Details

Time bar (total: 6.7m)

sample80.0ms

Algorithm
intervals
Results
45.0ms256×body80valid
12.0ms256×pre80true

simplify1.0s

Counts
1 → 1
Iterations
IterNodes
42384
3459
2104
133
015

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 2 (+ beta alpha)) 1.0)
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
3.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite494.0ms

Algorithm
rewrite-expression-head
Rules
4338×*-un-lft-identity
2696×times-frac
2176×distribute-lft-out
779×add-sqr-sqrt add-cube-cbrt
166×associate-/l*
102×associate-/r/
53×flip3-+ flip-+
51×div-inv
20×add-cbrt-cube add-exp-log
16×associate-/r*
13×add-log-exp
10×cbrt-undiv div-exp
6×sum-log
5×fma-def
4×expm1-log1p-u pow1 log1p-expm1-u associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1230
Calls
4 calls:
113.0ms
(+ (+ 2 (+ beta alpha)) 1.0)
75.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
166.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
26.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ 2 (+ beta alpha)) 1.0)
186.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
214.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
108.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.7s

Counts
1242 → 1242
Iterations
IterNodes
24032
11405
0608

prune14.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
0.1b
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.1b
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0))
3.6b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite694.0ms

Algorithm
rewrite-expression-head
Rules
14577×*-un-lft-identity
11720×times-frac
6745×distribute-lft-out
3526×add-sqr-sqrt add-cube-cbrt
422×associate-/l*
300×associate-/r/
172×associate-/r*
167×div-inv
135×flip3-+ flip-+
64×add-exp-log
44×div-exp
34×add-cbrt-cube
20×cbrt-undiv
6×rec-exp 1-exp
5×pow1 associate-/l/
4×expm1-log1p-u clear-num frac-2neg log1p-expm1-u add-log-exp
1×pow-flip inv-pow
Counts
4 → 3702
Calls
4 calls:
77.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
79.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
170.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0))
25.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series743.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))
199.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
201.0ms
(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0))
138.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify22.3s

Counts
3714 → 3714
Iterations
IterNodes
14280
01595

prune46.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))))
0.3b
(/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1))
3.6b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.6b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite782.0ms

Algorithm
rewrite-expression-head
Rules
19826×times-frac
19081×*-un-lft-identity
7284×distribute-lft-out
6512×add-sqr-sqrt
6506×add-cube-cbrt
5220×sqrt-prod
391×div-inv
306×associate-/r/
135×associate-/l*
134×flip3-+ flip-+
66×associate-/r*
39×add-exp-log
30×add-cbrt-cube
27×div-exp
18×cbrt-undiv
6×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×1-exp associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 hypot-def
Counts
4 → 5742
Calls
4 calls:
109.0ms
(/ (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))))
62.0ms
(/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1))
9.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
9.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series789.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))))
414.0ms
(/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1))
85.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
86.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify45.8s

Counts
5754 → 5754
Iterations
IterNodes
18920
02513

prune1.5m

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
1.2b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
3.0b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
59610×*-un-lft-identity
45320×times-frac
28340×distribute-lft-out
14750×sqrt-prod
13032×add-sqr-sqrt add-cube-cbrt
1908×associate-/l*
778×associate-/r/
760×sqrt-div
390×flip3-+ flip-+
389×div-inv
34×add-cbrt-cube add-exp-log
27×associate-/r*
20×cbrt-undiv div-exp
5×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
Counts
4 → 13238
Calls
4 calls:
162.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
253.0ms
(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
52.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
32.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

series719.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
248.0ms
(/ (/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
108.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
147.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

simplify14.1s

Counts
13250 → 13250
Iterations
IterNodes
16424
02918

prune2.6m

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

66.4% (1.1b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 3.4b

bsearch81.0ms

Steps
ItersRangePoint
9
6.19458565197337e+159
4.2871002840354243e+164
6.2498429104423194e+159

simplify4.0ms

Iterations
IterNodes
232
132
026

end0.0ms

sample1.2s

Algorithm
intervals
Results
799.0ms8000×body80valid
229.0ms8000×pre80true