1
8×add-cube-cbrt
7×associate-*r*
6×add-log-exp
5×associate-*r/
4×times-frac associate-/l*
3×sub-neg flip3-- associate-*l* associate-/r/ flip--
2×distribute-rgt-in pow-flip frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×frac-times distribute-rgt-neg-in diff-log associate-*l/ sqrt-prod *-commutative inv-pow unswap-sqr
Counts
4 → 130
Calls
4 calls:
78.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(/ 1 (* (/ 2.0 4.0) (/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))))
38.0ms
(/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))

series448.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
170.0ms
(/ 1 (* (/ 2.0 4.0) (/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))))
120.0ms
(/ (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a c))

simplify114.0ms

Counts
142 → 142
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08021962
146031471
250021401
done50021401

prune241.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes126.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02211
12211
done2211

end0.0ms

sample1.4s

Algorithm
intervals
Results
294.0ms4423×body160valid
276.0ms16584×pre80true
270.0ms8584×body80nan
120.0ms3577×body80valid