Details

sample159.0ms

Algorithm

intervals

Results

61.0ms	34×	body	2560	valid
32.0ms	186×	body	80	valid
16.0ms	18×	body	1280	valid
14.0ms	256×	pre	80	true
9.0ms	12×	body	640	valid
3.0ms	6×	body	320	valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	48
4	48
3	46
2	40
1	28
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0b	(fma p (* 4 p) (* x x))
0.5b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
17.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

6.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms	(fma p (* 4 p) (* x x))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
47.0ms	(fma p (* 4 p) (* x x))
88.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
62.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify944.0ms

Counts

66 → 66

Iterations

Iter	Nodes
4	2302
3	583
2	178
1	96
0	70

prune779.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
17.0b	(sqrt (fma p (* 4 p) (* x x)))
17.0b	(sqrt (fma p (* 4 p) (* x x)))
17.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
85.0ms	(sqrt (fma p (* 4 p) (* x x)))
96.0ms	(sqrt (fma p (* 4 p) (* x x)))
63.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify2.3s

Counts

71 → 71

Iterations

Iter	Nodes
5	3372
4	802
3	230
2	95
1	58
0	44

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
17.0b	(sqrt (fma p (* 4 p) (* x x)))
17.0b	(sqrt (fma p (* 4 p) (* x x)))
17.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
2.0ms	(sqrt (fma p (* 4 p) (* x x)))
3.0ms	(sqrt (fma p (* 4 p) (* x x)))
2.0ms	(sqrt (fma p (* 4 p) (* x x)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
67.0ms	(sqrt (fma p (* 4 p) (* x x)))
62.0ms	(sqrt (fma p (* 4 p) (* x x)))
95.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify2.3s

Counts

71 → 71

Iterations

Iter	Nodes
5	3372
4	802
3	230
2	95
1	58
0	44

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 14.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))
8.1b	(fma (/ x (* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)
17.0b	(sqrt (fma p (* 4 p) (* x x)))
17.0b	(sqrt (fma p (* 4 p) (* x x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 121

Calls

4 calls:

12.0ms	(* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))
0.0ms	(fma (/ x (* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))
96.0ms	(fma (/ x (* (sqrt (sqrt (fma p (* 4 p) (* x x)))) (sqrt (sqrt (fma p (* 4 p) (* x x)))))) 0.5 0.5)
79.0ms	(sqrt (fma p (* 4 p) (* x x)))
80.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify1.5s

Counts

133 → 133

Iterations

Iter	Nodes
4	3672
3	844
2	310
1	178
0	105

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.4b

regimes193.0ms

Accuracy

0% (0.7b remaining)

Error of 13.3b against oracle of 12.6b and baseline of 13.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	16
1	16
0	14

end0.0ms

sample3.0s

Algorithm

intervals

Results

806.0ms	603×	body	1280	valid
711.0ms	6091×	body	80	valid
618.0ms	735×	body	2560	valid
389.0ms	8000×	pre	80	true
142.0ms	316×	body	640	valid
67.0ms	141×	body	320	valid
37.0ms	46×	body	5120	valid
16.0ms	68×	body	160	valid