Details

sample71.0ms

Algorithm

intervals

Results

16.0ms	194×	body	80	valid
10.0ms	22×	body	640	valid
8.0ms	20×	body	1280	valid
7.0ms	256×	pre	80	true
4.0ms	15×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2747
3	478
2	106
1	31
0	15

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

0.1b

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

14.7b

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
156×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
24×	`associate-/l*`
20×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`flip3-+` `flip3--` `flip-+` `fma-udef` `flip--`

Counts

3 → 169

Calls

3 calls:

18.0ms

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

30.0ms

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

0.0ms

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

series622.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms

(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))

256.0ms

(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))

255.0ms

(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify2.0s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	2673
1	620
0	250

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
0.1b	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
1.5b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
3.1b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

305×	`times-frac`
278×	`*-un-lft-identity`
207×	`add-sqr-sqrt`
136×	`add-cube-cbrt`
82×	`associate-l`
40×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
24×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-r` `associate-/r/` `log1p-expm1-u`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`distribute-rgt-in` `frac-times` `associate-+l+` `clear-num` `frac-2neg` `distribute-lft-in` `associate-*r/`
1×	`+-commutative` `sum-log` `fma-def` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 288

Calls

4 calls:

13.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
31.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
104.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
27.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series991.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
211.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
419.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
276.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify1.4s

Counts

300 → 300

Iterations

Iter	Nodes
done	5001
1	1337
0	363

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha))))
0.1b	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
1.5b	(* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
3.1b	(+ (* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
381×	`*-un-lft-identity`
374×	`add-sqr-sqrt`
249×	`add-cube-cbrt`
169×	`prod-diff`
54×	`associate-l`
49×	`div-inv`
40×	`distribute-lft-out--` `difference-of-squares`
26×	`distribute-lft-out`
13×	`fma-neg`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-rgt-out--`
8×	`add-log-exp`
6×	`pow1`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-/r` `associate-r*` `associate-/r/` `log1p-expm1-u` `associate-/l/`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `associate-+l+` `distribute-lft-in` `flip3--` `div-exp` `prod-exp` `associate-*r/` `frac-sub` `cbrt-unprod` `flip--` `sub-div` `unswap-sqr`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 390

Calls

4 calls:

46.0ms	(- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha))))
125.0ms	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
111.0ms	(* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
38.0ms	(+ (* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series811.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha))))
243.0ms	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
203.0ms	(* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
213.0ms	(+ (* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify2.0s

Counts

402 → 402

Iterations

Iter	Nodes
done	5001
1	1639
0	551

prune3.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
0.3b	(* alpha (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
1.3b	(* beta (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
3.1b	(+ (* alpha (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
262×	`*-un-lft-identity`
250×	`add-sqr-sqrt`
108×	`associate-r`
84×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
37×	`distribute-lft-out`
29×	`div-inv`
16×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-rgt-out--`
12×	`associate-/l*`
8×	`pow1`
6×	`associate-l` `associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `log1p-expm1-u` `unswap-sqr` `associate-/l/`
3×	`cbrt-undiv` `div-exp`
2×	`pow-prod-down` `associate-r/` `-commutative`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3--` `div-sub` `frac-sub` `flip--` `sub-div`

Counts

4 → 249

Calls

4 calls:

85.0ms	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
160.0ms	(* alpha (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
164.0ms	(* beta (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
36.0ms	(+ (* alpha (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

series1.3s

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
297.0ms	(* alpha (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
292.0ms	(* beta (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
427.0ms	(+ (* alpha (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

simplify2.9s

Counts

261 → 261

Iterations

Iter	Nodes
done	5000
2	4642
1	985
0	337

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

regimes421.0ms

Accuracy

-1.2% (6.4b remaining)

Error of 12.2b against oracle of 5.8b and baseline of 12.1b

bsearch72.0ms

Steps

Iters	Range		Point
6	1.2666592301982906e+45	6.124437830376974e+45	6.021952390523363e+45

simplify10.0ms

Iterations

Iter	Nodes
done	43
2	43
1	42
0	38

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	6390×	body	80	valid
349.0ms	522×	body	1280	valid
296.0ms	8000×	pre	80	true
171.0ms	539×	body	640	valid
80.0ms	350×	body	320	valid
31.0ms	199×	body	160	valid