Details

sample179.0ms

Algorithm

intervals

Results

64.0ms	85×	body	1280	valid
31.0ms	260×	body	80	valid
30.0ms	54×	body	640	valid
12.0ms	30×	body	320	valid
4.0ms	15×	body	160	valid

simplify330.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	57	12
3	87	12
4	114	12
5	132	12
6	151	12
7	173	12
8	175	12
done	175	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.5b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

20.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
36.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series439.0ms

Counts

2 → 6

Calls

2 calls:

144.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
294.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.4s

Counts

57 → 57

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	100	839
1	213	806
2	1313	696
done	5001	690

prune208.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 215

Calls

3 calls:

29.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
46.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
19.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

series1.1s

Counts

3 → 9

Calls

3 calls:

519.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
362.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
173.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

simplify2.3s

Counts

224 → 224

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	266	5478
1	638	4865
2	3101	4508
done	5000	4399

prune847.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma a1 a1 (* a2 a2)) (cos th))
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)))

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

1519×	`sqrt-prod`
1501×	`times-frac`
858×	`add-sqr-sqrt`
770×	`*-un-lft-identity`
758×	`add-cube-cbrt`
392×	`cbrt-prod`
379×	`associate-r`
79×	`add-exp-log`
49×	`add-cbrt-cube`
36×	`div-exp`
34×	`associate-/l*`
30×	`unswap-sqr`
29×	`div-inv`
21×	`prod-exp` `associate-/r*`
19×	`cbrt-undiv`
13×	`cbrt-unprod`
12×	`pow1`
10×	`associate-l`
7×	`pow-flip` `sqrt-pow1`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`frac-2neg` `pow1/3` `pow-prod-down` `clear-num` `*-commutative` `pow-div`
1×	`frac-times` `associate-r/` `associate-l/` `associate-/l/` `inv-pow`

Counts

4 → 967

Calls

4 calls:

11.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
298.0ms	(* (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (fabs (cbrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
41.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
13.0ms	(/ 1 (sqrt (sqrt 2.0)))

series1.3s

Counts

4 → 8

Calls

4 calls:

164.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
1.2s	(* (/ (* (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)))

simplify2.8s

Counts

975 → 975

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	860	26143
1	3015	21653
done	5001	20930

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos th) (sqrt (fabs (cbrt (sqrt 2.0)))))
0.8b	(* (/ (cos th) (sqrt (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)))

rewrite617.0ms

Algorithm

rewrite-expression-head

Rules

1696×	`times-frac`
1673×	`sqrt-prod`
1134×	`add-sqr-sqrt`
818×	`*-un-lft-identity`
782×	`add-cube-cbrt`
420×	`cbrt-prod`
376×	`associate-r`
87×	`unswap-sqr`
54×	`add-exp-log`
37×	`associate-/l*`
34×	`add-cbrt-cube`
30×	`div-inv`
27×	`associate-/r*`
26×	`div-exp`
22×	`associate-l`
14×	`cbrt-undiv`
10×	`pow1` `prod-exp`
7×	`pow-flip` `sqrt-pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `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 → 1053

Calls

4 calls:

14.0ms	(/ (cos th) (sqrt (fabs (cbrt (sqrt 2.0)))))
372.0ms	(* (/ (cos th) (sqrt (fabs (cbrt (sqrt 2.0))))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))))
51.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
20.0ms	(/ 1 (sqrt (sqrt 2.0)))

series979.0ms

Counts

4 → 8

Calls

4 calls:

188.0ms	(/ (cos th) (sqrt (fabs (cbrt (sqrt 2.0)))))
791.0ms	(* (/ (cos th) (sqrt (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)))

simplify3.1s

Counts

1061 → 1061

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	882	26268
1	3067	21743
done	5001	21219

prune3.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes359.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b 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

sample6.3s

Algorithm

intervals

Results

2.1s	8065×	body	80	valid
1.7s	2490×	body	1280	valid
1.3s	2091×	body	640	valid
307.0ms	1047×	body	320	valid
164.0ms	555×	body	160	valid