Details

sample66.0ms

Algorithm

intervals

Results

37.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
4	2431
3	460
2	106
1	35
0	15

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize39.0ms

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))

3.4b

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

rewrite378.0ms

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:

64.0ms

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

205.0ms

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

46.0ms

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

series500.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms

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

228.0ms

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

102.0ms

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

simplify2.2s

Counts

1218 → 1218

Iterations

Iter	Nodes
2	3914
1	1375
0	587

prune14.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite392.0ms

Algorithm

rewrite-expression-head

Rules

1399×	`*-un-lft-identity`
729×	`times-frac`
721×	`distribute-lft-out`
268×	`add-sqr-sqrt`
238×	`add-cube-cbrt`
192×	`associate-r`
54×	`add-exp-log`
48×	`associate-/r/`
34×	`add-cbrt-cube`
33×	`associate-/l*`
29×	`flip3-+` `flip-+`
24×	`div-exp`
21×	`associate-l`
20×	`div-inv`
17×	`associate-/r*`
14×	`cbrt-undiv`
12×	`prod-exp`
9×	`unswap-sqr`
8×	`frac-add`
7×	`pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 586

Calls

4 calls:

27.0ms	(/ 1 (+ (+ beta alpha) 2))
90.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) (+ 2 1.0)))
208.0ms	(* (/ 1 (+ (+ beta alpha) 2)) (/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) (+ 2 1.0))))
43.0ms	(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2))

series538.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (+ (+ beta alpha) 2))
167.0ms	(/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) (+ 2 1.0)))
230.0ms	(* (/ 1 (+ (+ beta alpha) 2)) (/ (/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2)) (+ (+ beta alpha) (+ 2 1.0))))
82.0ms	(/ (+ 1.0 (fma alpha beta (+ beta alpha))) (+ (+ beta alpha) 2))

simplify2.3s

Counts

598 → 598

Iterations

Iter	Nodes
2	4833
1	1365
0	422

prune7.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (/ (/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) 1) 1) (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))))
3.6b	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.6b	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.6b	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac` `add-exp-log`
58×	`div-exp`
41×	`*-un-lft-identity`
35×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
24×	`add-cbrt-cube`
19×	`prod-exp`
18×	`cbrt-undiv` `cbrt-div` `1-exp`
12×	`cbrt-prod`
9×	`flip3-+` `flip-+` `div-inv`
8×	`associate-/r/`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `frac-times` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`associate-l/` `associate-r/`
1×	`clear-num` `associate-/r*` `frac-2neg` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

175.0ms	(/ (/ (/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) 1) 1) (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))))
5.0ms	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.0ms	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
4.0ms	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series841.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (/ (/ (* (cbrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))) 1) 1) (* (cbrt (+ (+ 2 (+ beta alpha)) 1.0)) (cbrt (+ (+ 2 (+ beta alpha)) 1.0))))
67.0ms	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
492.0ms	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))
94.0ms	(cbrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify2.3s

Counts

166 → 166

Iterations

Iter	Nodes
3	5951
2	1650
1	749
0	322

prune2.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize62.0ms

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)))
0.7b	(* (/ (/ (/ (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))))
3.3b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.3b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite3.0s

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:

219.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
2.3s	(* (/ (/ (/ (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))))
5.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
6.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series912.0ms

Counts

4 → 12

Calls

4 calls:

563.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 2 (+ beta alpha)) 1.0)))
221.0ms	(* (/ (/ (/ (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))))
63.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
66.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify7.0s

Counts

5085 → 5085

Iterations

Iter	Nodes
1	6060
0	1862

prune1.5m

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.7b

regimes142.0ms

Accuracy

52% (1.2b remaining)

Error of 2.4b against oracle of 1.1b and baseline of 3.7b

bsearch80.0ms

Steps

Iters	Range		Point
7	1.075388870107967e+167	5.681342417267281e+168	4.0898973557336655e+168

simplify4.0ms

Iterations

Iter	Nodes
2	26
1	26
0	19

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
357.0ms	8000×	pre	80	true