Details

Time bar (total: 16.9s)

sample84.0ms

Algorithm
intervals
Results
17.0ms143×body160valid
15.0ms253×body80nan
14.0ms509×pre80true
7.0ms113×body80valid

simplify99.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite132.0ms

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:
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
32.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
51.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
110.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.0s

Counts
82 → 82
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01541565
14191461
219261245
done50011239

prune274.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(- (- b) (sqrt (- (* 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)))))

rewrite239.0ms

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:
14.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
102.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
74.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
241.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
300.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.1s

Counts
163 → 163
Iterations

Useful iterations: 2 (698.0ms)

IterNodesCost
02475048
16594512
238214174
done50014174

prune586.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

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:
89.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series510.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
197.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify3.1s

Counts
97 → 97
Iterations

Useful iterations: 2 (720.0ms)

IterNodesCost
01762262
15432068
243271766
done50001766

prune394.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
168×times-frac
153×add-exp-log
87×add-cbrt-cube
77×add-sqr-sqrt *-un-lft-identity div-exp
43×prod-exp
41×add-cube-cbrt
40×cbrt-undiv
38×associate-/r*
23×cbrt-unprod
20×associate-/r/
18×distribute-lft-out-- difference-of-squares
13×div-inv
9×rec-exp distribute-rgt-neg-in 1-exp sqrt-prod
8×flip3-- flip-- add-log-exp
5×pow1 associate-/l*
3×frac-2neg clear-num
2×diff-log
1×associate--l- neg-sub0 sub-neg pow-flip neg-log inv-pow
Counts
4 → 229
Calls
4 calls:
89.0ms
(/ (* a 2.0) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms
(/ 1 (/ (* a 2.0) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
85.0ms
(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series759.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (* a 2.0) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
134.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
228.0ms
(/ 1 (/ (* a 2.0) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
271.0ms
(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify631.0ms

Counts
241 → 241
Iterations

Useful iterations: done (622.0ms)

IterNodesCost
03568029
110807456
done50016492

prune756.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes248.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01725
12223
22323
done2323

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.6s4385×body160valid
741.0ms16610×pre80true
709.0ms8610×body80nan
331.0ms3615×body80valid