Details

sample80.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
13.0ms	256×	pre	80	true

simplify1.0s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize42.0ms

Local error

Found 3 expressions with local error:

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))

4.8b

(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite436.0ms

Algorithm

rewrite-expression-head

Rules

4322×	`*-un-lft-identity`
2696×	`times-frac`
2167×	`distribute-lft-out`
777×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
52×	`flip3-+` `flip-+`
51×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`associate-/l/`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

3 → 1209

Calls

3 calls:

65.0ms

(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

231.0ms

(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))

44.0ms

(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series551.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms

(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))

264.0ms

(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))

106.0ms

(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.3s

Counts

1218 → 1218

Iterations

Iter	Nodes
2	3891
1	1369
0	587

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
0.5b	(/ 1 (sqrt (+ 2 (+ beta alpha))))
2.6b	(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))))
3.4b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

21849×	`*-un-lft-identity`
21842×	`times-frac`
8671×	`distribute-lft-out`
6965×	`add-sqr-sqrt` `add-cube-cbrt`
6205×	`sqrt-prod`
751×	`associate-/r/`
718×	`sqrt-div`
392×	`div-inv`
361×	`flip3-+` `flip-+`
249×	`associate-/r*`
54×	`add-exp-log`
42×	`associate-/l*`
36×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`pow1`
5×	`associate-/l/`
4×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 6482

Calls

4 calls:

122.0ms	(/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
21.0ms	(/ 1 (sqrt (+ 2 (+ beta alpha))))
107.0ms	(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))))
50.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ (/ 1 (sqrt (+ 2 (+ beta alpha)))) (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))))
105.0ms	(/ 1 (sqrt (+ 2 (+ beta alpha))))
300.0ms	(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))))
152.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (+ 2 (+ beta alpha))))

simplify21.8s

Counts

6494 → 6494

Iterations

Iter	Nodes
1	9870
0	2718

prune13.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
0.5b	(* (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
4.8b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
4.8b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

703×	`*-un-lft-identity`
321×	`distribute-lft-out`
319×	`times-frac`
210×	`sqrt-prod`
140×	`add-sqr-sqrt`
112×	`add-cube-cbrt`
77×	`swap-sqr`
29×	`associate-r` `associate-l`
28×	`associate-/r/`
19×	`pow1` `add-cbrt-cube` `add-exp-log` `associate-/l*`
16×	`associate-/r*` `flip3-+` `flip-+`
14×	`div-inv`
9×	`unswap-sqr`
8×	`sqrt-pow1` `pow1/2`
7×	`cbrt-undiv` `div-exp`
5×	`pow-prod-up` `associate-/l/`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `pow-sqr`
2×	`prod-exp` `cbrt-unprod`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 376

Calls

4 calls:

149.0ms	(/ (/ (* (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
129.0ms	(* (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
30.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
44.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (/ (* (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
101.0ms	(* (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))))
130.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))
147.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify1.3s

Counts

388 → 388

Iterations

Iter	Nodes
2	3022
1	789
0	328

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.6b

localize68.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
1.2b	(* (/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))))
4.7b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.7b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

17148×	`*-un-lft-identity`
13907×	`times-frac`
7902×	`distribute-lft-out`
5553×	`sqrt-prod`
5326×	`add-sqr-sqrt`
4132×	`add-cube-cbrt`
1905×	`associate-r`
717×	`associate-l`
234×	`associate-/r/`
211×	`associate-/l*`
207×	`unswap-sqr`
173×	`add-exp-log`
153×	`div-inv`
122×	`div-exp`
119×	`flip3-+` `flip-+`
93×	`add-cbrt-cube`
54×	`cbrt-undiv`
32×	`prod-exp`
20×	`1-exp`
16×	`cbrt-unprod`
10×	`sqrt-div`
9×	`associate-/r*`
8×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 5073

Calls

4 calls:

163.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
1.9s	(* (/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))))
9.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
7.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series962.0ms

Counts

4 → 12

Calls

4 calls:

577.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
209.0ms	(* (/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) 1) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))) (/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0))))
98.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
76.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify8.2s

Counts

5085 → 5085

Iterations

Iter	Nodes
1	6059
0	1862

prune10.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.6b

regimes183.0ms

Accuracy

53.9% (1.2b remaining)

Error of 2.5b against oracle of 1.3b and baseline of 3.9b

bsearch146.0ms

Steps

Iters	Range		Point
8	1.3095755543340861e+200	9.078109045320583e+202	8.004231800207308e+201

simplify12.0ms

Iterations

Iter	Nodes
2	46
1	46
0	36

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
715.0ms	8000×	pre	80	true