Details

Time bar (total: 16.2s)

sample148.0ms

Algorithm
intervals
Results
32.0ms35×body2560valid
28.0ms184×body80valid
23.0ms15×body640valid
20.0ms28×body1280valid
11.0ms86×body80nan
6.0ms4×body5120valid
3.0ms8×body320valid
1.0ms5×body160valid

simplify129.0ms

Counts
1 → 1
Iterations
IterNodes
done95
795
694
592
484
367
243
124
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.6b
(- (* b b) (* (* 4 a) c))
1.7b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
81.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
7.0ms
(- (* b b) (* (* 4 a) c))
59.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
52.0ms
(- (* b b) (* (* 4 a) c))
111.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
112.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done2000
32000
21158
1394
0161

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
0.6b
(- (* b b) (* (* 4 a) c))
8.4b
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip-- distribute-lft-out--
3×associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
16.0ms
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
7.0ms
(- (* b b) (* (* 4 a) c))
43.0ms
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
58.0ms
(- (* b b) (* (* 4 a) c))
170.0ms
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
103.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.0s

Counts
109 → 109
Iterations
IterNodes
done2002
32002
21134
1410
0179

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.6b
(- (* b b) (* (* 4 a) c))
1.7b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
79.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
11.0ms
(- (* b b) (* (* 4 a) c))
47.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
65.0ms
(- (* b b) (* (* 4 a) c))
106.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done2000
32000
21158
1394
0161

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a))
0.6b
(- (* b b) (* (* 4 a) c))
12.6b
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a)) (/ b a))
24.6b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac associate-*r* add-exp-log
10×sqrt-div
9×add-cbrt-cube sqrt-prod
8×add-log-exp
7×pow1 flip3-- flip--
6×associate-*l* frac-sub unswap-sqr
4×frac-times associate-*l/ prod-exp insert-posit16
3×associate-*r/ un-div-inv
2×sub-neg diff-log div-exp cbrt-unprod div-inv sub-div
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 distribute-rgt-out-- pow1/2 1-exp pow-prod-down *-commutative
Counts
4 → 98
Calls
4 calls:
25.0ms
(* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a))
7.0ms
(- (* b b) (* (* 4 a) c))
21.0ms
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a)) (/ b a))
12.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a))
78.0ms
(- (* b b) (* (* 4 a) c))
120.0ms
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (/ 1 a)) (/ b a))
76.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
110 → 110
Iterations
IterNodes
done2000
32000
21551
1522
0199

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.9b

regimes206.0ms

Accuracy

84.4% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.4b

bsearch157.0ms

Steps
ItersRangePoint
10
8.296670056881522e-85
2.5972983117194536e-74
2.326372645943808e-74
7
-1.8217288728729631e+111
-6.606823090402082e+109
-1.0027271082217074e+110

simplify7.0ms

Iterations
IterNodes
done31
131
027

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.3s1126×body2560valid
835.0ms5836×body80valid
607.0ms915×body1280valid
396.0ms236×body320valid
359.0ms2976×body80nan
230.0ms417×body640valid
97.0ms119×body5120valid
26.0ms115×body160valid