Details

Time bar (total: 6.2s)

sample41.0ms

Algorithm
intervals
Results
8.0ms39×body2560valid
6.0ms36×body1280valid
6.0ms165×body80valid
3.0ms87×body80nan
2.0ms13×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms4×body160valid

simplify47.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37916
49216
510016
done10016

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b
(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:
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify472.0ms

Counts
82 → 82
Iterations

Useful iterations: done (470.0ms)

IterNodesCost
01541565
14131461
214561245
done50001235

prune235.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
56.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify755.0ms

Counts
92 → 92
Iterations

Useful iterations: done (753.0ms)

IterNodesCost
01811881
14941677
220271400
done50011399

prune247.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
5.2b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* 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))
36.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* 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))
184.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
160 → 160
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02525624
16595105
226164359
done50004343

prune605.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes187.0ms

Accuracy

81.4% (5.2b remaining)

Error of 10.9b against oracle of 5.7b and baseline of 33.8b

bsearch102.0ms

Steps
ItersRangePoint
9
2.365685850767504e-168
1.2053288471691685e-161
1.1860189201379418e-161
8
-1.4395777107888637e+138
-2.299948591329529e+133
-1.9827654008890006e+134

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02941
13841
done3841

end0.0ms

sample1.1s

Algorithm
intervals
Results
230.0ms1025×body2560valid
219.0ms5914×body80valid
160.0ms891×body1280valid
104.0ms2997×body80nan
64.0ms450×body640valid
28.0ms107×body5120valid
21.0ms209×body320valid
7.0ms104×body160valid