Details

Time bar (total: 16.9s)

sample197.0ms

Algorithm
intervals
Results
64.0ms554×pre80true
45.0ms148×body160valid
39.0ms298×body80nan
15.0ms108×body80valid

simplify126.0ms

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.3b

localize44.0ms

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)
29.2b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite62.0ms

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))
3.0ms
(sqrt (fma b b (* (* a -4) c)))
40.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
16.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series439.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(fma b b (* (* a -4) c))
93.0ms
(sqrt (fma b b (* (* a -4) c)))
165.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
114.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
32589
2949
1405
0180

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.8b

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

prune108.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.8b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

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:
16.0ms
(/ (* a c) b)
29.0ms
(/ (* -2 (/ (* a c) b)) a)

series56.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(/ (* a c) b)
24.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify2.9s

Counts
59 → 59
Iterations
IterNodes
36399
21058
1267
0103

prune667.0ms

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 8.7b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
87×times-frac
62×*-un-lft-identity add-cube-cbrt
48×sqrt-prod
45×add-cbrt-cube add-exp-log
22×associate-*r* associate-*l*
16×cbrt-undiv div-exp
15×associate-/r*
13×prod-exp cbrt-unprod
unswap-sqr
associate-/l*
pow1
associate-*r/ div-inv
expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
clear-num frac-2neg associate-/l/
frac-times associate-*l/
pow-prod-down *-commutative
Counts
4 → 195
Calls
4 calls:
5.0ms
(/ a (sqrt b))
6.0ms
(/ c (sqrt b))
45.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) a)
33.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ a (sqrt b))
45.0ms
(/ c (sqrt b))
51.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) a)
57.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.0s

Counts
207 → 207
Iterations
IterNodes
23212
1832
0297

prune2.2s

Pruning

37 alts after pruning (36 fresh and 1 done)

Merged error: 8.7b

regimes1.0s

Accuracy

47.6% (7.3b remaining)

Error of 16.1b against oracle of 8.8b and baseline of 22.7b

bsearch6.0ms

Steps
ItersRangePoint
0
622.2323332746612
633.6454832653068
627.9389082699839

simplify5.0ms

Iterations
IterNodes
229
129
024

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.7s4495×body160valid
1.2s8699×body80nan
1.1s16699×pre80true
522.0ms3505×body80valid