Details

Time bar (total: 12.7s)

sample39.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms195×body80valid
4.0ms21×body1280valid
3.0ms81×body80nan
3.0ms19×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify52.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.4b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
37.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
3.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
49.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify851.0ms

Counts
161 → 161
Iterations

Useful iterations: done (845.0ms)

IterNodesCost
02804083
16653911
219743753
done50013752

prune452.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
3251×times-frac
1760×add-sqr-sqrt
1505×*-un-lft-identity
1251×add-cube-cbrt
254×difference-of-squares
130×sqrt-prod
129×div-inv
127×distribute-lft-out--
71×associate-/r*
64×add-exp-log
54×div-exp
25×add-cbrt-cube
15×cbrt-undiv 1-exp associate-/r/
13×associate-/l*
8×add-log-exp
6×rec-exp
5×pow1
3×flip3-- flip--
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 1088
Calls
4 calls:
56.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (/ 1 1) (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.7s

Counts
1100 → 1100
Iterations

Useful iterations: done (4.7s)

IterNodesCost
0148347686
1443338020
done500037966

prune622.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* (/ 1 a) (/ 1 2.0)))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log
33×prod-exp
22×add-cbrt-cube
16×div-exp
15×add-sqr-sqrt
11×frac-times
10×pow1 *-un-lft-identity
9×cbrt-unprod
8×rec-exp flip3-- 1-exp flip-- add-log-exp
7×associate-*r/
6×add-cube-cbrt associate-*l*
5×associate-*l/ sqrt-prod
4×cbrt-undiv difference-of-squares
3×pow-prod-down un-div-inv
2×sub-neg sqrt-div diff-log distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 95
Calls
4 calls:
74.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* (/ 1 a) (/ 1 2.0)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* (/ 1 a) (/ 1 2.0)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify991.0ms

Counts
107 → 107
Iterations

Useful iterations: done (987.0ms)

IterNodesCost
02162523
15972165
217641791
done50011790

prune236.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
19.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (317.0ms)

IterNodesCost
0811248
11901104
25991036
320141028
done50001028

prune245.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes170.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.3b

bsearch139.0ms

Steps
ItersRangePoint
10
3.056596725548563e-78
7.076105677608322e-63
3.446447862996811e-75
10
-1.852183237050365e+100
-1.9127319211193897e+86
-4.123103533644211e+95

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02942
13742
done3742

end0.0ms

sample1.1s

Algorithm
intervals
Results
255.0ms1096×body2560valid
227.0ms5880×body80valid
157.0ms852×body1280valid
107.0ms2945×body80nan
72.0ms471×body640valid
30.0ms109×body5120valid
23.0ms211×body320valid
8.0ms107×body160valid