Details

sample46.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify2.9s

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize51.0ms

Local error

Found 3 expressions with local error:

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)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`associate-/l/`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

3 → 459

Calls

3 calls:

322.0ms

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

517.0ms

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

257.0ms

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

series526.0ms

Counts

3 → 9

Calls

3 calls:

187.0ms

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

231.0ms

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

107.0ms

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

simplify2.9s

Counts

468 → 468

Iterations

Iter	Nodes
done	5000
2	4448
1	1399
0	588

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

3614×	`times-frac`
2164×	`*-un-lft-identity`
1424×	`add-sqr-sqrt` `add-cube-cbrt`
370×	`distribute-lft-out`
192×	`associate-/l*`
152×	`associate-/r/`
89×	`div-inv`
84×	`associate-/r*`
65×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1` `associate-/l/`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1344

Calls

4 calls:

209.0ms	(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
189.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
417.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
281.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
184.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
228.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
128.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify4.7s

Counts

1356 → 1356

Iterations

Iter	Nodes
done	5005
1	4252
0	1600

prune6.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))))
0.2b	(/ 1 (sqrt (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ 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)))

rewrite951.0ms

Algorithm

rewrite-expression-head

Rules

1116×	`times-frac`
660×	`*-un-lft-identity`
500×	`add-sqr-sqrt` `add-cube-cbrt`
472×	`sqrt-prod`
130×	`associate-/r*`
80×	`distribute-lft-out`
62×	`associate-/r/`
36×	`div-inv`
28×	`flip3-+` `flip-+`
16×	`add-exp-log`
14×	`associate-/l*`
12×	`add-cbrt-cube`
8×	`pow1`
6×	`div-exp` `pow-flip`
4×	`expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`rec-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `inv-pow`

Counts

4 → 622

Calls

4 calls:

181.0ms	(/ 1 (sqrt (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))))
156.0ms	(/ 1 (sqrt (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))))
302.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
277.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(/ 1 (sqrt (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))))
264.0ms	(/ 1 (sqrt (/ (+ (+ alpha beta) (* 2 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))))
143.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
115.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.0s

Counts

634 → 634

Iterations

Iter	Nodes
done	5004
2	2797
1	1122
0	618

prune5.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2))) (+ (+ alpha (+ beta 2)) 1.0))
0.1b	(* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2)))
0.3b	(/ 1 (* (* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2))) (+ (+ alpha (+ beta 2)) 1.0)))
3.4b	(/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite861.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
54×	`add-exp-log`
47×	`distribute-lft-out`
44×	`times-frac`
34×	`add-sqr-sqrt` `frac-times` `add-cbrt-cube`
29×	`flip3-+` `add-cube-cbrt` `flip-+`
27×	`associate-l`
22×	`prod-exp`
21×	`associate-/r/`
18×	`associate-*r/`
17×	`pow1` `associate-*l/`
14×	`div-exp`
12×	`cbrt-unprod`
11×	`associate-r`
8×	`cbrt-undiv` `associate-/l*`
7×	`pow-prod-down`
5×	`associate-/r*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `pow-flip`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative` `unswap-sqr` `associate-/l/`
1×	`inv-pow`

Counts

4 → 206

Calls

4 calls:

280.0ms	(* (* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2))) (+ (+ alpha (+ beta 2)) 1.0))
129.0ms	(* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2)))
368.0ms	(/ 1 (* (* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2))) (+ (+ alpha (+ beta 2)) 1.0)))
76.0ms	(/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha))))

series910.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(* (* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2))) (+ (+ alpha (+ beta 2)) 1.0))
171.0ms	(* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2)))
247.0ms	(/ 1 (* (* (/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ alpha (+ beta 2))) (+ (+ alpha (+ beta 2)) 1.0)))
152.0ms	(/ (+ alpha (+ beta 2)) (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify3.0s

Counts

218 → 218

Iterations

Iter	Nodes
done	5000
2	4700
1	1055
0	291

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes113.0ms

Accuracy

71.4% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 3.4b

bsearch122.0ms

Steps

Iters	Range		Point
10	8.66163765993512e+145	9.653347967105197e+157	2.7175934019048462e+157

simplify4.0ms

Iterations

Iter	Nodes
done	36
1	36
0	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

693.0ms	8000×	body	80	valid
317.0ms	8000×	pre	80	true