Details

sample536.0ms

Algorithm

intervals

Results

165.0ms	50×	body	1280	valid
113.0ms	54×	body	640	valid
65.0ms	74×	body	80	nan
60.0ms	147×	body	80	valid
24.0ms	17×	body	320	valid
13.0ms	14×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2046
5	644
4	269
3	138
2	87
1	45
0	20

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ F (sin B))
7.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
19.0b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite30.0ms

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:

5.0ms	(/ x (tan B))
5.0ms	(/ F (sin B))
14.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series776.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ x (tan B))
53.0ms	(/ F (sin B))
232.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
343.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.4s

Counts

139 → 139

Iterations

Iter	Nodes
3	4249
2	1379
1	517
0	244

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
19.0b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

5.0ms	(/ 1 (sin B))
35.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
19.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.0s

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (sin B))
223.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
499.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
274.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify4.3s

Counts

142 → 142

Iterations

Iter	Nodes
3	4435
2	1447
1	523
0	221

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
19.0b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `pow1/3`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
4.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series697.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (sin B))
141.0ms	(cbrt (sin B))
142.0ms	(cbrt (sin B))
287.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify2.0s

Counts

74 → 74

Iterations

Iter	Nodes
4	3325
3	1299
2	526
1	225
0	108

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
7.2b	(* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (/ F (sin B)))
19.0b	(sqrt (fma 2 x (fma F F 2)))
19.0b	(sqrt (fma 2 x (fma F F 2)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
58×	`add-sqr-sqrt`
47×	`prod-exp`
44×	`unpow-prod-down`
28×	`sqrt-prod`
25×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
18×	`pow-to-exp` `add-cbrt-cube` `pow-exp` `unswap-sqr`
12×	`swap-sqr` `sqr-pow`
11×	`associate-l`
10×	`times-frac` `div-exp`
8×	`pow1`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative`
1×	`pow2` `associate-*r/` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 158

Calls

4 calls:

31.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
46.0ms	(* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (/ F (sin B)))
1.0ms	(sqrt (fma 2 x (fma F F 2)))
1.0ms	(sqrt (fma 2 x (fma F F 2)))

series663.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
216.0ms	(* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (/ F (sin B)))
186.0ms	(sqrt (fma 2 x (fma F F 2)))
172.0ms	(sqrt (fma 2 x (fma F F 2)))

simplify3.6s

Counts

170 → 170

Iterations

Iter	Nodes
3	6511
2	1632
1	525
0	204

prune2.7s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 10.7b

regimes523.0ms

Accuracy

0% (0.9b remaining)

Error of 11.0b against oracle of 10.1b and baseline of 11.0b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	21
1	21
0	19

end0.0ms

sample14.2s

Algorithm

intervals

Results

5.1s	1636×	body	1280	valid
3.2s	1395×	body	640	valid
3.2s	4772×	body	80	valid
1.2s	695×	body	320	valid
711.0ms	1707×	body	80	nan
346.0ms	367×	body	160	valid