Details

Time bar (total: 47.1s)

sample163.0ms

Algorithm
intervals
Results
41.0ms310×body80nan
40.0ms566×pre80true
37.0ms132×body160valid
18.0ms124×body80valid

simplify164.0ms

Counts
1 → 1
Iterations
IterNodes
8105
7105
6104
5102
494
377
244
125
014

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.9b

localize38.0ms

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)))
0.3b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
27.9b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite33.0ms

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))
1.0ms
(sqrt (fma b b (* (* a -4) c)))
17.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
13.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series463.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(fma b b (* (* a -4) c))
91.0ms
(sqrt (fma b b (* (* a -4) c)))
142.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
149.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
32589
2949
1405
0180

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.1b

localize9.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
10
00

prune112.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.1b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:
12.0ms
(/ (* a c) b)
16.0ms
(/ (* -2 (/ (* a c) b)) a)

series79.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(/ (* a c) b)
36.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify3.3s

Counts
59 → 59
Iterations
IterNodes
36399
21058
1267
0103

prune676.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 9.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
5405×times-frac
2273×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
405×distribute-lft-neg-in distribute-rgt-neg-in
166×div-inv
150×associate-/l*
135×neg-mul-1
56×associate-/r*
31×add-cbrt-cube add-exp-log
19×cbrt-undiv div-exp
12×associate-/r/
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×associate-/l/
Counts
3 → 1774
Calls
3 calls:
22.0ms
(/ (/ b a) c)
29.0ms
(/ (/ 2 (/ (/ b a) c)) (- a))
14.0ms
(/ 2 (/ (/ b a) c))

series113.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ (/ b a) c)
44.0ms
(/ (/ 2 (/ (/ b a) c)) (- a))
34.0ms
(/ 2 (/ (/ b a) c))

simplify12.1s

Counts
1783 → 1783
Iterations
IterNodes
17328
02788

prune20.4s

Pruning

48 alts after pruning (46 fresh and 2 done)

Merged error: 9.0b

regimes1.2s

Accuracy

46.8% (7.2b remaining)

Error of 16.2b against oracle of 9.0b and baseline of 22.6b

bsearch5.0ms

Steps
ItersRangePoint
0
1072.0421178334989
1095.414553911296
1083.7283358723973

simplify5.0ms

Iterations
IterNodes
229
129
024

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.0s4543×body160valid
1.2s8582×body80nan
1.1s16582×pre80true
513.0ms3456×body80valid
0.0ms1×body320valid