Details

sample264.0ms

Algorithm

intervals

Results

92.0ms	72×	body	1280	valid
18.0ms	130×	body	80	valid
15.0ms	24×	body	640	valid
12.0ms	21×	body	320	valid
8.0ms	256×	pre	80	true
2.0ms	9×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	24
5	24
4	23
3	21
2	18
1	14
0	9

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (sin v) (fma (cos v) e 1))
0.1b	(* (/ (sin v) (fma (cos v) e 1)) e)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 65

Calls

2 calls:

16.0ms	(/ (sin v) (fma (cos v) e 1))
44.0ms	(* (/ (sin v) (fma (cos v) e 1)) e)

series204.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (sin v) (fma (cos v) e 1))
153.0ms	(* (/ (sin v) (fma (cos v) e 1)) e)

simplify5.7s

Counts

71 → 71

Iterations

Iter	Nodes
3	3229
2	943
1	298
0	125

prune654.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sin v) (sqrt (fma (cos v) e 1)))
0.0b	(* (/ 1 (sqrt (fma (cos v) e 1))) (* (/ (sin v) (sqrt (fma (cos v) e 1))) e))
0.0b	(/ 1 (sqrt (fma (cos v) e 1)))
0.1b	(* (/ (sin v) (sqrt (fma (cos v) e 1))) e)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `inv-pow`

Counts

4 → 192

Calls

4 calls:

17.0ms	(/ (sin v) (sqrt (fma (cos v) e 1)))
38.0ms	(* (/ 1 (sqrt (fma (cos v) e 1))) (* (/ (sin v) (sqrt (fma (cos v) e 1))) e))
5.0ms	(/ 1 (sqrt (fma (cos v) e 1)))
14.0ms	(* (/ (sin v) (sqrt (fma (cos v) e 1))) e)

series383.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (sin v) (sqrt (fma (cos v) e 1)))
82.0ms	(* (/ 1 (sqrt (fma (cos v) e 1))) (* (/ (sin v) (sqrt (fma (cos v) e 1))) e))
59.0ms	(/ 1 (sqrt (fma (cos v) e 1)))
138.0ms	(* (/ (sin v) (sqrt (fma (cos v) e 1))) e)

simplify1.2s

Counts

204 → 204

Iterations

Iter	Nodes
2	2143
1	717
0	273

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (fma (cos v) e 1)))
0.1b	(/ (sqrt (fma (cos v) e 1)) (sin v))
0.1b	(* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e)
0.2b	(/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

304×	`times-frac`
193×	`add-sqr-sqrt`
175×	`*-un-lft-identity`
172×	`add-cube-cbrt`
89×	`sqrt-prod`
71×	`associate-l`
40×	`add-exp-log`
31×	`associate-/r*`
22×	`add-cbrt-cube`
17×	`div-exp`
12×	`associate-/l*`
11×	`div-inv`
9×	`pow1`
8×	`cbrt-undiv`
7×	`prod-exp` `unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `pow-flip` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `cbrt-unprod`
2×	`associate-/r/` `inv-pow`
1×	`sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 309

Calls

4 calls:

10.0ms	(/ 1 (sqrt (fma (cos v) e 1)))
16.0ms	(/ (sqrt (fma (cos v) e 1)) (sin v))
21.0ms	(* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e)
8.0ms	(/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (sqrt (fma (cos v) e 1)))
121.0ms	(/ (sqrt (fma (cos v) e 1)) (sin v))
172.0ms	(* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e)
134.0ms	(/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v)))

simplify2.7s

Counts

321 → 321

Iterations

Iter	Nodes
2	2882
1	1056
0	409

prune4.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (fma (cos v) e 1) -1/2) (* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e))
0.1b	(/ (sqrt (fma (cos v) e 1)) (sin v))
0.1b	(* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e)
0.2b	(/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

286×	`times-frac`
180×	`add-sqr-sqrt`
162×	`*-un-lft-identity`
159×	`add-cube-cbrt`
112×	`add-exp-log`
78×	`associate-l`
77×	`sqrt-prod`
52×	`prod-exp`
36×	`div-exp`
34×	`add-cbrt-cube`
25×	`associate-/r*`
10×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
9×	`associate-/l*`
8×	`pow-to-exp` `pow-exp`
7×	`pow1` `unswap-sqr`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down`
2×	`clear-num` `frac-2neg` `associate-l/` `associate-/r/` `-commutative`
1×	`pow-prod-down` `associate-*r/` `pow-flip` `inv-pow` `sqr-pow`

Counts

4 → 309

Calls

4 calls:

43.0ms	(* (pow (fma (cos v) e 1) -1/2) (* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e))
6.0ms	(/ (sqrt (fma (cos v) e 1)) (sin v))
27.0ms	(* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e)
10.0ms	(/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (pow (fma (cos v) e 1) -1/2) (* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e))
120.0ms	(/ (sqrt (fma (cos v) e 1)) (sin v))
154.0ms	(* (/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v))) e)
93.0ms	(/ 1 (/ (sqrt (fma (cos v) e 1)) (sin v)))

simplify2.8s

Counts

321 → 321

Iterations

Iter	Nodes
2	2945
1	1120
0	409

prune4.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes144.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	13
1	13
0	11

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.0s	1566×	body	1280	valid
1.4s	1269×	body	640	valid
1.1s	4306×	body	80	valid
394.0ms	8000×	pre	80	true
282.0ms	566×	body	320	valid
188.0ms	293×	body	160	valid