Details

Time bar (total: 41.4s)

sample84.0ms

Algorithm
intervals
Results
47.0ms256×body80valid
13.0ms256×pre80true

simplify845.0ms

Counts
1 → 1
Iterations
IterNodes
42244
3434
2100
133
015

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* alpha beta) (+ beta alpha))
0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
4.8b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite877.0ms

Algorithm
rewrite-expression-head
Rules
4323×*-un-lft-identity
2696×times-frac
2167×distribute-lft-out
778×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*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+r+
Counts
4 → 1217
Calls
4 calls:
23.0ms
(+ (* alpha beta) (+ beta alpha))
277.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
281.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
214.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series584.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* alpha beta) (+ beta alpha))
204.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
234.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
120.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.6s

Counts
1229 → 1229
Iterations
IterNodes
24330
11451
0608

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ beta alpha) (* alpha beta))
0.0b
(/ (/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
4.8b
(/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
4323×*-un-lft-identity
2696×times-frac
2167×distribute-lft-out
778×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*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 insert-posit16 associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+l+
Counts
4 → 1217
Calls
4 calls:
37.0ms
(+ (+ beta alpha) (* alpha beta))
265.0ms
(/ (/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
397.0ms
(/ (/ (/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
291.0ms
(/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (+ beta alpha) (* alpha beta))
199.0ms
(/ (/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
245.0ms
(/ (/ (/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
149.0ms
(/ (+ 1.0 (+ (+ beta alpha) (* alpha beta))) (+ 2 (+ beta alpha)))

simplify2.6s

Counts
1229 → 1229
Iterations
IterNodes
24423
11446
0607

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize53.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (/ (* (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta)))) (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))) 1) (/ (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta)))) (+ 2 (+ beta alpha))))
5.0b
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))
5.0b
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))
5.0b
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))

rewrite733.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
50×times-frac
48×add-sqr-sqrt
41×associate-*r*
37×add-exp-log
35×cbrt-prod
29×distribute-lft-out
27×add-cube-cbrt
18×add-cbrt-cube
14×prod-exp
13×div-exp
9×unswap-sqr
8×cbrt-unprod
7×cbrt-undiv associate-*l*
6×pow1 cbrt-div
4×flip3-+ 1-exp flip-+ insert-posit16 add-log-exp
3×pow1/3
2×associate-/r/ div-inv
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 131
Calls
4 calls:
574.0ms
(* (/ (* (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta)))) (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))) 1) (/ (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta)))) (+ 2 (+ beta alpha))))
56.0ms
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))
50.0ms
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))
51.0ms
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (/ (* (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta)))) (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))) 1) (/ (cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta)))) (+ 2 (+ beta alpha))))
68.0ms
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))
82.0ms
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))
92.0ms
(cbrt (+ 1.0 (+ (+ beta alpha) (* alpha beta))))

simplify977.0ms

Counts
143 → 143
Iterations
IterNodes
22039
1715
0220

prune789.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
1.2b
(* (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))))
4.7b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
4.7b
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

rewrite3.4s

Algorithm
rewrite-expression-head
Rules
17148×*-un-lft-identity
13907×times-frac
7902×distribute-lft-out
5553×sqrt-prod
5322×add-sqr-sqrt
4132×add-cube-cbrt
1905×associate-*r*
717×associate-*l*
234×associate-/r/
211×associate-/l*
207×unswap-sqr
173×add-exp-log
153×div-inv
122×div-exp
119×flip3-+ flip-+
93×add-cbrt-cube
54×cbrt-undiv
32×prod-exp
20×1-exp
16×cbrt-unprod
10×sqrt-div
9×associate-/r*
8×pow1
4×insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 5063
Calls
4 calls:
388.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
2.4s
(* (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))))
60.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
69.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series904.0ms

Counts
4 → 12
Calls
4 calls:
529.0ms
(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
232.0ms
(* (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))))
60.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
83.0ms
(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify7.7s

Counts
5075 → 5075
Iterations
IterNodes
15899
01857

prune9.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.6b

regimes106.0ms

Accuracy

14.1% (2.4b remaining)

Error of 3.7b against oracle of 1.3b and baseline of 4.1b

bsearch88.0ms

Steps
ItersRangePoint
6
213942974053.52148
2655905981000.518
2593180110544.6416

simplify10.0ms

Iterations
IterNodes
237
137
029

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.6s8000×body80valid
279.0ms8000×pre80true