Details

sample588.0ms

Algorithm

intervals

Results

151.0ms	52×	body	640	valid
139.0ms	50×	body	1280	valid
102.0ms	148×	body	80	valid
32.0ms	23×	body	320	valid
25.0ms	64×	body	80	nan
12.0ms	13×	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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ x (tan B))
8.7b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
20.6b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite33.0ms

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

series728.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ F (sin B))
143.0ms	(/ x (tan B))
235.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
275.0ms	(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

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.2b

localize66.0ms

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)
0.9b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
20.6b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite35.0ms

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:

8.0ms	(/ x (tan B))
10.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
12.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series880.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ x (tan B))
145.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
268.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
276.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.8s

Counts

117 → 117

Iterations

Iter	Nodes
3	4742
2	1239
1	456
0	220

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.9b	(/ (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
2.4b	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
20.6b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite19.0ms

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×	`expm1-log1p-u` `pow1`
4×	`insert-posit16` `log1p-expm1-u` `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` `log1p-udef` `clear-num` `pow-pow` `frac-2neg` `div-sub` `div-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef`

Counts

4 → 91

Calls

4 calls:

10.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
5.0ms	(/ (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
0.0ms	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.1s

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
564.0ms	(/ (expm1 (log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
169.0ms	(log1p (* (pow (fma 2 x (fma F F 2)) -1/2) F))
268.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify1.9s

Counts

103 → 103

Iterations

Iter	Nodes
3	3446
2	1001
1	391
0	192

prune1.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.9b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
20.6b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

30.0ms	(/ (* x (cos B)) (sin B))
10.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
12.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series782.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (* x (cos B)) (sin B))
123.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
213.0ms	(/ (* (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)

simplify3.6s

Counts

110 → 110

Iterations

Iter	Nodes
3	6287
2	1422
1	469
0	206

prune1.4s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 4.9b

regimes539.0ms

Accuracy

59% (2.4b remaining)

Error of 7.3b against oracle of 4.9b and baseline of 10.7b

bsearch334.0ms

Steps

Iters	Range		Point
8	-6.746633779531078e+84	-7.849749075654118e+81	-5.495021983986923e+84

simplify16.0ms

Iterations

Iter	Nodes
2	36
1	36
0	32

end0.0ms

sample14.8s

Algorithm

intervals

Results

5.3s	1662×	body	1280	valid
3.6s	1427×	body	640	valid
3.1s	4726×	body	80	valid
1.1s	707×	body	320	valid
947.0ms	1624×	body	80	nan
317.0ms	344×	body	160	valid