Details

Time bar (total: 38.8s)

sample50.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
6.0ms256×pre80true

simplify895.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3589
2119
133
014

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize22.0ms

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)))

rewrite146.0ms

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:
5.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
24.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
56.0ms
(/ (/ (/ (+ 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))))
24.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series623.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ 1.0 (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)))
246.0ms
(/ (/ (/ (+ 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))))
123.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.6s

Counts
434 → 434
Iterations
IterNodes
done5001
11328
0516

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))))
0.5b
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
1.8b
(/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
2.9b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

rewrite557.0ms

Algorithm
rewrite-expression-head
Rules
7388×times-frac
3887×*-un-lft-identity
2997×add-sqr-sqrt add-cube-cbrt
1713×sqrt-prod
445×distribute-lft-out
190×div-inv
129×associate-/r*
54×add-exp-log
36×div-exp
34×add-cbrt-cube
32×associate-/l*
25×associate-/r/
20×cbrt-undiv
6×pow1
4×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp log1p-expm1-u add-log-exp
3×pow-flip associate-/l/
1×sqrt-pow1 flip3-+ pow1/2 flip-+ inv-pow
Counts
4 → 2330
Calls
4 calls:
119.0ms
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))))
11.0ms
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
19.0ms
(/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
21.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))))
94.0ms
(/ 1 (sqrt (fma 2.0 1.0 (+ beta alpha))))
304.0ms
(/ (fma 2.0 1.0 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))))
169.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

simplify3.6s

Counts
2342 → 2342
Iterations
IterNodes
done5000
02232

prune11.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 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)))))
0.1b
(/ (sqrt (/ (/ (+ 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)))
3.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite974.0ms

Algorithm
rewrite-expression-head
Rules
1770×times-frac
1168×*-un-lft-identity
897×add-sqr-sqrt
694×add-cube-cbrt
681×sqrt-prod
227×distribute-lft-out
226×associate-*r*
169×associate-*l*
63×associate-/l*
53×div-inv
45×unswap-sqr
27×add-exp-log
22×add-cbrt-cube
10×associate-/r* div-exp
7×cbrt-undiv
6×pow1 prod-exp
5×associate-/l/
4×expm1-log1p-u flip3-+ associate-/r/ cbrt-unprod flip-+ log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×1-exp
1×frac-times sqrt-div pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 830
Calls
4 calls:
812.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 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)))))
43.0ms
(/ (sqrt (/ (/ (+ 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))))
15.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
23.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series602.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(* (/ (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))) 1) (/ (sqrt (/ (/ (+ 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)))))
174.0ms
(/ (sqrt (/ (/ (+ 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))))
113.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
104.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify3.6s

Counts
842 → 842
Iterations
IterNodes
done5000
12899
01014

prune5.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.3b

localize118.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
48×times-frac
40×add-sqr-sqrt add-cube-cbrt
16×distribute-lft-out associate-/l*
12×associate-/r* add-cbrt-cube add-exp-log
8×associate-/l/
4×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ log1p-expm1-u div-inv add-log-exp
Counts
4 → 140
Calls
4 calls:
17.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
15.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
28.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
30.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series473.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
115.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
122.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
108.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify1.1s

Counts
152 → 152
Iterations
IterNodes
done5001
2745
1180
079

prune1.7s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 1.3b

regimes214.0ms

Accuracy

48.6% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch158.0ms

Steps
ItersRangePoint
9
6.517508680297973e+213
6.266295390107009e+222
3.8920302051817933e+214

simplify11.0ms

Iterations
IterNodes
done42
142
034

end0.0ms

sample1.3s

Algorithm
intervals
Results
815.0ms8000×body80valid
157.0ms8000×pre80true