Details

sample264.0ms

Algorithm

intervals

Results

108.0ms	57×	body	1280	valid
38.0ms	48×	body	640	valid
28.0ms	144×	body	80	valid
11.0ms	19×	body	320	valid
8.0ms	52×	body	80	nan
4.0ms	12×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1755
4	384
3	169
2	91
1	43
0	20

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ 1.0 (tan B))
7.4b	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
17.6b	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity` `add-cube-cbrt`
34×	`pow-unpow`
22×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down`
7×	`associate-l`
6×	`associate-/r` `prod-exp` `associate-/l` `unswap-sqr`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`
3×	`neg-sub0` `pow-to-exp` `cbrt-undiv` `pow-neg` `neg-mul-1` `div-sub` `pow-exp` `distribute-frac-neg` `pow-sub`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/` `cbrt-unprod`
1×	`pow-pow` `tan-quot` `associate-r/` `associate-/r/` `-commutative`

Counts

4 → 160

Calls

4 calls:

4.0ms	(/ F (sin B))
5.0ms	(/ 1.0 (tan B))
19.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
7.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

series908.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ F (sin B))
53.0ms	(/ 1.0 (tan B))
600.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
184.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

simplify2.5s

Counts

172 → 172

Iterations

Iter	Nodes
done	5001
2	3725
1	801
0	304

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B))
0.2b	(/ F (* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B)))
17.5b	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

9.0ms	(/ 1.0 (tan B))
23.0ms	(* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B))
26.0ms	(/ F (* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B)))
6.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1.0 (tan B))
656.0ms	(* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B))
557.0ms	(/ F (* (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)) (sin B)))
261.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

simplify1.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
2	2520
1	643
0	256

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* (* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))) (/ 1 (sin B)))
0.3b	(* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0)))
17.6b	(pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
48×	`add-sqr-sqrt` `times-frac`
43×	`*-un-lft-identity` `add-cube-cbrt`
34×	`pow-unpow`
31×	`prod-exp`
20×	`add-cbrt-cube` `associate-r`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `div-exp`
7×	`pow1` `pow-neg` `unpow-prod-down` `associate-*r/` `distribute-frac-neg` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`neg-sub0` `expm1-log1p-u` `rec-exp` `1-exp` `div-sub` `associate-l` `un-div-inv` `log1p-expm1-u` `pow-sub` `add-log-exp`
3×	`frac-times` `cbrt-undiv` `associate-/r` `neg-mul-1` `associate-l/` `div-inv` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`*-commutative`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `tan-quot` `associate-/r/`

Counts

4 → 165

Calls

4 calls:

10.0ms	(/ 1.0 (tan B))
61.0ms	(* (* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))) (/ 1 (sin B)))
21.0ms	(* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0)))
10.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1.0 (tan B))
629.0ms	(* (* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))) (/ 1 (sin B)))
343.0ms	(* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0)))
210.0ms	(pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))

simplify3.7s

Counts

177 → 177

Iterations

Iter	Nodes
done	5001
2	4565
1	923
0	326

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* F (/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))) (/ 1 (sin B)))
0.3b	(* F (/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
0.4b	(/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
17.5b	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
94×	`prod-exp`
66×	`times-frac`
65×	`add-sqr-sqrt`
58×	`div-exp`
53×	`*-un-lft-identity`
50×	`add-cube-cbrt`
38×	`associate-r`
32×	`add-cbrt-cube`
29×	`rec-exp` `1-exp`
26×	`unpow-prod-down`
19×	`pow-to-exp` `pow-exp`
13×	`pow-unpow`
12×	`pow1` `cbrt-unprod`
10×	`sqr-pow`
7×	`cbrt-undiv` `associate-/r*` `unswap-sqr`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `associate-*r/` `un-div-inv` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/l*`
2×	`frac-times` `associate-l/` `-commutative`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 226

Calls

4 calls:

53.0ms	(* (* F (/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))) (/ 1 (sin B)))
29.0ms	(* F (/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
7.0ms	(/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
4.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

522.0ms	(* (* F (/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))) (/ 1 (sin B)))
339.0ms	(* F (/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
1.1s	(/ 1 (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
183.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify765.0ms

Counts

238 → 238

Iterations

Iter	Nodes
done	5000
1	1123
0	372

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes494.0ms

Accuracy

96% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 11.3b

bsearch339.0ms

Steps

Iters	Range		Point
6	6968.3439428623215	61777.909360781356	32193.2639020248
7	-1.2568193720415405e+97	-7.379293722406342e+94	-7.571341863158053e+94

simplify5.0ms

Iterations

Iter	Nodes
done	43
1	43
0	37

end0.0ms

sample10.1s

Algorithm

intervals

Results

4.7s	1674×	body	1280	valid
1.9s	1403×	body	640	valid
1.5s	4747×	body	80	valid
595.0ms	684×	body	320	valid
520.0ms	1704×	body	80	nan
346.0ms	347×	body	160	valid