Details

Time bar (total: 2.5m)

sample47.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
6.0ms256×pre80true

simplify515.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3589
2119
133
014

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
3.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
6×add-log-exp
4×expm1-log1p-u pow1 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg flip3-+ flip-+
2×associate-/r/
1×+-commutative associate-+r+ sum-log fma-udef
Counts
4 → 422
Calls
4 calls:
4.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
37.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
54.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
21.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series623.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
210.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
260.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
126.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify637.0ms

Counts
434 → 434
Iterations
IterNodes
done5001
11328
0516

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.3b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ (+ 3.0 beta) alpha))
3.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
872×times-frac
765×*-un-lft-identity
360×add-sqr-sqrt add-cube-cbrt
229×distribute-lft-out
72×associate-/l*
31×div-inv
19×add-cbrt-cube add-exp-log
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×flip3-+ associate-/r/ flip-+
Counts
3 → 457
Calls
3 calls:
39.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
112.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ (+ 3.0 beta) alpha))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series531.0ms

Counts
3 → 9
Calls
3 calls:
203.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
233.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ (+ 3.0 beta) alpha))
94.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify735.0ms

Counts
466 → 466
Iterations
IterNodes
done5001
11311
0504

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ beta (+ 3.0 alpha)) (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
0.2b
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
0.5b
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
3.6b
(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite3.4s

Algorithm
rewrite-expression-head
Rules
51668×times-frac
33630×*-un-lft-identity
18552×add-sqr-sqrt add-cube-cbrt
10464×sqrt-prod
8635×distribute-lft-out
1435×div-inv
165×associate-/l*
138×associate-/r/
100×associate-/r*
79×add-exp-log
57×div-exp
49×add-cbrt-cube
32×cbrt-undiv
13×pow1
8×pow-flip
6×pow-div
5×rec-exp sqrt-pow1 pow1/2 1-exp
4×expm1-log1p-u clear-num frac-2neg log1p-expm1-u add-log-exp associate-/l/
2×inv-pow
1×flip3-+ flip-+
Counts
4 → 12086
Calls
4 calls:
430.0ms
(/ (/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ beta (+ 3.0 alpha)) (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
28.0ms
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
11.0ms
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
27.0ms
(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(/ (/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ beta (+ 3.0 alpha)) (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
74.0ms
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
109.0ms
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
116.0ms
(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify4.7s

Counts
12098 → 12098
Iterations
IterNodes
done7053
07053

prune49.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ beta (+ 3.0 alpha)) (+ 1.0 (fma alpha beta (+ beta alpha))))) (fma 2.0 1.0 (+ beta alpha)))
0.2b
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
0.5b
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
3.6b
(/ (+ beta (+ 3.0 alpha)) (+ 1.0 (fma alpha beta (+ beta alpha))))

rewrite4.3s

Algorithm
rewrite-expression-head
Rules
60903×times-frac
38302×*-un-lft-identity
21945×add-sqr-sqrt add-cube-cbrt
12624×sqrt-prod
9269×distribute-lft-out
3571×associate-/l*
1287×div-inv
1094×associate-/r/
546×flip3-+ flip-+
66×add-exp-log
47×div-exp
42×add-cbrt-cube
27×cbrt-undiv
19×associate-/r*
13×pow1
8×pow-flip
6×pow-div
5×sqrt-pow1 pow1/2
4×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp log1p-expm1-u add-log-exp associate-/l/
2×inv-pow
Counts
4 → 14477
Calls
4 calls:
1.2s
(/ (/ (/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ beta (+ 3.0 alpha)) (+ 1.0 (fma alpha beta (+ beta alpha))))) (fma 2.0 1.0 (+ beta alpha)))
16.0ms
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
5.0ms
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
59.0ms
(/ (+ beta (+ 3.0 alpha)) (+ 1.0 (fma alpha beta (+ beta alpha))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(/ (/ (/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (+ beta (+ 3.0 alpha)) (+ 1.0 (fma alpha beta (+ beta alpha))))) (fma 2.0 1.0 (+ beta alpha)))
66.0ms
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
108.0ms
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
148.0ms
(/ (+ beta (+ 3.0 alpha)) (+ 1.0 (fma alpha beta (+ beta alpha))))

simplify6.5s

Counts
14489 → 14489
Iterations
IterNodes
done10192
010192

prune1.1m

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes207.0ms

Accuracy

60.3% (1.4b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 3.5b

bsearch97.0ms

Steps
ItersRangePoint
8
1.8081809151522212e+136
9.209084411088349e+140
8.976072120634706e+140

simplify5.0ms

Iterations
IterNodes
done37
137
030

end0.0ms

sample1.2s

Algorithm
intervals
Results
760.0ms8000×body80valid
171.0ms8000×pre80true