Details

sample578.0ms

Algorithm

intervals

Results

280.0ms	67×	body	1280	valid
78.0ms	38×	body	640	valid
71.0ms	148×	body	80	valid
25.0ms	18×	body	320	valid
18.0ms	43×	body	80	nan
10.0ms	9×	body	160	valid

simplify9.0s

Counts

1 → 1

Iterations

Iter	Nodes
7	7678
6	1967
5	632
4	261
3	141
2	88
1	47
0	20

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize54.0ms

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) (sin B)) F)
0.3b	(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
19.2b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

7.0ms	(/ x (tan B))
27.0ms	(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
7.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series913.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ x (tan B))
275.0ms	(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
194.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
310.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.3s

Counts

162 → 162

Iterations

Iter	Nodes
3	4568
2	1466
1	577
0	271

prune2.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.3b	(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
0.4b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
19.2b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

5.0ms	(/ 1 (sin B))
45.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
14.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
7.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series681.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (sin B))
208.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) F)
212.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
238.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.2s

Counts

156 → 156

Iterations

Iter	Nodes
3	3925
2	1492
1	562
0	235

prune2.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))) F)
0.3b	(/ 1 (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2)))
0.3b	(/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))
19.2b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

332×	`times-frac`
199×	`add-sqr-sqrt`
177×	`*-un-lft-identity`
173×	`add-cube-cbrt`
80×	`unpow-prod-down` `associate-l`
68×	`add-exp-log`
37×	`div-exp`
32×	`associate-/r*`
28×	`sqr-pow`
20×	`add-cbrt-cube`
13×	`prod-exp`
10×	`div-inv`
9×	`unswap-sqr`
8×	`pow-to-exp` `pow1` `rec-exp` `1-exp` `pow-exp`
7×	`cbrt-undiv`
6×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`pow-pow` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 322

Calls

4 calls:

43.0ms	(* (/ 1 (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))) F)
17.0ms	(/ 1 (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2)))
19.0ms	(/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series898.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (/ 1 (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))) F)
131.0ms	(/ 1 (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2)))
278.0ms	(/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))
321.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify1.3s

Counts

334 → 334

Iterations

Iter	Nodes
2	3140
1	1163
0	450

prune5.5s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 11.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ F (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2)))
0.3b	(/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))
19.2b	(pow (fma 2 x (fma F F 2)) -1/2)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
35×	`associate-/r*`
22×	`add-exp-log`
17×	`sqr-pow`
13×	`add-cbrt-cube`
11×	`div-exp`
9×	`associate-/l*`
7×	`div-inv`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 222

Calls

4 calls:

6.0ms	(/ x (tan B))
24.0ms	(/ F (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2)))
18.0ms	(/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series797.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ x (tan B))
164.0ms	(/ F (/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2)))
234.0ms	(/ (sin B) (pow (fma 2 x (fma F F 2)) -1/2))
269.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify1.3s

Counts

234 → 234

Iterations

Iter	Nodes
2	3067
1	967
0	422

prune3.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes418.0ms

Accuracy

97.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 10.4b

bsearch920.0ms

Steps

Iters	Range		Point
4	0.0006943122548678707	0.0010557686559065818	0.0010356528232137428
10	-6.815698304523642e+37	-1.8928229479135326e+25	-2.048028622360406e+25

simplify15.0ms

Iterations

Iter	Nodes
2	35
1	35
0	32

end0.0ms

sample13.0s

Algorithm

intervals

Results

5.4s	1752×	body	1280	valid
2.8s	1362×	body	640	valid
2.2s	4720×	body	80	valid
1.3s	706×	body	320	valid
707.0ms	1689×	body	80	nan
288.0ms	360×	body	160	valid