Details

sample61.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3944
3	680
2	123
1	36
0	15

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.3b

localize29.0ms

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))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
587×	`*-un-lft-identity`
341×	`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×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `fma-def` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 480

Calls

4 calls:

131.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
281.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
473.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
296.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
189.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
227.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
128.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.1s

Counts

492 → 492

Iterations

Iter	Nodes
done	5000
2	4622
1	1452
0	614

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b	(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1)))
1.8b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1))))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
54×	`times-frac`
34×	`add-sqr-sqrt`
32×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
17×	`flip3-+` `flip-+`
14×	`associate-/r/`
13×	`add-log-exp`
12×	`distribute-lft-out`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `sum-log`
4×	`expm1-log1p-u` `associate-/r` `associate-l` `associate-l/` `associate-*r/` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 158

Calls

4 calls:

117.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
337.0ms	(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1)))
347.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1))))
277.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
36.0ms	(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1)))
210.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ alpha beta) (* 2 1))))
104.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.2s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	3770
1	799
0	259

prune837.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta)) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (* 2 1)))
0.0b	(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta))
1.8b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta)) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (* 2 1))))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
116×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
55×	`flip3-+` `flip-+`
42×	`associate-*l/`
41×	`distribute-lft-out`
32×	`frac-add`
30×	`associate-/r/`
22×	`associate-/l*`
20×	`frac-times`
13×	`add-cbrt-cube` `add-exp-log`
10×	`associate-*r/`
7×	`associate-/r*` `div-inv`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l/`
2×	`distribute-rgt-in` `associate-+l+` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `fma-def` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 235

Calls

4 calls:

188.0ms	(+ (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta)) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (* 2 1)))
356.0ms	(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta))
485.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta)) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (* 2 1))))
277.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta)) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (* 2 1)))
33.0ms	(* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta))
227.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ alpha beta)) (* (+ (+ (+ alpha beta) (* 2 1)) 1.0) (* 2 1))))
139.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.5s

Counts

247 → 247

Iterations

Iter	Nodes
done	5003
1	1394
0	437

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

localize86.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b	(/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))
0.1b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
16.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

193×	`times-frac`
189×	`*-un-lft-identity`
91×	`add-sqr-sqrt` `add-cube-cbrt`
49×	`distribute-lft-out`
29×	`associate-/l*`
25×	`difference-of-squares`
16×	`associate-/r/`
13×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
11×	`associate-/r*`
8×	`div-inv`
7×	`flip3--` `flip--`
6×	`sum-log`
5×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`expm1-log1p-u` `pow1` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `fma-def` `frac-2neg`
1×	`+-commutative` `associate-+l+` `div-sub`

Counts

4 → 233

Calls

4 calls:

95.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
116.0ms	(/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))
529.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
280.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
60.0ms	(/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))
207.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
154.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))

simplify2.5s

Counts

245 → 245

Iterations

Iter	Nodes
done	5004
2	2921
1	926
0	353

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

regimes114.0ms

Accuracy

51.6% (1.5b remaining)

Error of 2.8b against oracle of 1.3b and baseline of 4.3b

bsearch136.0ms

Steps

Iters	Range		Point
10	1.972616410681917e+143	1.347314599677347e+159	1.3353325288374214e+154

simplify4.0ms

Iterations

Iter	Nodes
done	37
1	37
0	25

end0.0ms

sample1.8s

Algorithm

intervals

Results

867.0ms	8000×	body	80	valid
731.0ms	8000×	pre	80	true