Details

Time bar (total: 18.3s)

sample229.0ms

Algorithm
intervals
Results
56.0ms271×body80nan
27.0ms127×body320valid
20.0ms527×pre80true
12.0ms90×body160valid
4.0ms15×body640valid
2.0ms24×body80valid

simplify151.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

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))
24.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite334.0ms

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)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
262.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series469.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
60.0ms
(- (* b b) (* (* 4.0 a) c))
145.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
158.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01541565
14011461
213421245
done50011233

prune269.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- 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)))))

rewrite250.0ms

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))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
133.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
79.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series695.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms
(- (* b b) (* (* 4.0 a) c))
247.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
263.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.5s

Counts
163 → 163
Iterations

Useful iterations: 2 (569.0ms)

IterNodesCost
02475048
16124510
224984166
done50014166

prune700.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
338×times-frac
263×add-sqr-sqrt
252×*-un-lft-identity
151×add-cube-cbrt
107×add-exp-log
85×associate-*r*
65×add-cbrt-cube
50×distribute-lft-out-- difference-of-squares
47×div-exp
35×prod-exp
30×associate-/l*
25×cbrt-undiv distribute-rgt-neg-in sqrt-prod
21×cbrt-unprod
16×associate-/r/
11×div-inv
10×associate-/r*
9×flip3-- flip--
7×pow1 associate-*l*
6×rec-exp 1-exp add-log-exp
4×unswap-sqr
2×frac-2neg clear-num
1×frac-times sub-neg pow-flip diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 329
Calls
4 calls:
69.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
289.0ms
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series996.0ms

Counts
4 → 12
Calls
4 calls:
510.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
62.0ms
(- (* b b) (* (* 4.0 a) c))
185.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
239.0ms
(* (/ (* (* a c) 4.0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.7s

Counts
341 → 341
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
043510074
112189067
242058096
done50018096

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (* (* a c) 4.0) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(* (/ (/ (* (* a c) 4.0) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 a))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
138×add-sqr-sqrt
123×*-un-lft-identity
103×add-exp-log
63×add-cbrt-cube
57×add-cube-cbrt
55×associate-*l*
45×div-exp
35×prod-exp
32×distribute-lft-out-- difference-of-squares
26×cbrt-undiv
19×cbrt-unprod
18×div-inv
16×distribute-rgt-neg-in sqrt-prod
13×associate-*r*
10×add-log-exp
7×associate-/r* associate-/l*
6×pow1 unswap-sqr
5×rec-exp 1-exp
4×flip3-- associate-/r/ flip--
3×diff-log
2×sub-neg
1×associate--l- neg-sub0 frac-times frac-2neg associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative associate-/l/
Counts
4 → 231
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(- (* b b) (* (* 4.0 a) c))
85.0ms
(/ (/ (* (* a c) 4.0) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
224.0ms
(* (/ (/ (* (* a c) 4.0) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 a))

series665.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(- (* b b) (* (* 4.0 a) c))
284.0ms
(/ (/ (* (* a c) 4.0) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
222.0ms
(* (/ (/ (* (* a c) 4.0) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 a))

simplify2.5s

Counts
243 → 243
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
03587320
110556937
240266037
done50016037

prune711.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes152.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01723
12123
done2123

end0.0ms

sample2.6s

Algorithm
intervals
Results
548.0ms3616×body320valid
418.0ms16274×pre80true
410.0ms8274×body80nan
304.0ms2978×body160valid
106.0ms515×body640valid
46.0ms891×body80valid