Details

Time bar (total: 17.8s)

sample397.0ms

Algorithm
intervals
Results
87.0ms249×body80nan
56.0ms505×pre80true
37.0ms118×body320valid
20.0ms91×body160valid
8.0ms20×body640valid
4.0ms27×body80valid

simplify168.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize31.0ms

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))
28.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite162.0ms

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:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(- (* b b) (* (* 4.0 a) c))
180.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
146.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune324.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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))
0.2b
(/ (/ (+ 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)))))

rewrite262.0ms

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:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
99.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
86.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series691.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(- (* b b) (* (* 4.0 a) c))
222.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
277.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.6s

Counts
163 → 163
Iterations

Useful iterations: 2 (640.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune644.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite287.0ms

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:
140.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
102.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(- (* b b) (* (* 4.0 a) c))
199.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.9s

Counts
97 → 97
Iterations

Useful iterations: 2 (657.0ms)

IterNodesCost
01762262
14932066
225591750
done50011750

prune390.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
0.3b
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))))
0.3b
(/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
0.8b
(pow (* 4.0 (* a c)) 3)

rewrite724.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
33×times-frac
31×*-un-lft-identity
30×add-exp-log add-cbrt-cube
24×difference-of-squares
23×add-cube-cbrt
21×sqr-pow
19×pow1
13×associate-/l*
12×prod-exp cbrt-unprod
9×unpow-prod-down pow-prod-down
4×cbrt-undiv associate-*r/ div-exp associate-/r* associate-/r/ associate-/l/ distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow flip3-+ associate-*r* pow-exp flip-+ rem-cube-cbrt
2×flip3-- frac-2neg 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 → 137
Calls
4 calls:
102.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
370.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))))
222.0ms
(/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
23.0ms
(pow (* 4.0 (* a c)) 3)

series795.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
374.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))))
203.0ms
(/ (- (pow b 6) (pow (* 4.0 (* a c)) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
103.0ms
(pow (* 4.0 (* a c)) 3)

simplify770.0ms

Counts
149 → 149
Iterations

Useful iterations: done (763.0ms)

IterNodesCost
03265840
18695460
done50014919

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes183.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01927
12525
done2525

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.2s8051×body80nan
1.1s3634×body320valid
1.1s2967×body160valid
712.0ms16051×pre80true
191.0ms500×body640valid
67.0ms899×body80valid