Details

Time bar (total: 15.2s)

sample180.0ms

Algorithm
intervals
Results
44.0ms140×body160valid
39.0ms265×body80nan
35.0ms521×pre80true
20.0ms40×body320valid
12.0ms76×body80valid

simplify500.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.9b

localize36.0ms

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)
35.8b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite36.0ms

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)))
18.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
14.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series408.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(fma b b (* (* a -4) c))
86.0ms
(sqrt (fma b b (* (* a -4) c)))
144.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
126.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify974.0ms

Counts
126 → 126
Iterations
IterNodes
32593
2949
1407
0180

prune1.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.9b

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

prune83.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite49.0ms

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:
34.0ms
(/ (* -2 (/ (* a c) b)) a)
10.0ms
(/ (* a c) b)

series65.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(/ (* -2 (/ (* a c) b)) a)
36.0ms
(/ (* a c) b)

simplify2.6s

Counts
59 → 59
Iterations
IterNodes
36707
21077
1267
0103

prune676.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.8b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
19×add-sqr-sqrt
16×add-cbrt-cube
14×times-frac
13×*-un-lft-identity associate-*l*
12×add-cube-cbrt
9×div-exp
8×prod-exp
5×cbrt-undiv
4×pow1 cbrt-unprod
3×associate-*r* associate-/l* unswap-sqr
2×expm1-log1p-u rec-exp 1-exp associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
1×clear-num associate-/r* frac-2neg pow-prod-down associate-/r/ *-commutative
Counts
2 → 67
Calls
2 calls:
18.0ms
(/ -2 (* (/ 1 c) b))
21.0ms
(* (/ 1 c) b)

series48.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(/ -2 (* (/ 1 c) b))
21.0ms
(* (/ 1 c) b)

simplify1.3s

Counts
73 → 73
Iterations
IterNodes
32473
2723
1255
0115

prune519.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.8b

regimes633.0ms

Accuracy

13.3% (6.1b remaining)

Error of 11.2b against oracle of 5.1b and baseline of 12.2b

bsearch94.0ms

Steps
ItersRangePoint
5
0.001979392778192651
0.00619171073995458
0.002027355084314286

simplify11.0ms

Iterations
IterNodes
229
129
024

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.4s16416×pre80true
1.3s4797×body160valid
1.2s8416×body80nan
567.0ms1373×body320valid
325.0ms1830×body80valid