Details

Time bar (total: 35.6s)

sample45.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
5.0ms256×pre80true

simplify819.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3589
2119
133
014

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize44.0ms

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))))
3.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite213.0ms

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:
9.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
39.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
82.0ms
(/ (/ (/ (+ 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))))
30.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series608.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
228.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
238.0ms
(/ (/ (/ (+ 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))))
108.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.6s

Counts
434 → 434
Iterations
IterNodes
done5001
11328
0516

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize83.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
0.6b
(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
3.3b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.3b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite410.0ms

Algorithm
rewrite-expression-head
Rules
3583×times-frac
2190×*-un-lft-identity
1966×sqrt-prod
1552×add-sqr-sqrt
1546×add-cube-cbrt
322×distribute-lft-out
179×associate-/l*
65×div-inv
18×add-cbrt-cube add-exp-log
13×associate-/r*
9×cbrt-undiv div-exp
6×pow1 sqrt-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/r/ hypot-def associate-/l/
Counts
4 → 1496
Calls
4 calls:
121.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
29.0ms
(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
12.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
7.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series644.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (+ 1.0 (fma 2.0 1.0 (+ beta alpha)))))
242.0ms
(/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
98.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
90.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify3.2s

Counts
1508 → 1508
Iterations
IterNodes
done5001
13037
01176

prune7.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize109.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (sqrt (sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
3.3b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.3b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.3b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
122×sqrt-prod
70×*-un-lft-identity
60×times-frac
59×add-sqr-sqrt
50×add-cube-cbrt
10×sqrt-div distribute-lft-out associate-/l*
7×pow1
6×associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
2×associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 150
Calls
4 calls:
24.0ms
(/ (sqrt (sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
13.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
13.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
11.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(/ (sqrt (sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
88.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
93.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
65.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify1.9s

Counts
162 → 162
Iterations
IterNodes
done5000
21531
1473
0226

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize35.0ms

Local error

Found 4 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 2.0 1.0 (+ beta alpha))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
0.3b
(/ 1 (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
3.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
3551×times-frac
2334×*-un-lft-identity
1402×add-sqr-sqrt add-cube-cbrt
466×distribute-lft-out
271×associate-/r*
96×div-inv
54×add-exp-log
36×div-exp
34×add-cbrt-cube
27×associate-/l*
20×cbrt-undiv
6×associate-/r/
5×pow1 associate-/l/
4×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp log1p-expm1-u add-log-exp
2×flip3-+ flip-+
1×pow-flip inv-pow
Counts
4 → 1290
Calls
4 calls:
19.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
63.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
96.0ms
(/ 1 (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
14.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series944.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
355.0ms
(/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))))
244.0ms
(/ 1 (/ (+ 1.0 (fma 2.0 1.0 (+ beta alpha))) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))))
128.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify4.7s

Counts
1302 → 1302
Iterations
IterNodes
done5001
14066
01307

prune6.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

regimes146.0ms

Accuracy

20.6% (2.0b remaining)

Error of 3.3b against oracle of 1.4b and baseline of 3.8b

bsearch81.0ms

Steps
ItersRangePoint
8
7.075738003349105e+57
4.9544948277492785e+60
3.1091191902615784e+60

simplify5.0ms

Iterations
IterNodes
done30
130
024

end0.0ms

sample1.1s

Algorithm
intervals
Results
660.0ms8000×body80valid
237.0ms8000×pre80true