Details

sample423.0ms

Algorithm

intervals

Results

150.0ms	47×	body	640	valid
86.0ms	41×	body	1280	valid
56.0ms	175×	body	80	valid
23.0ms	22×	body	320	valid
11.0ms	41×	body	80	nan
6.0ms	9×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ F (sin B))
6.9b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
17.1b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite75.0ms

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:

10.0ms	(/ x (tan B))
10.0ms	(/ F (sin B))
43.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
6.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series707.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ x (tan B))
75.0ms	(/ F (sin B))
220.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
302.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.0s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	1636
1	547
0	244

prune983.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
1.3b	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
17.1b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

56×	`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`
9×	`div-exp`
8×	`associate-l`
7×	`pow1` `unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `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` `tan-quot` `associate-*r/` `associate-/r/` `un-div-inv`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/ x (tan B))
9.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
31.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series792.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ x (tan B))
141.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
238.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
281.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify1.9s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	1618
1	605
0	255

prune970.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
1.3b	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
17.1b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

23.0ms	(/ (* x (cos B)) (sin B))
25.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
46.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series723.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* x (cos B)) (sin B))
126.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
223.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
262.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.1s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	1840
1	621
0	243

prune972.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.4b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (tan B) x))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
1.3b	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
17.1b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 175

Calls

4 calls:

13.0ms	(/ 1 (/ (tan B) x))
18.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
52.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series791.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1 (/ (tan B) x))
150.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
222.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
285.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.0s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	2234
1	846
0	333

prune936.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.4b

regimes588.0ms

Accuracy

0% (0.7b remaining)

Error of 10.7b against oracle of 10.0b and baseline of 10.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample14.0s

Algorithm

intervals

Results

5.0s	1570×	body	1280	valid
3.7s	1366×	body	640	valid
2.8s	4857×	body	80	valid
1.1s	730×	body	320	valid
733.0ms	1684×	body	80	nan
364.0ms	348×	body	160	valid