Details

Time bar (total: 7.5s)

sample52.0ms

Algorithm
intervals
Results
11.0ms159×body160valid
9.0ms504×pre80true
8.0ms248×body80nan
5.0ms46×body320valid
2.0ms51×body80valid

simplify46.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify510.0ms

Counts
82 → 82
Iterations

Useful iterations: done (507.0ms)

IterNodesCost
01541565
14061461
213611245
done50011235

prune194.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

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:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
33.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
49.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series413.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
163.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
124.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify742.0ms

Counts
163 → 163
Iterations

Useful iterations: done (736.0ms)

IterNodesCost
02545790
16705273
223874513
done50004511

prune448.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
29.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
121.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify782.0ms

Counts
97 → 97
Iterations

Useful iterations: done (779.0ms)

IterNodesCost
01842432
15462259
223251818
done50011817

prune275.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
66×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
18×add-exp-log add-cbrt-cube distribute-lft-out-- difference-of-squares
10×div-inv associate-/l* add-log-exp
9×distribute-rgt-neg-in sqrt-prod
8×associate-/r*
7×cbrt-undiv div-exp
4×pow1
3×flip3-- diff-log flip-- associate-/l/
2×sub-neg frac-2neg prod-exp clear-num associate-/r/ cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 135
Calls
4 calls:
29.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(/ (+ 0 (* 4.0 (* a c))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))

series282.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(/ (+ 0 (* 4.0 (* a c))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))

simplify904.0ms

Counts
147 → 147
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
02314448
16143966
228573706
done50003705

prune340.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes92.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
11717
done1717

end0.0ms

sample1.4s

Algorithm
intervals
Results
337.0ms4829×body160valid
292.0ms16283×pre80true
279.0ms8283×body80nan
142.0ms1358×body320valid
64.0ms1813×body80valid