Details

Time bar (total: 12.9s)

sample90.0ms

Algorithm
intervals
Results
19.0ms162×body160valid
18.0ms37×body320valid
16.0ms495×pre80true
14.0ms239×body80nan
3.0ms57×body80valid

simplify77.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma b b (* (* a -4) c))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.2b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
38.9b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite49.0ms

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
add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
pow1 distribute-lft-out--
expm1-log1p-u insert-posit16 log1p-expm1-u
associate-/r*
flip3-- flip-- associate-/l/
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)))
33.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
12.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series442.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(fma b b (* (* a -4) c))
120.0ms
(sqrt (fma b b (* (* a -4) c)))
139.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
105.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify2.1s

Counts
126 → 126
Iterations
IterNodes
done5000
33635
21008
1423
0180

prune680.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.1b

localize9.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune103.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
cbrt-undiv div-exp
add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
prod-exp cbrt-unprod
expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
10.0ms
(/ (* a c) b)
25.0ms
(/ (* -2 (/ (* a c) b)) a)

series56.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(/ (* a c) b)
34.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify1.3s

Counts
59 → 59
Iterations
IterNodes
done5000
21285
1282
0103

prune439.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.1b

localize37.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ b (* a c))
0.3b
(/ 1 (/ b (* a c)))
0.3b
(/ (* -2 (/ 1 (/ b (* a c)))) a)

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
39×times-frac
37×add-cbrt-cube div-exp
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
17×cbrt-undiv prod-exp
11×associate-/r*
cbrt-unprod div-inv associate-/l*
rec-exp 1-exp
pow1
expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
associate-/l/
associate-*r/ associate-/r/ un-div-inv pow-flip inv-pow
Counts
3 → 121
Calls
3 calls:
18.0ms
(/ b (* a c))
29.0ms
(/ 1 (/ b (* a c)))
61.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) a)

series81.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(/ b (* a c))
27.0ms
(/ 1 (/ b (* a c)))
26.0ms
(/ (* -2 (/ 1 (/ b (* a c)))) a)

simplify1.6s

Counts
130 → 130
Iterations
IterNodes
done5001
21813
1482
0192

prune501.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 5.1b

regimes600.0ms

Accuracy

11.8% (6.4b remaining)

Error of 11.5b against oracle of 5.1b and baseline of 12.3b

bsearch42.0ms

Steps
ItersRangePoint
3
0.001235527435550306
0.0015236040748043695
0.0012535322255036849

simplify5.0ms

Iterations
IterNodes
done28
128
024

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.5s4823×body160valid
1.3s7968×body80nan
767.0ms15968×pre80true
359.0ms1305×body320valid
192.0ms1872×body80valid