Details

Time bar (total: 13.4s)

sample125.0ms

Algorithm
intervals
Results
40.0ms303×body80nan
24.0ms134×body160valid
22.0ms559×pre80true
13.0ms53×body320valid
6.0ms69×body80valid

simplify104.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
377
244
125
014

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma b b (* (* a -4) c))
0.0b
(sqrt (fma b b (* (* a -4) c)))
0.2b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
36.2b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
0.0ms
(fma b b (* (* a -4) c))
2.0ms
(sqrt (fma b b (* (* a -4) c)))
31.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
14.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series437.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(fma b b (* (* a -4) c))
87.0ms
(sqrt (fma b b (* (* a -4) c)))
163.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
126.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify2.2s

Counts
126 → 126
Iterations
IterNodes
done5000
33635
21008
1423
0180

prune611.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.5b

localize16.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune71.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2 (/ (* a c) b)) a)
0.3b
(/ (* a c) b)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
8×cbrt-undiv div-exp
6×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
5×prod-exp cbrt-unprod
2×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
17.0ms
(/ (* -2 (/ (* a c) b)) a)
10.0ms
(/ (* a c) b)

series70.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ (* -2 (/ (* a c) b)) a)
42.0ms
(/ (* a c) b)

simplify1.6s

Counts
59 → 59
Iterations
IterNodes
done5002
21421
1280
0103

prune367.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 4.4b

localize30.0ms

Local error

Found 2 expressions with local error:

0.3b
(* a (/ c b))
0.3b
(/ (* -2 (* a (/ c b))) a)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
17×add-sqr-sqrt
13×times-frac associate-*r*
12×*-un-lft-identity add-cube-cbrt
7×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×pow1
3×associate-/r* associate-*l* associate-*r/
2×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
1×clear-num frac-2neg pow-prod-down *-commutative associate-/l* associate-/l/
Counts
2 → 64
Calls
2 calls:
10.0ms
(* a (/ c b))
41.0ms
(/ (* -2 (* a (/ c b))) a)

series56.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(* a (/ c b))
35.0ms
(/ (* -2 (* a (/ c b))) a)

simplify1.3s

Counts
70 → 70
Iterations
IterNodes
done5003
21295
1331
0122

prune246.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 4.4b

regimes604.0ms

Accuracy

10% (6.1b remaining)

Error of 11.2b against oracle of 5.0b and baseline of 11.8b

bsearch33.0ms

Steps
ItersRangePoint
2
0.1033833431865932
0.1127640550401266
0.10455593216828488

simplify10.0ms

Iterations
IterNodes
done29
129
024

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.6s4816×body160valid
1.4s16203×pre80true
1.1s8203×body80nan
596.0ms1410×body320valid
285.0ms1774×body80valid