Details

sample51.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify836.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
4	2006
3	680
2	123
1	36
0	15

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize32.0ms

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)))

rewrite1.3s

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:

136.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
408.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
502.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
240.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
207.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
233.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
125.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts

492 → 492

Iterations

Iter	Nodes
done	2008
2	2008
1	1452
0	614

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize36.0ms

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)))

rewrite1.0s

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`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
9×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `sum-log` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 479

Calls

4 calls:

37.0ms	(+ (+ alpha beta) (* beta alpha))
279.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
416.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
253.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (+ alpha beta) (* beta alpha))
147.0ms	(/ (/ (+ (+ (+ 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))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
105.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.5s

Counts

491 → 491

Iterations

Iter	Nodes
done	2007
2	2007
1	1475
0	616

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize60.0ms

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

rewrite1.7s

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×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `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 → 934

Calls

4 calls:

770.0ms	(* (/ (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)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
350.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
242.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
324.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (/ (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)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
170.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
104.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
115.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.1s

Counts

946 → 946

Iterations

Iter	Nodes
done	2000
1	2000
0	1189

prune5.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize122.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.2b	(* (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1)) 1) (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
8.9b	(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

2367×	`times-frac`
1491×	`add-sqr-sqrt`
1270×	`sqrt-prod`
1263×	`*-un-lft-identity`
749×	`add-cube-cbrt`
366×	`associate-r`
250×	`associate-l`
167×	`distribute-lft-out`
150×	`unswap-sqr`
44×	`associate-/r/`
35×	`div-inv`
24×	`flip3-+` `flip-+`
23×	`add-exp-log`
18×	`add-cbrt-cube`
8×	`pow1` `div-exp`
6×	`prod-exp`
5×	`cbrt-undiv` `rem-sqrt-square`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r*` `sqrt-div`
2×	`sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `hypot-def`

Counts

4 → 953

Calls

4 calls:

133.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
287.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
1.3s	(* (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1)) 1) (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
235.0ms	(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
107.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
158.0ms	(* (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1)) 1) (/ (sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
176.0ms	(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))

simplify2.8s

Counts

965 → 965

Iterations

Iter	Nodes
done	2001
1	2001
0	1400

prune7.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes131.0ms

Accuracy

38.6% (1.5b remaining)

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

bsearch60.0ms

Steps

Iters	Range		Point
5	1.3154968375234933e+114	3.987194372781887e+114	3.9275252152036123e+114

simplify10.0ms

Iterations

Iter	Nodes
done	36
1	36
0	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
299.0ms	8000×	pre	80	true