Details

Time bar (total: 30.7s)

sample68.0ms

Algorithm
intervals
Results
39.0ms256×body80valid
10.0ms256×pre80true

simplify643.0ms

Counts
1 → 1
Iterations
IterNodes
done2001
42001
3641
2119
136
015

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-cbrt-cube add-exp-log
13×add-log-exp
10×cbrt-undiv associate-/r* div-exp
6×sum-log
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
1×+-commutative associate-+l+
Counts
4 → 469
Calls
4 calls:
115.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
292.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
408.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
210.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
176.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
175.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
108.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.3s

Counts
481 → 481
Iterations
IterNodes
done2005
22005
11435
0606

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize29.0ms

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 1))) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

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-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* 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 → 467
Calls
4 calls:
26.0ms
(+ (+ alpha beta) (* beta alpha))
289.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
407.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
313.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ alpha beta) (* beta alpha))
162.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
209.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
105.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.4s

Counts
479 → 479
Iterations
IterNodes
done2002
22002
11457
0608

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
0.1b
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
1930×times-frac
1248×*-un-lft-identity
945×add-sqr-sqrt
777×sqrt-prod
742×add-cube-cbrt
258×associate-*r*
243×distribute-lft-out
193×associate-*l*
104×associate-/r/
71×associate-/l*
54×flip3-+ flip-+
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×cbrt-unprod insert-posit16 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 → 926
Calls
4 calls:
878.0ms
(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
333.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
273.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
371.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series687.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1)))))
182.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
123.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
155.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.4s

Counts
938 → 938
Iterations
IterNodes
done2000
12000
01183

prune6.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1)) 1) (* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
543×times-frac
363×sqrt-prod
330×*-un-lft-identity
252×add-sqr-sqrt add-cube-cbrt
214×associate-*l*
92×add-exp-log
51×add-cbrt-cube
39×prod-exp distribute-lft-out
38×div-exp
24×associate-/r/
18×cbrt-unprod
16×cbrt-undiv div-inv
15×flip3-+ flip-+
13×1-exp
12×associate-/l*
9×pow1 associate-/r*
6×associate-/l/
5×frac-times associate-*r/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*l/
1×associate-*r* *-commutative
Counts
4 → 372
Calls
4 calls:
901.0ms
(* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1)) 1) (* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))))
254.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
237.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
206.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1)) 1) (* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))))
102.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
87.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
107.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.5s

Counts
384 → 384
Iterations
IterNodes
done2003
22003
11704
0615

prune3.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes116.0ms

Accuracy

38.7% (1.5b remaining)

Error of 2.7b against oracle of 1.2b and baseline of 3.6b

bsearch63.0ms

Steps
ItersRangePoint
5
1.3154968375234933e+114
3.987194372781887e+114
3.9275252152036123e+114

simplify4.0ms

Iterations
IterNodes
done36
136
027

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8000×body80valid
264.0ms8000×pre80true