Details

Time bar (total: 12.9s)

sample121.0ms

Algorithm
intervals
Results
29.0ms147×body160valid
26.0ms260×body80nan
25.0ms516×pre80true
11.0ms109×body80valid

simplify147.0ms

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: 29.7b

localize40.0ms

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)
29.6b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite30.0ms

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))
1.0ms
(sqrt (fma b b (* (* a -4) c)))
16.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
11.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series455.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(fma b b (* (* a -4) c))
124.0ms
(sqrt (fma b b (* (* a -4) c)))
137.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
123.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify2.1s

Counts
126 → 126
Iterations
IterNodes
done5000
33635
21008
1423
0180

prune640.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.4b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune115.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 8.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* -2 (/ (* a c) b)) a)
0.3b
(/ (* a c) b)

rewrite34.0ms

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:
24.0ms
(/ (* -2 (/ (* a c) b)) a)
9.0ms
(/ (* a c) b)

series49.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(/ (* -2 (/ (* a c) b)) a)
29.0ms
(/ (* a c) b)

simplify1.1s

Counts
59 → 59
Iterations
IterNodes
done5002
21421
1280
0103

prune311.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 8.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) a)
0.3b
(/ (/ (* a c) (sqrt b)) (sqrt b))
0.4b
(/ (* a c) (sqrt b))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
111×times-frac
60×sqrt-prod
52×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
37×add-cbrt-cube add-exp-log
17×cbrt-undiv div-exp
15×associate-/r*
12×associate-/l*
10×div-inv
prod-exp cbrt-unprod
expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
associate-/l/
associate-*r/
Counts
3 → 157
Calls
3 calls:
36.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) a)
14.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
9.0ms
(/ (* a c) (sqrt b))

series181.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) a)
52.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
66.0ms
(/ (* a c) (sqrt b))

simplify1.7s

Counts
166 → 166
Iterations
IterNodes
done5000
22519
1648
0242

prune666.0ms

Pruning

41 alts after pruning (40 fresh and 1 done)

Merged error: 8.3b

regimes952.0ms

Accuracy

47.6% (7.3b remaining)

Error of 16.3b against oracle of 9.0b and baseline of 23.0b

bsearch24.0ms

Steps
ItersRangePoint
2
2241.248812300401
2693.9337634355593
2297.8344311922956

simplify5.0ms

Iterations
IterNodes
done29
129
024

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.2s8697×body80nan
940.0ms4438×body160valid
851.0ms16697×pre80true
712.0ms3561×body80valid
0.0msbody320valid