Details

sample532.0ms

Algorithm

intervals

Results

113.0ms	48×	body	1280	valid
64.0ms	13×	body	160	valid
59.0ms	41×	body	640	valid
52.0ms	159×	body	80	valid
22.0ms	21×	body	320	valid
16.0ms	47×	body	80	nan

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1982
5	908
4	393
3	188
2	99
1	47
0	20

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ x (tan B))
6.4b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
14.5b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
30×	`times-frac`
22×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
8×	`unpow-prod-down`
7×	`associate-l`
6×	`associate-/r` `prod-exp` `associate-/l` `unswap-sqr`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `pow-exp` `div-inv`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`pow-pow` `tan-quot` `associate-r/` `associate-/r/` `-commutative`

Counts

4 → 127

Calls

4 calls:

11.0ms	(/ F (sin B))
12.0ms	(/ x (tan B))
40.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
10.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series770.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ F (sin B))
161.0ms	(/ x (tan B))
222.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
308.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	1640
1	547
0	244

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
14.5b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`add-exp-log`
19×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
7×	`unpow-prod-down` `associate-l`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `div-inv`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 105

Calls

4 calls:

13.0ms	(/ x (tan B))
26.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
14.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series796.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ x (tan B))
241.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
129.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
296.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify3.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4779
2	1354
1	481
0	220

prune879.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
14.5b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
20×	`associate-l`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`times-frac`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r`
5×	`div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-/r*` `pow-exp` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `associate-/l`

Counts

4 → 109

Calls

4 calls:

27.0ms	(* (/ x (sin B)) (cos B))
17.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
21.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
5.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series792.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (/ x (sin B)) (cos B))
272.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
106.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
260.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.0s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
2	1606
1	533
0	227

prune958.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.6b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) F)
0.3b	(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) F))
14.9b	(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
14.9b	(pow (fma 2 x (fma F F 2)) (/ -1/2 2))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
30×	`add-sqr-sqrt`
26×	`pow-unpow`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`prod-exp`
18×	`times-frac`
14×	`associate-l`
13×	`unpow-prod-down`
11×	`add-cbrt-cube`
10×	`pow-to-exp` `pow-exp`
6×	`pow1`
5×	`sqr-pow`
4×	`expm1-log1p-u` `associate-r` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-pow` `*-commutative` `div-inv`

Counts

4 → 121

Calls

4 calls:

24.0ms	(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) F)
50.0ms	(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) F))
4.0ms	(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
4.0ms	(pow (fma 2 x (fma F F 2)) (/ -1/2 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

394.0ms	(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) F)
149.0ms	(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) F))
267.0ms	(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
269.0ms	(pow (fma 2 x (fma F F 2)) (/ -1/2 2))

simplify2.3s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	1592
1	542
0	205

prune989.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.6b

regimes389.0ms

Accuracy

0% (0.7b remaining)

Error of 11.1b against oracle of 10.4b and baseline of 11.1b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample9.8s

Algorithm

intervals

Results

4.2s	1683×	body	1280	valid
2.1s	1409×	body	640	valid
1.5s	4706×	body	80	valid
905.0ms	1644×	body	80	nan
583.0ms	719×	body	320	valid
218.0ms	349×	body	160	valid