Details

Time bar (total: 13.4s)

sample66.0ms

Algorithm
intervals
Results
13.0ms277×body80nan
12.0ms112×body320valid
10.0ms533×pre80true
7.0ms98×body160valid
3.0ms19×body640valid
1.0ms27×body80valid

simplify47.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37916
49216
510016
done10016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite56.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify492.0ms

Counts
82 → 82
Iterations

Useful iterations: done (489.0ms)

IterNodesCost
01541565
14131461
214611245
done50001235

prune178.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

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

rewrite110.0ms

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))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
54.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series453.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
178.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
148.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify1.4s

Counts
163 → 163
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02505760
16595251
226344489
done50004467

prune436.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))) (* 2.0 a))
0.4b
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite430.0ms

Algorithm
rewrite-expression-head
Rules
115×add-sqr-sqrt
114×times-frac
77×*-un-lft-identity
45×add-cube-cbrt
42×difference-of-squares
40×associate-/l*
33×add-exp-log add-cbrt-cube
21×sqr-pow
19×pow1
16×distribute-lft-out--
12×sqrt-prod
11×prod-exp cbrt-unprod
9×unpow-prod-down pow-prod-down
7×cbrt-undiv div-exp
6×distribute-rgt-neg-in associate-/r/
4×associate-/r* div-inv add-log-exp
3×pow-unpow flip3-- pow-pow associate-*r* pow-exp flip-- associate-/l/ rem-cube-cbrt
2×frac-2neg flip3-+ associate-*r/ clear-num flip-+
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 190
Calls
4 calls:
327.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))) (* 2.0 a))
24.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
64.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
6.0ms
(pow (* (* 4.0 a) c) 3)

series479.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))) (* 2.0 a))
74.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
124.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
58.0ms
(pow (* (* 4.0 a) c) 3)

simplify1.9s

Counts
202 → 202
Iterations

Useful iterations: 2 (400.0ms)

IterNodesCost
042010147
110889588
249568640
done50008640

prune909.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (* 4.0 (* a c)) 0) a)
0.4b
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
39×times-frac
37×*-un-lft-identity
29×add-cube-cbrt
24×difference-of-squares
23×add-exp-log add-cbrt-cube
21×sqr-pow
19×pow1
13×associate-/l*
9×unpow-prod-down pow-prod-down prod-exp cbrt-unprod
6×associate-/r*
4×associate-/l/ distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow flip3-+ associate-*r* pow-exp flip-+ rem-cube-cbrt
2×cbrt-undiv frac-2neg associate-*r/ div-exp clear-num associate-/r/ div-inv
1×distribute-rgt-in cube-mult pow-to-exp flip3-- distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative flip--
Counts
4 → 139
Calls
4 calls:
18.0ms
(/ (+ (* 4.0 (* a c)) 0) a)
22.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
65.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
7.0ms
(pow (* (* 4.0 a) c) 3)

series275.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (+ (* 4.0 (* a c)) 0) a)
78.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
132.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
56.0ms
(pow (* (* 4.0 a) c) 3)

simplify3.2s

Counts
151 → 151
Iterations

Useful iterations: 2 (338.0ms)

IterNodesCost
02934522
17594216
241213946
done50003946

prune720.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
03149
14149
24547
done4547

end0.0ms

sample1.7s

Algorithm
intervals
Results
391.0ms3624×body320valid
312.0ms16210×pre80true
284.0ms8210×body80nan
217.0ms2991×body160valid
69.0ms472×body640valid
35.0ms913×body80valid