Details

Time bar (total: 14.6s)

sample106.0ms

Algorithm
intervals
Results
29.0ms284×body80nan
26.0ms149×body160valid
21.0ms540×pre80true
10.0ms107×body80valid

simplify160.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

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)
29.3b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite53.0ms

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

series434.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(fma b b (* (* a -4) c))
88.0ms
(sqrt (fma b b (* (* a -4) c)))
147.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
113.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.2s

Counts
126 → 126
Iterations
IterNodes
32589
2949
1405
0180

prune600.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.3b

localize17.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
10
00

prune100.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.3b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

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)
19.0ms
(/ (* a c) b)

series69.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ (* -2 (/ (* a c) b)) a)
36.0ms
(/ (* a c) b)

simplify3.4s

Counts
59 → 59
Iterations
IterNodes
36739
21081
1265
0103

prune348.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.3b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
92×add-sqr-sqrt
83×*-un-lft-identity add-cube-cbrt
44×associate-*l*
31×add-cbrt-cube add-exp-log
16×associate-/r*
13×cbrt-undiv div-exp
10×div-inv
6×prod-exp cbrt-unprod
5×pow1
4×associate-/l*
3×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×clear-num frac-2neg associate-*l/ associate-/r/
1×pow-prod-down *-commutative associate-/l/
Counts
3 → 171
Calls
3 calls:
27.0ms
(* (/ -2 (/ b a)) c)
33.0ms
(/ (* (/ -2 (/ b a)) c) a)
11.0ms
(/ -2 (/ b a))

series110.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(* (/ -2 (/ b a)) c)
30.0ms
(/ (* (/ -2 (/ b a)) c) a)
19.0ms
(/ -2 (/ b a))

simplify1.1s

Counts
180 → 180
Iterations
IterNodes
22390
1700
0260

prune799.0ms

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 8.2b

regimes973.0ms

Accuracy

44% (7.7b remaining)

Error of 16.7b against oracle of 9.0b and baseline of 22.7b

bsearch5.0ms

Steps
ItersRangePoint
0
2862.7645223887616
2921.618168739223
2892.1913455639924

simplify12.0ms

Iterations
IterNodes
229
129
024

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.4s16403×pre80true
1.3s4500×body160valid
1.1s8403×body80nan
542.0ms3500×body80valid