Details

Time bar (total: 42.3s)

sample90.0ms

Algorithm
intervals
Results
58.0ms256×body80valid
12.0ms256×pre80true

simplify753.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
3809
2127
136
015

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize39.0ms

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))
2.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite789.0ms

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:
13.0ms
(+ (* alpha beta) (+ beta alpha))
221.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
296.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
185.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (* alpha beta) (+ beta alpha))
183.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
219.0ms
(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
101.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.9s

Counts
1229 → 1229
Iterations
IterNodes
done5000
11641
0608

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ 2 (+ beta alpha)))
0.0b
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
0.1b
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
2.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite543.0ms

Algorithm
rewrite-expression-head
Rules
168×*-un-lft-identity
83×times-frac
71×distribute-lft-out
64×add-exp-log
63×add-sqr-sqrt
46×add-cube-cbrt
38×add-cbrt-cube
28×div-exp
26×associate-*l*
21×associate-*r*
16×associate-/r* prod-exp
15×cbrt-undiv
10×associate-/r/
8×cbrt-unprod associate-/l*
7×pow1
6×flip3-+ flip-+ unswap-sqr associate-/l/
5×rec-exp 1-exp div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×frac-times associate-*l/ associate-*r/ un-div-inv
1×pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 211
Calls
4 calls:
27.0ms
(/ 1 (+ 2 (+ beta alpha)))
224.0ms
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
141.0ms
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
145.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ 1 (+ 2 (+ beta alpha)))
181.0ms
(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
196.0ms
(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
114.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.1s

Counts
223 → 223
Iterations
IterNodes
done5001
1815
0255

prune800.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b
(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
0.9b
(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
2.4b
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
19157×*-un-lft-identity
13943×times-frac
9343×distribute-lft-out
3996×add-sqr-sqrt add-cube-cbrt
967×associate-/r*
394×associate-/r/
200×div-inv
196×flip3-+ flip-+
54×add-exp-log
39×associate-/l*
36×div-exp
34×add-cbrt-cube
20×cbrt-undiv
5×pow1 associate-/l/
4×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
1×pow-flip inv-pow
Counts
4 → 4520
Calls
4 calls:
206.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
301.0ms
(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
239.0ms
(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
118.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series794.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
279.0ms
(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
214.0ms
(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
111.0ms
(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify6.9s

Counts
4532 → 4532
Iterations
IterNodes
done5002
14702
01531

prune7.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.1b

localize111.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (/ (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1)) (/ (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (/ (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
2.7b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.7b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
2.7b
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
7453×*-un-lft-identity
5671×times-frac
3546×distribute-lft-out
2226×cbrt-prod
1930×add-sqr-sqrt
1904×associate-*r*
1633×add-cube-cbrt
562×add-exp-log
370×div-exp
168×prod-exp
142×add-cbrt-cube
126×cbrt-undiv
110×associate-/r/
72×1-exp unswap-sqr
60×cbrt-unprod div-inv
57×flip3-+ flip-+
30×associate-*l*
6×pow1 cbrt-div
4×insert-posit16 add-log-exp
3×pow1/3
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 2192
Calls
4 calls:
1.3s
(* (/ (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1)) (/ (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (/ (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
32.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
37.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
40.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series657.0ms

Counts
4 → 12
Calls
4 calls:
335.0ms
(* (/ (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (* (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))) 1) 1)) (/ (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (/ (/ (cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
94.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
111.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
116.0ms
(cbrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify5.3s

Counts
2204 → 2204
Iterations
IterNodes
done5001
01541

prune6.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.1b

regimes141.0ms

Accuracy

0% (2.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done24
124
015

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.7s8000×body80valid
337.0ms8000×pre80true