Details

sample397.0ms

Algorithm

intervals

Results

106.0ms	53×	body	1280	valid
64.0ms	48×	body	80	nan
50.0ms	38×	body	640	valid
47.0ms	157×	body	80	valid
16.0ms	18×	body	320	valid
6.0ms	10×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

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: 10.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
5.2b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
14.1b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite44.0ms

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))
19.0ms	(* 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)))

series1.2s

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1.0 (tan B))
135.0ms	(* x (/ 1.0 (tan B)))
558.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
498.0ms	(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

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.1b	(/ (* x 1.0) (tan B))
5.2b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
14.1b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite57.0ms

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:

11.0ms	(/ F (sin B))
22.0ms	(/ (* x 1.0) (tan 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))))
16.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ F (sin B))
186.0ms	(/ (* x 1.0) (tan B))
512.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (/ (* x 1.0) (tan B))))
468.0ms	(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	1811	1610
done	5001	1575

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ 1 (sin B)))
5.2b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
14.1b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

26.0ms	(/ (* x 1.0) (tan B))
35.0ms	(* F (/ 1 (sin B)))
1.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
15.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (* x 1.0) (tan B))
72.0ms	(* F (/ 1 (sin B)))
517.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (/ (* x 1.0) (tan B))))
466.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

132 → 132

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	315	1938
1	761	1757
2	1971	1607
done	5001	1572

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(* F (/ 1 (sin B)))
5.2b	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
14.1b	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

33.0ms	(/ (* x (cos B)) (sin B))
19.0ms	(* 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))) (- (* 1.0 (/ (* x (cos B)) (sin 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:

168.0ms	(/ (* x (cos B)) (sin B))
86.0ms	(* F (/ 1 (sin B)))
463.0ms	(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (* F (/ 1 (sin B))) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
539.0ms	(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify1.5s

Counts

131 → 131

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	304	1991
1	746	1810
2	1948	1648
done	5001	1612

prune807.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 10.0b

regimes415.0ms

Accuracy

0% (0.4b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 13.5b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	29
1	30	29
2	34	29
3	40	29
done	40	29

end0.0ms

sample10.5s

Algorithm

intervals

Results

4.2s	1689×	body	1280	valid
2.1s	1326×	body	640	valid
1.4s	4866×	body	80	valid
1.4s	690×	body	320	valid
453.0ms	1614×	body	80	nan
182.0ms	329×	body	160	valid