Details

sample349.0ms

Algorithm

intervals

Results

139.0ms	60×	body	1280	valid
43.0ms	46×	body	640	valid
34.0ms	142×	body	80	valid
15.0ms	23×	body	320	valid
10.0ms	13×	body	160	valid
10.0ms	52×	body	80	nan

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	20	27
1	43	26
2	91	24
3	169	24
4	366	24
5	915	24
6	3219	24
done	5001	24

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
18.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
37×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
14×	`associate-r`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unpow-prod-down` `associate-l` `associate-/r` `associate-/l`
2×	`tan-quot` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `fma-udef` `pow-sub` `sqr-pow`

Counts

4 → 123

Calls

4 calls:

6.0ms	(/ 1.0 (tan B))
32.0ms	(* x (/ 1.0 (tan B)))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
9.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ 1.0 (tan B))
203.0ms	(* x (/ 1.0 (tan B)))
515.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
495.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.6s

Counts

135 → 135

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	285	1919
1	690	1835
2	1768	1712
3	4856	1677
done	5000	1677

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
6.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
18.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

23.0ms	(/ (* x 1.0) (tan B))
12.0ms	(/ F (sin B))
1.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
23.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (* x 1.0) (tan B))
102.0ms	(/ F (sin B))
486.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
461.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.6s

Counts

123 → 123

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	292	1805
1	677	1732
2	1805	1610
done	5000	1575

prune957.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.3b	(* F (/ 1 (sin B)))
6.8b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
18.2b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`times-frac`
37×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`pow-unpow`
18×	`add-exp-log`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r`
11×	`add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unpow-prod-down` `associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod`
1×	`neg-sub0` `pow-to-exp` `pow-neg` `neg-mul-1` `pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 129

Calls

4 calls:

13.0ms	(/ 1 (sin B))
29.0ms	(* F (/ 1 (sin B)))
0.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
8.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (sin B))
99.0ms	(* F (/ 1 (sin B)))
481.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
477.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.8s

Counts

141 → 141

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	287	1957
1	681	1733
2	1631	1606
3	4309	1571
done	5000	1566

prune995.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 12.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* F (/ 1 (sin B)))
0.3b	(pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0))))
6.8b	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0)) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
17.8b	(pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
29×	`add-cube-cbrt` `times-frac`
28×	`pow-unpow`
16×	`add-exp-log`
13×	`unpow-prod-down` `associate-r`
9×	`cbrt-prod` `add-cbrt-cube`
7×	`pow1`
5×	`pow-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-l` `unswap-sqr` `sqr-pow`
2×	`pow-pow` `div-exp` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `neg-sub0` `distribute-lft-neg-in` `pow-neg` `neg-mul-1` `rec-exp` `distribute-rgt-neg-in` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `pow-sub`

Counts

4 → 116

Calls

4 calls:

19.0ms	(* F (/ 1 (sin B)))
6.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0))))
1.0ms	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0)) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
17.0ms	(pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

96.0ms	(* F (/ 1 (sin B)))
1.0s	(pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0))))
732.0ms	(fma (pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0)) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
755.0ms	(pow (pow (fma 2.0 x (fma F F 2.0)) (- (* (cbrt 1.0) (cbrt 1.0)))) (/ (cbrt 1.0) 2.0))

simplify1.6s

Counts

128 → 128

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	336	2894
1	855	2563
2	2284	2408
done	5001	2294

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.9b

regimes486.0ms

Accuracy

0% (0.4b remaining)

Error of 13.6b against oracle of 13.2b and baseline of 13.6b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	33
1	31	33
2	37	33
done	37	33

end0.0ms

sample9.7s

Algorithm

intervals

Results

3.4s	1690×	body	1280	valid
2.2s	1394×	body	640	valid
2.2s	4747×	body	80	valid
754.0ms	675×	body	320	valid
448.0ms	1652×	body	80	nan
186.0ms	368×	body	160	valid