Details

sample64.0ms

Algorithm

intervals

Results

39.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify852.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	835
2	131
1	36
0	15

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
2.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

4338×	`*-un-lft-identity`
2696×	`times-frac`
2176×	`distribute-lft-out`
779×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
5×	`fma-def`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1234

Calls

4 calls:

91.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
84.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
163.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
33.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
166.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
218.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
124.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.7s

Counts

1246 → 1246

Iterations

Iter	Nodes
done	5000
1	1531
0	612

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ 2 (+ beta alpha)))
0.0b	(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
0.1b	(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
2.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

168×	`*-un-lft-identity`
83×	`times-frac`
71×	`distribute-lft-out`
64×	`add-exp-log`
63×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
38×	`add-cbrt-cube`
28×	`div-exp`
26×	`associate-l`
21×	`associate-r`
16×	`associate-/r*` `prod-exp`
15×	`cbrt-undiv`
10×	`associate-/r/`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `unswap-sqr` `associate-/l/`
5×	`rec-exp` `1-exp` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 219

Calls

4 calls:

33.0ms	(/ 1 (+ 2 (+ beta alpha)))
132.0ms	(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
142.0ms	(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
28.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1 (+ 2 (+ beta alpha)))
165.0ms	(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))
241.0ms	(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
103.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.0s

Counts

231 → 231

Iterations

Iter	Nodes
done	5000
1	815
0	262

prune905.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
0.9b	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
2.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite852.0ms

Algorithm

rewrite-expression-head

Rules

19157×	`*-un-lft-identity`
13943×	`times-frac`
9343×	`distribute-lft-out`
3996×	`add-sqr-sqrt` `add-cube-cbrt`
967×	`associate-/r*`
394×	`associate-/r/`
200×	`div-inv`
196×	`flip3-+` `flip-+`
54×	`add-exp-log`
39×	`associate-/l*`
36×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 4528

Calls

4 calls:

58.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
213.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
148.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
41.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
273.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
187.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
125.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify7.8s

Counts

4540 → 4540

Iterations

Iter	Nodes
done	5002
1	4817
0	1539

prune7.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ 1 (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
0.3b	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
2.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
2.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

20375×	`*-un-lft-identity`
17107×	`times-frac`
9246×	`distribute-lft-out`
5217×	`add-sqr-sqrt` `add-cube-cbrt`
4896×	`sqrt-prod`
1271×	`associate-/r*`
446×	`associate-/r/`
228×	`div-inv`
220×	`flip3-+` `flip-+`
38×	`add-exp-log`
23×	`div-exp`
18×	`add-cbrt-cube`
14×	`associate-/l*`
9×	`rec-exp` `1-exp` `pow-flip`
8×	`pow1` `cbrt-undiv` `sqrt-div`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`inv-pow`
1×	`sqrt-pow1` `pow1/2` `remove-double-div`

Counts

4 → 5205

Calls

4 calls:

87.0ms	(/ 1 (/ 1 (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
239.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
29.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
59.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series649.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ 1 (/ 1 (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
165.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (sqrt (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))))
114.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
123.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify7.9s

Counts

5217 → 5217

Iterations

Iter	Nodes
done	5000
0	2615

prune13.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.1b

regimes145.0ms

Accuracy

59.3% (1.0b remaining)

Error of 2.4b against oracle of 1.4b and baseline of 3.8b

bsearch121.0ms

Steps

Iters	Range		Point
9	2.965725879441872e+182	5.601521842704995e+187	1.4753714951235848e+185

simplify8.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
281.0ms	8000×	pre	80	true