Details

sample507.0ms

Algorithm

intervals

Results

127.0ms	51×	body	1280	valid
95.0ms	154×	body	80	valid
69.0ms	39×	body	640	valid
25.0ms	21×	body	320	valid
21.0ms	57×	body	80	nan
8.0ms	11×	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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ x (tan B))
7.1b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
17.8b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite42.0ms

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	(/ F (sin B))
6.0ms	(/ x (tan B))
23.0ms	(* (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)

series734.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ F (sin B))
113.0ms	(/ x (tan B))
250.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
293.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.4s

Counts

139 → 139

Iterations

Iter	Nodes
3	4408
2	1378
1	517
0	244

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 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)
17.8b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite61.0ms

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:

16.0ms	(/ x (tan B))
21.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
18.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series764.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ x (tan B))
249.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
169.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
237.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
3	4954
2	1243
1	456
0	220

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
0.2b	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
17.8b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

8.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
1.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
10.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.3s

Counts

4 → 12

Calls

4 calls:

626.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
212.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
163.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
308.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	3314
2	985
1	385
0	190

prune1.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.6b

localize61.0ms

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)
17.8b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite62.0ms

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:

29.0ms	(* (/ x (sin B)) (cos B))
20.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
9.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (/ x (sin B)) (cos B))
246.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
146.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
695.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify5.5s

Counts

121 → 121

Iterations

Iter	Nodes
3	6092
2	1565
1	514
0	227

prune1.8s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 9.6b

regimes489.0ms

Accuracy

0% (0.6b remaining)

Error of 10.8b against oracle of 10.2b and baseline of 10.8b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	17
1	17
0	16

end0.0ms

sample14.3s

Algorithm

intervals

Results

5.6s	1662×	body	1280	valid
3.0s	1442×	body	640	valid
2.4s	4724×	body	80	valid
1.1s	1638×	body	80	nan
1.1s	719×	body	320	valid
744.0ms	333×	body	160	valid