Details

Time bar (total: 15.4s)

sample61.0ms

Algorithm
intervals
Results
12.0ms279×body80nan
10.0ms144×body160valid
10.0ms535×pre80true
4.0ms112×body80valid

simplify76.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
30.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite163.0ms

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:
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01541565
14011461
213411245
done50001233

prune256.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite209.0ms

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))))
83.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series624.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
199.0ms
(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
70.0ms
(- (* b b) (* (* 4.0 a) c))
244.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.6s

Counts
163 → 163
Iterations

Useful iterations: 2 (566.0ms)

IterNodesCost
02505048
16254510
227644166
done50004166

prune522.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (pow b 4) (* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c))))))))
0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (pow b 4) (* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))))
0.4b
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite462.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
58×*-un-lft-identity times-frac
36×difference-of-squares
34×add-cube-cbrt
23×add-exp-log add-cbrt-cube
21×sqr-pow
19×pow1
13×associate-/l*
12×distribute-lft-out--
11×associate-/r*
9×unpow-prod-down pow-prod-down prod-exp cbrt-unprod
8×sqrt-prod
4×distribute-rgt-neg-in associate-/r/ associate-/l/ add-log-exp
3×pow-unpow pow-pow flip3-+ associate-*r* pow-exp flip-+ rem-cube-cbrt
2×cbrt-undiv flip3-- frac-2neg associate-*r/ div-exp clear-num flip-- div-inv
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 161
Calls
4 calls:
269.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (pow b 4) (* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c))))))))
77.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (pow b 4) (* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))))
83.0ms
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
27.0ms
(pow (* (* 4.0 a) c) 3)

series701.0ms

Counts
4 → 12
Calls
4 calls:
407.0ms
(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (pow b 4) (* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c))))))))
142.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (pow b 4) (* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))))
77.0ms
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
75.0ms
(pow (* (* 4.0 a) c) 3)

simplify2.4s

Counts
173 → 173
Iterations

Useful iterations: 2 (829.0ms)

IterNodesCost
03347440
18246993
243006605
done50006605

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
0.4b
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
0.8b
(pow (* (* 4.0 a) c) 3)
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
34×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-unpow pow-pow associate-*r* pow-exp rem-cube-cbrt
4×associate-*r/ add-log-exp
2×distribute-rgt-in cube-mult pow-to-exp unpow-prod-down distribute-lft-in flip3-+ unpow3 cube-prod associate-*l* *-commutative flip-+ sqr-pow
Counts
4 → 100
Calls
4 calls:
83.0ms
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
132.0ms
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
36.0ms
(pow (* (* 4.0 a) c) 3)
32.0ms
(pow (* (* 4.0 a) c) 3)

series291.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
96.0ms
(* (* (* 4.0 a) c) (+ (* b b) (* (* 4.0 a) c)))
54.0ms
(pow (* (* 4.0 a) c) 3)
58.0ms
(pow (* (* 4.0 a) c) 3)

simplify1.4s

Counts
112 → 112
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01011634
12841506
215061242
done50011222

prune808.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes271.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03585
14683
done4683

end0.0ms

sample2.3s

Algorithm
intervals
Results
471.0ms4452×body160valid
434.0ms16609×pre80true
428.0ms8609×body80nan
187.0ms3548×body80valid