Details

sample141.0ms

Algorithm

intervals

Results

33.0ms	195×	body	80	valid
31.0ms	27×	body	2560	valid
27.0ms	256×	pre	80	true
14.0ms	16×	body	1280	valid
6.0ms	5×	body	5120	valid
4.0ms	7×	body	320	valid
2.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	50
4	50
3	48
2	42
1	30
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma p (* 4 p) (* x x))
0.0b	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.7b	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
16.1b	(sqrt (fma p (* 4 p) (* x x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`fma-udef`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 80

Calls

4 calls:

0.0ms	(fma p (* 4 p) (* x x))
9.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
0.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
2.0ms	(sqrt (fma p (* 4 p) (* x x)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma p (* 4 p) (* x x))
76.0ms	(/ x (sqrt (fma p (* 4 p) (* x x))))
133.0ms	(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
66.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify916.0ms

Counts

92 → 92

Iterations

Iter	Nodes
4	2387
3	769
2	311
1	167
0	108

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma p (* 4 p) (* x x))
0.2b	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
3.6b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
16.1b	(sqrt (fma p (* 4 p) (* x x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`times-frac` `associate-r`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`div-exp` `cbrt-unprod` `fma-udef`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

0.0ms	(fma p (* 4 p) (* x x))
12.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
0.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
1.0ms	(sqrt (fma p (* 4 p) (* x x)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma p (* 4 p) (* x x))
96.0ms	(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
99.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
52.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify2.0s

Counts

100 → 100

Iterations

Iter	Nodes
4	3789
3	1343
2	547
1	268
0	130

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.8b

localize92.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
16.1b	(sqrt (fma p (* 4 p) (* x x)))
16.1b	(sqrt (fma p (* 4 p) (* x x)))
16.1b	(sqrt (fma p (* 4 p) (* x x)))

rewrite9.0ms

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 (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
2.0ms	(sqrt (fma p (* 4 p) (* x x)))
2.0ms	(sqrt (fma p (* 4 p) (* x x)))
2.0ms	(sqrt (fma p (* 4 p) (* x x)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
78.0ms	(sqrt (fma p (* 4 p) (* x x)))
57.0ms	(sqrt (fma p (* 4 p) (* x x)))
93.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify5.4s

Counts

71 → 71

Iterations

Iter	Nodes
5	6211
4	1165
3	283
2	107
1	63
0	45

prune971.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.8b

localize58.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
16.1b	(sqrt (fma p (* 4 p) (* x x)))
16.1b	(sqrt (fma p (* 4 p) (* x x)))
16.1b	(sqrt (fma p (* 4 p) (* x x)))

rewrite5.0ms

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 (/ 1 (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)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
52.0ms	(sqrt (fma p (* 4 p) (* x x)))
56.0ms	(sqrt (fma p (* 4 p) (* x x)))
53.0ms	(sqrt (fma p (* 4 p) (* x x)))

simplify3.7s

Counts

71 → 71

Iterations

Iter	Nodes
5	6211
4	1165
3	283
2	107
1	63
0	45

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.8b

regimes125.0ms

Accuracy

0% (0.4b remaining)

Error of 13.5b against oracle of 13.0b and baseline of 13.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	24
1	24
0	19

end0.0ms

sample2.6s

Algorithm

intervals

Results

814.0ms	751×	body	2560	valid
653.0ms	6020×	body	80	valid
404.0ms	634×	body	1280	valid
280.0ms	8000×	pre	80	true
111.0ms	305×	body	640	valid
88.0ms	152×	body	320	valid
49.0ms	68×	body	5120	valid
13.0ms	70×	body	160	valid