Details

Time bar (total: 17.0s)

sample85.0ms

Algorithm
intervals
Results
17.0ms204×body80valid
14.0ms29×body2560valid
14.0ms31×body1280valid
8.0ms106×body80nan
3.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify106.0ms

Counts
1 → 1
Iterations
IterNodes
done111
5111
4102
378
244
124
014

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0)
0.8b
(- (* b b) (* (* c a) 4.0))
0.8b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.3b
(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite181.0ms

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-- 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 → 84
Calls
4 calls:
110.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0)
6.0ms
(- (* b b) (* (* c a) 4.0))
46.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0)
72.0ms
(- (* b b) (* (* c a) 4.0))
113.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
113.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.4s

Counts
96 → 96
Iterations
IterNodes
done5001
21542
1378
0153

prune568.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
0.8b
(- (* b b) (* (* c a) 4.0))
0.8b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.3b
(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite112.0ms

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×associate-/r* add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out--
4×flip3-- 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 → 83
Calls
4 calls:
43.0ms
(/ 2.0 (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
13.0ms
(- (* b b) (* (* c a) 4.0))
45.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
9.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ 2.0 (- (sqrt (- (* b b) (* (* c a) 4.0))) b))
75.0ms
(- (* b b) (* (* c a) 4.0))
123.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
108.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.4s

Counts
95 → 95
Iterations
IterNodes
done5000
21573
1375
0158

prune564.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
0.8b
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.3b
(sqrt (- (* b b) (* (* c a) 4.0)))
24.3b
(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite101.0ms

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×flip3-- add-cbrt-cube sqrt-div add-exp-log flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
38.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
47.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
7.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
105.0ms
(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
82.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
82.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))

simplify3.1s

Counts
72 → 72
Iterations
IterNodes
done5001
34798
2826
1198
081

prune569.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.8b

localize154.0ms

Local error

Found 4 expressions with local error:

24.3b
(sqrt (- (* b b) (* (* c a) 4.0)))
25.1b
(cbrt (- (* b b) (* (* c a) 4.0)))
25.1b
(cbrt (- (* b b) (* (* c a) 4.0)))
25.1b
(cbrt (- (* b b) (* (* c a) 4.0)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-- add-cbrt-cube add-exp-log flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
13.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
9.0ms
(cbrt (- (* b b) (* (* c a) 4.0)))
9.0ms
(cbrt (- (* b b) (* (* c a) 4.0)))
9.0ms
(cbrt (- (* b b) (* (* c a) 4.0)))

series569.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sqrt (- (* b b) (* (* c a) 4.0)))
130.0ms
(cbrt (- (* b b) (* (* c a) 4.0)))
175.0ms
(cbrt (- (* b b) (* (* c a) 4.0)))
180.0ms
(cbrt (- (* b b) (* (* c a) 4.0)))

simplify2.3s

Counts
66 → 66
Iterations
IterNodes
done5002
33680
2718
1210
090

prune685.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.8b

regimes373.0ms

Accuracy

85.8% (3.4b remaining)

Error of 14.1b against oracle of 10.7b and baseline of 34.5b

bsearch125.0ms

Steps
ItersRangePoint
5
4.244596206919672e-17
1.6775967427727985e-16
4.330541687749955e-17
8
-1.4137780731624028e+101
-4.084920897753177e+97
-1.3906582137854214e+101

simplify7.0ms

Iterations
IterNodes
done39
139
033

end0.0ms

sample3.1s

Algorithm
intervals
Results
712.0ms2875×body80nan
602.0ms5865×body80valid
493.0ms434×body640valid
439.0ms1057×body2560valid
357.0ms902×body1280valid
59.0ms124×body5120valid
45.0ms112×body160valid
44.0ms224×body320valid