Details

sample61.0ms

Algorithm

intervals

Results

34.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify959.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2384
3	459
2	104
1	33
0	15

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize43.0ms

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)))

rewrite385.0ms

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:

68.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
58.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
151.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
40.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
192.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
604.0ms	(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
140.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.0s

Counts

1246 → 1246

Iterations

Iter	Nodes
2	4034
1	1422
0	612

prune4.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.2b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite785.0ms

Algorithm

rewrite-expression-head

Rules

14483×	`*-un-lft-identity`
11682×	`times-frac`
6707×	`distribute-lft-out`
3513×	`add-sqr-sqrt` `add-cube-cbrt`
512×	`associate-/l*`
316×	`associate-/r/`
179×	`div-inv`
138×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
41×	`associate-/r*`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 3689

Calls

4 calls:

26.0ms	(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))
89.0ms	(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))
213.0ms	(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
44.0ms	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))

series685.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))
176.0ms	(/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha)))
262.0ms	(/ (/ (/ 1 (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
136.0ms	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify6.8s

Counts

3701 → 3701

Iterations

Iter	Nodes
1	4292
0	1610

prune12.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
0.6b	(/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
2.4b	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
2.4b	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

27028×	`*-un-lft-identity`
25874×	`times-frac`
11370×	`distribute-lft-out`
10728×	`sqrt-prod`
8422×	`add-sqr-sqrt` `add-cube-cbrt`
756×	`associate-/l*`
588×	`associate-/r/`
344×	`div-inv`
256×	`flip3-+` `flip-+`
84×	`sqrt-div`
47×	`add-exp-log`
34×	`div-exp`
26×	`associate-/r*` `add-cbrt-cube`
14×	`cbrt-undiv`
7×	`1-exp`
6×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp`

Counts

4 → 7626

Calls

4 calls:

213.0ms	(/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
222.0ms	(/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
86.0ms	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
90.0ms	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
197.0ms	(/ (/ (/ 1 (sqrt (/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha)))))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
120.0ms	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))
157.0ms	(/ (+ 2 (+ beta alpha)) (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify22.5s

Counts

7638 → 7638

Iterations

Iter	Nodes
1	9845
0	3752

prune38.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (- 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
1.5b	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
2.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
12.9b	(* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (- 2 (+ beta alpha)))

rewrite454.0ms

Algorithm

rewrite-expression-head

Rules

518×	`*-un-lft-identity`
417×	`times-frac`
193×	`distribute-lft-out`
187×	`add-sqr-sqrt`
176×	`add-cube-cbrt`
110×	`associate-l`
54×	`difference-of-squares`
34×	`add-cbrt-cube` `add-exp-log`
31×	`associate-/l*`
26×	`associate-/r/`
24×	`prod-diff`
15×	`associate-/r*`
14×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-exp`
13×	`div-inv`
12×	`flip3-+` `flip-+`
8×	`associate-/l/`
6×	`pow1` `flip3--` `associate-r` `prod-exp` `cbrt-unprod` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `unswap-sqr`
2×	`sub-neg` `associate-*l/` `distribute-lft-out--`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 413

Calls

4 calls:

147.0ms	(/ (* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (- 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
72.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
45.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
180.0ms	(* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (- 2 (+ beta alpha)))

series1.0s

Counts

4 → 12

Calls

4 calls:

285.0ms	(/ (* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (- 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
251.0ms	(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha))))
125.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
346.0ms	(* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (- (* 2 2) (* (+ beta alpha) (+ beta alpha)))) (- 2 (+ beta alpha)))

simplify3.7s

Counts

425 → 425

Iterations

Iter	Nodes
2	5428
1	1444
0	480

prune3.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes135.0ms

Accuracy

74.8% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 3.5b

bsearch121.0ms

Steps

Iters	Range		Point
9	5.720656236215882e+160	1.474456540048641e+169	5.874077370608373e+160

simplify10.0ms

Iterations

Iter	Nodes
2	31
1	31
0	26

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
262.0ms	8000×	pre	80	true