Details

Time bar (total: 13.3s)

sample23.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms256×pre80true

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01435
13335
211035
348035
4239835
done500035

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* beta alpha))
172.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
257.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
147.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
142.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
152.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify554.0ms

Counts
475 → 475
Iterations

Useful iterations: done (528.0ms)

IterNodesCost
060425900
1150925129
done500024972

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b
(/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite995.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* beta alpha))
300.0ms
(/ (/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
371.0ms
(/ (/ (/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
271.0ms
(/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
140.0ms
(/ (/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms
(/ (/ (/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
77.0ms
(/ (+ (pow (+ (+ alpha beta) (* beta alpha)) 1) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify571.0ms

Counts
475 → 475
Iterations

Useful iterations: done (544.0ms)

IterNodesCost
060627208
1151325117
done500024960

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ (/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
3.6b
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))
3.6b
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))

rewrite377.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
150×sqrt-prod
132×*-un-lft-identity
92×add-sqr-sqrt
90×add-cube-cbrt
55×associate-/l*
21×distribute-lft-out
18×add-exp-log
14×associate-/r/ add-cbrt-cube
12×cbrt-div flip3-+ sqrt-div flip-+
7×cbrt-undiv div-exp associate-/r*
6×pow1
4×frac-times div-inv add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×sqrt-undiv
Counts
4 → 228
Calls
4 calls:
90.0ms
(/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
179.0ms
(/ (/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
47.0ms
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))
48.0ms
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))

series569.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
370.0ms
(/ (/ (sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
45.0ms
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))
51.0ms
(sqrt (+ 1.0 (+ (+ alpha beta) (* beta alpha))))

simplify917.0ms

Counts
240 → 240
Iterations

Useful iterations: done (906.0ms)

IterNodesCost
03269833
17919235
222308864
done50008856

prune752.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.1b
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.3b
(* (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.6b
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite570.0ms

Algorithm
rewrite-expression-head
Rules
239×times-frac
194×*-un-lft-identity
144×add-sqr-sqrt
116×add-cube-cbrt
66×associate-*r*
50×add-exp-log
38×distribute-lft-out
32×add-cbrt-cube
26×associate-/r/
24×div-exp
19×associate-/l*
18×associate-*l*
15×flip3-+ flip-+
13×cbrt-undiv div-inv
10×prod-exp
9×add-log-exp
8×unswap-sqr
7×associate-/r*
6×pow1 cbrt-unprod
3×rec-exp 1-exp sum-log associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times associate-+l+ associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 266
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* beta alpha))
91.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
321.0ms
(* (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
130.0ms
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
70.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
153.0ms
(* (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
78.0ms
(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Counts
278 → 278
Iterations

Useful iterations: 2 (744.0ms)

IterNodesCost
037810097
111919469
241748734
done50008734

prune572.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes70.0ms

Accuracy

56.2% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch60.0ms

Steps
ItersRangePoint
8
4.8266542845792594e+173
1.0069133071674746e+178
8.48564295701033e+177

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02870
14268
done4268

end0.0ms

sample550.0ms

Algorithm
intervals
Results
311.0ms8000×body80valid
99.0ms8000×pre80true