Details

sample756.0ms

Algorithm

intervals

Results

482.0ms	38×	body	640	valid
95.0ms	54×	body	1280	valid
40.0ms	157×	body	80	valid
15.0ms	54×	body	80	nan
12.0ms	14×	body	320	valid
9.0ms	16×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (- 1.0) (tan B)) x (* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B))))
0.2b	(/ (- 1.0) (tan B))
7.3b	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
16.2b	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

0.0ms	(fma (/ (- 1.0) (tan B)) x (* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B))))
7.0ms	(/ (- 1.0) (tan B))
40.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
14.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

729.0ms	(fma (/ (- 1.0) (tan B)) x (* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B))))
53.0ms	(/ (- 1.0) (tan B))
606.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) (/ F (sin B)))
210.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

simplify3.7s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	4667
1	1006
0	368

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0) (tan B))
0.2b	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) F)
0.4b	(* (* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) F) (/ 1 (sin B)))
16.2b	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 192

Calls

4 calls:

18.0ms	(/ (- 1.0) (tan B))
20.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) F)
36.0ms	(* (* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) F) (/ 1 (sin B)))
5.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- 1.0) (tan B))
320.0ms	(* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) F)
508.0ms	(* (* (pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0)) F) (/ 1 (sin B)))
215.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

simplify3.9s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
2	4931
1	1017
0	360

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt F)
0.6b	(cbrt F)
0.6b	(cbrt F)
16.2b	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow-unpow`
30×	`times-frac`
28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`neg-mul-1` `unpow-prod-down` `pow1/3`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `pow-pow` `div-sub` `pow-exp` `distribute-frac-neg` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt F)
1.0ms	(cbrt F)
1.0ms	(cbrt F)
5.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

278.0ms	(cbrt F)
314.0ms	(cbrt F)
314.0ms	(cbrt F)
222.0ms	(pow (fma F F (fma x 2.0 2.0)) (/ (- 1.0) 2.0))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	1433
1	427
0	157

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

8.3b	(pow (* (cbrt (fma F F (fma x 2.0 2.0))) (cbrt (fma F F (fma x 2.0 2.0)))) (/ (- 1.0) 2.0))
17.0b	(cbrt (fma F F (fma x 2.0 2.0)))
17.0b	(cbrt (fma F F (fma x 2.0 2.0)))
17.0b	(cbrt (fma F F (fma x 2.0 2.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow-unpow`
30×	`times-frac`
27×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
9×	`cbrt-prod` `distribute-lft-neg-in` `pow-pow` `distribute-rgt-neg-in` `pow1/3`
7×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`neg-mul-1`
2×	`pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up`
1×	`pow2` `neg-sub0` `pow-to-exp` `pow-neg` `unpow-prod-down` `pow-plus` `div-sub` `prod-exp` `distribute-frac-neg` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

18.0ms	(pow (* (cbrt (fma F F (fma x 2.0 2.0))) (cbrt (fma F F (fma x 2.0 2.0)))) (/ (- 1.0) 2.0))
1.0ms	(cbrt (fma F F (fma x 2.0 2.0)))
1.0ms	(cbrt (fma F F (fma x 2.0 2.0)))
1.0ms	(cbrt (fma F F (fma x 2.0 2.0)))

series930.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(pow (* (cbrt (fma F F (fma x 2.0 2.0))) (cbrt (fma F F (fma x 2.0 2.0)))) (/ (- 1.0) 2.0))
165.0ms	(cbrt (fma F F (fma x 2.0 2.0)))
201.0ms	(cbrt (fma F F (fma x 2.0 2.0)))
202.0ms	(cbrt (fma F F (fma x 2.0 2.0)))

simplify1.7s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	2019
1	539
0	193

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes535.0ms

Accuracy

97.3% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 10.8b

bsearch375.0ms

Steps

Iters	Range		Point
6	0.6893947674185039	4.9803363081918155	4.890764603747723
8	-1026.6337297585196	-0.05943255384193945	-1011.2161346004847

simplify13.0ms

Iterations

Iter	Nodes
done	54
3	54
2	51
1	47
0	36

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.7s	1709×	body	1280	valid
2.0s	1420×	body	640	valid
1.4s	4667×	body	80	valid
610.0ms	710×	body	320	valid
525.0ms	1640×	body	80	nan
214.0ms	354×	body	160	valid