Details

Time bar (total: 15.1s)

sample166.0ms

Algorithm
intervals
Results
54.0ms300×body80nan
41.0ms151×body160valid
32.0ms556×pre80true
14.0ms105×body80valid

simplify145.0ms

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.7b

localize46.0ms

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

rewrite28.0ms

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)
8.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series452.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(fma b b (* (* a -4) c))
91.0ms
(sqrt (fma b b (* (* a -4) c)))
169.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
116.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.9s

Counts
126 → 126
Iterations
IterNodes
32589
2949
1405
0180

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.9b

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

prune77.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.9b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite50.0ms

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:
31.0ms
(/ (* -2 (/ (* a c) b)) a)
18.0ms
(/ (* a c) b)

series78.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (* -2 (/ (* a c) b)) a)
43.0ms
(/ (* a c) b)

simplify2.8s

Counts
59 → 59
Iterations
IterNodes
36739
21081
1265
0103

prune525.0ms

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 8.8b

localize40.0ms

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
7×prod-exp cbrt-unprod
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×associate-/l/
1×associate-*r/
Counts
3 → 157
Calls
3 calls:
20.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) a)
25.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
20.0ms
(/ (* a c) (sqrt b))

series182.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(/ (* -2 (/ (/ (* a c) (sqrt b)) (sqrt b))) a)
48.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
80.0ms
(/ (* a c) (sqrt b))

simplify685.0ms

Counts
166 → 166
Iterations
IterNodes
22277
1633
0242

prune1.2s

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 8.8b

regimes859.0ms

Accuracy

46.6% (7.4b remaining)

Error of 16.2b against oracle of 8.9b and baseline of 22.7b

bsearch14.0ms

Steps
ItersRangePoint
1
2613.6351163624354
2762.567042685954
2650.8680979433148

simplify5.0ms

Iterations
IterNodes
229
129
024

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.5s8561×body80nan
1.2s4497×body160valid
1.0s16561×pre80true
517.0ms3503×body80valid