Details

sample205.0ms

Algorithm

intervals

Results

105.0ms	114×	body	2560	valid
41.0ms	72×	body	1280	valid
23.0ms	263×	body	80	nan
14.0ms	33×	body	640	valid
6.0ms	19×	body	320	valid
3.0ms	12×	body	160	valid
1.0ms	6×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	3462
5	1131
4	454
3	177
2	65
1	24
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (fma (* -5 v) v 1) (fma v v -1))
0.4b	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 41

Calls

2 calls:

6.0ms	(/ (fma (* -5 v) v 1) (fma v v -1))
1.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

series93.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (fma (* -5 v) v 1) (fma v v -1))
5.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))

simplify2.7s

Counts

47 → 47

Iterations

Iter	Nodes
4	4085
3	928
2	344
1	152
0	86

prune432.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 1 expressions with local error:

0.4b	(acos (fma 4 (fma (* v v) (* v v) (* v v)) -1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

1×	`acos-asin` `add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

1.0ms

(acos (fma 4 (fma (* v v) (* v v) (* v v)) -1))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(acos (fma 4 (fma (* v v) (* v v) (* v v)) -1))

simplify4.0s

Counts

14 → 14

Iterations

Iter	Nodes
6	2415
5	1084
4	420
3	172
2	74
1	41
0	25

prune125.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ PI 2) (asin (fma 4 (fma (* v v) (* v v) (* v v)) -1)))
0.4b	(asin (fma 4 (fma (* v v) (* v v) (* v v)) -1))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
43×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
13×	`fma-neg`
4×	`div-inv` `add-log-exp`
2×	`expm1-log1p-u` `pow1` `asin-acos` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate--r-`

Counts

2 → 82

Calls

2 calls:

24.0ms	(- (/ PI 2) (asin (fma 4 (fma (* v v) (* v v) (* v v)) -1)))
2.0ms	(asin (fma 4 (fma (* v v) (* v v) (* v v)) -1))

series49.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (/ PI 2) (asin (fma 4 (fma (* v v) (* v v) (* v v)) -1)))
5.0ms	(asin (fma 4 (fma (* v v) (* v v) (* v v)) -1))

simplify3.0s

Counts

88 → 88

Iterations

Iter	Nodes
4	4559
3	1493
2	582
1	288
0	134

prune410.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
1.0b	(sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
1.0b	(sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
1.0b	(* (sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

1.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
1.0ms	(sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
1.0ms	(sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
14.0ms	(* (sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (/ (fma (* -5 v) v 1) (fma v v -1)))
13.0ms	(sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
14.0ms	(sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1))))
3.0ms	(* (sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1)))) (sqrt (acos (/ (fma (* -5 v) v 1) (fma v v -1)))))

simplify2.3s

Counts

107 → 107

Iterations

Iter	Nodes
5	3433
4	905
3	399
2	227
1	125
0	72

prune627.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes105.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
1	11
0	11

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.5s	2987×	body	2560	valid
1.9s	2547×	body	1280	valid
1.1s	1212×	body	640	valid
883.0ms	7867×	body	80	nan
260.0ms	617×	body	320	valid
106.0ms	423×	body	160	valid
29.0ms	214×	body	80	valid