Details

sample124.0ms

Algorithm

intervals

Results

44.0ms	77×	body	1280	valid
22.0ms	56×	body	640	valid
21.0ms	227×	body	80	valid
7.0ms	25×	body	320	valid
3.0ms	14×	body	160	valid

simplify307.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	57	12
3	87	12
4	114	12
5	132	12
6	150	12
7	170	12
8	172	12
done	172	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `sqrt-prod`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
25.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
26.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series506.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma a1 a1 (* a2 a2))
146.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
313.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.3s

Counts

70 → 70

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	103	947
1	201	911
2	750	777
3	3465	759
done	5000	758

prune312.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

234×	`sqrt-prod`
216×	`times-frac`
96×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
14×	`associate-/l*`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `fma-udef`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 225

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
17.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
16.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
25.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series994.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma a1 a1 (* a2 a2))
178.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
444.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
319.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.2s

Counts

237 → 237

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	269	5586
1	616	4970
2	1742	4533
done	5001	4463

prune903.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (fabs (cbrt (sqrt 2.0))))
0.4b	(* (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

1519×	`sqrt-prod`
1504×	`times-frac`
856×	`add-sqr-sqrt`
770×	`*-un-lft-identity`
758×	`add-cube-cbrt`
392×	`cbrt-prod`
376×	`associate-r`
82×	`add-exp-log`
52×	`add-cbrt-cube`
38×	`div-exp`
35×	`associate-/l*`
30×	`div-inv`
29×	`unswap-sqr`
24×	`associate-/r*`
21×	`cbrt-undiv` `prod-exp`
13×	`cbrt-unprod`
10×	`pow1`
7×	`pow-flip` `sqrt-pow1` `associate-l`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow1/2` `clear-num`
2×	`pow1/3` `pow-div`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 970

Calls

4 calls:

12.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (fabs (cbrt (sqrt 2.0))))
261.0ms	(* (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
42.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
19.0ms	(/ 1 (sqrt (sqrt 2.0)))

series1.5s

Counts

4 → 8

Calls

4 calls:

398.0ms	(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (fabs (cbrt (sqrt 2.0))))
1.1s	(* (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify2.5s

Counts

978 → 978

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	858	26378
1	2515	21749
done	5000	20572

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (fabs (cbrt 2.0)))) (sqrt (sqrt (cbrt 2.0))))
0.3b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

2709×	`times-frac`
2472×	`sqrt-prod`
1007×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
255×	`cbrt-prod`
93×	`div-inv`
83×	`associate-/l*`
23×	`add-exp-log` `add-cbrt-cube`
21×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `pow1/3` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 1160

Calls

4 calls:

90.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (fabs (cbrt 2.0)))) (sqrt (sqrt (cbrt 2.0))))
23.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)

series2.1s

Counts

4 → 8

Calls

4 calls:

1.7s	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (fabs (cbrt 2.0)))) (sqrt (sqrt (cbrt 2.0))))
474.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify1.8s

Counts

1168 → 1168

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	1135	48078
1	2521	43324
done	5001	42993

prune4.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes297.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	22	25
done	22	25

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	2525×	body	1280	valid
1.2s	2049×	body	640	valid
875.0ms	7986×	body	80	valid
847.0ms	1057×	body	320	valid
105.0ms	503×	body	160	valid