Details

Time bar (total: 27.0s)

sample82.0ms

Algorithm
intervals
Results
21.0ms210×body80valid
16.0ms23×body2560valid
13.0ms25×body1280valid
8.0ms84×body80nan
3.0ms8×body640valid
2.0ms9×body320valid
2.0ms2×body5120valid
0.0ms2×body160valid

simplify108.0ms

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

prune433.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.8b
(- (* b b) (* (* 4 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
127×add-sqr-sqrt
50×*-un-lft-identity
40×difference-of-squares
36×unswap-sqr
29×sqrt-prod
18×times-frac associate-*l*
17×distribute-lft-out--
16×add-cube-cbrt
8×add-log-exp
6×add-cbrt-cube swap-sqr add-exp-log *-commutative associate-/l*
5×pow1
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 → 130
Calls
4 calls:
1.3s
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
80.0ms
(- (* b b) (* (* 4 a) c))
744.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
200.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
70.0ms
(- (* b b) (* (* 4 a) c))
103.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
100.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.3s

Counts
142 → 142
Iterations
IterNodes
done5003
21445
1489
0206

prune746.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b))
0.8b
(- (* b b) (* (* 4 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
127×add-sqr-sqrt
50×*-un-lft-identity
40×difference-of-squares
36×unswap-sqr
29×sqrt-prod
18×times-frac associate-*l*
17×distribute-lft-out--
16×add-cube-cbrt
8×add-log-exp
6×associate-/r* add-cbrt-cube swap-sqr add-exp-log *-commutative
5×pow1
4×flip3-- insert-posit16 flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 129
Calls
4 calls:
587.0ms
(/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b))
105.0ms
(- (* b b) (* (* 4 a) c))
734.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
134.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b))
56.0ms
(- (* b b) (* (* 4 a) c))
120.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
92.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
141 → 141
Iterations
IterNodes
done5001
21379
1446
0201

prune721.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
0.8b
(- (* b b) (* (* 4 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite3.0s

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
49×*-un-lft-identity
39×unswap-sqr
34×difference-of-squares
26×sqrt-prod
24×associate-*l*
19×add-cube-cbrt
18×frac-times
14×distribute-lft-out--
13×flip3-- associate-*r* add-exp-log flip--
11×times-frac
10×associate-/l*
9×associate-/r* add-cbrt-cube associate-*r/
8×add-log-exp
7×pow1 *-commutative
6×swap-sqr
4×clear-num prod-exp insert-posit16
3×frac-2neg un-div-inv
2×sub-neg sqrt-div diff-log div-exp associate-*l/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down div-inv
Counts
4 → 157
Calls
4 calls:
1.9s
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
77.0ms
(- (* b b) (* (* 4 a) c))
755.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
161.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
51.0ms
(- (* b b) (* (* 4 a) c))
103.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
87.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts
169 → 169
Iterations
IterNodes
done5001
22062
1660
0258

prune762.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.5b

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
1.0b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
50×sqrt-prod
36×unswap-sqr
34×*-un-lft-identity difference-of-squares
18×associate-*l*
14×distribute-lft-out--
8×add-log-exp
6×pow1 swap-sqr *-commutative add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 106
Calls
4 calls:
750.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
731.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
169.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
154.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
110.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.4s

Counts
118 → 118
Iterations
IterNodes
done5003
33883
2933
1286
0128

prune676.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.5b

regimes388.0ms

Accuracy

81% (5.2b remaining)

Error of 10.9b against oracle of 5.6b and baseline of 33.1b

bsearch468.0ms

Steps
ItersRangePoint
8
5.451909898538592e-70
5.081728108716245e-67
1.546013236023957e-67
7
6.366271362828677e-80
2.0474353944207673e-78
1.6168702840263923e-79
8
1.9015403840268286e-125
4.787339246176752e-121
1.3353078790738604e-121
7
-9.460060253608456e+39
-2.573022393154551e+38
-9.348931433494438e+39

simplify12.0ms

Iterations
IterNodes
done48
148
038

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.9s1084×body2560valid
837.0ms5870×body80valid
786.0ms907×body1280valid
372.0ms3007×body80nan
241.0ms447×body640valid
120.0ms101×body5120valid
106.0ms232×body320valid
50.0ms109×body160valid