Details

sample160.0ms

Algorithm

intervals

Results

52.0ms	89×	body	1280	valid
29.0ms	70×	body	640	valid
23.0ms	264×	body	80	valid
12.0ms	42×	body	320	valid
4.0ms	20×	body	160	valid

simplify222.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

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)))
33.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series490.0ms

Counts

2 → 6

Calls

2 calls:

144.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
346.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.0s

Counts

57 → 57

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	100	839
1	198	806
2	744	692
3	3458	674
done	5000	673

prune217.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b

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

0.3b

(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

0.3b

(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
36×	`cbrt-prod`
35×	`add-exp-log` `add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
18×	`sqrt-prod`
13×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `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 → 127

Calls

3 calls:

19.0ms

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

35.0ms

(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

32.0ms

(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.5s

Counts

3 → 9

Calls

3 calls:

200.0ms

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

958.0ms

(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

322.0ms

(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify1.2s

Counts

136 → 136

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	212	3744
1	470	3405
2	1754	2941
done	5001	2924

prune626.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
0.2b	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
0.3b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-exp-log`
180×	`cbrt-prod`
171×	`times-frac`
117×	`add-sqr-sqrt`
100×	`div-exp`
97×	`prod-exp`
83×	`*-un-lft-identity`
78×	`add-cube-cbrt`
77×	`add-cbrt-cube`
67×	`associate-r`
52×	`cbrt-undiv`
45×	`cbrt-unprod`
36×	`sqrt-prod`
29×	`div-inv`
16×	`unswap-sqr`
13×	`associate-/r*`
12×	`rec-exp` `1-exp`
10×	`associate-l`
8×	`pow1`
6×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-r/` `associate-l/` `associate-/l/`

Counts

4 → 305

Calls

4 calls:

10.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
54.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
168.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
34.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series2.6s

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
1.1s	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
344.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
936.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify2.6s

Counts

317 → 317

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	429	11603
1	1159	10894
2	4583	9019
done	5002	8969

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
0.2b	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
0.3b	(* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))))
0.3b	(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-exp-log`
140×	`add-sqr-sqrt`
134×	`times-frac`
121×	`cbrt-prod`
101×	`div-exp`
96×	`prod-exp`
80×	`*-un-lft-identity`
79×	`add-cube-cbrt`
76×	`add-cbrt-cube`
53×	`cbrt-undiv`
47×	`associate-r` `sqrt-prod`
44×	`cbrt-unprod`
38×	`associate-l`
21×	`associate-/r*`
19×	`unswap-sqr`
12×	`rec-exp` `1-exp`
8×	`pow1`
6×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 303

Calls

4 calls:

53.0ms	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
199.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
69.0ms	(* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))))
15.0ms	(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))

series3.4s

Counts

4 → 12

Calls

4 calls:

1.6s	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
325.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
1.0s	(* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))))
470.0ms	(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))

simplify2.9s

Counts

315 → 315

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	418	9505
1	1069	8899
2	4028	6962
done	5000	6688

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes331.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	34
1	22	34
done	22	34

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	2521×	body	1280	valid
687.0ms	2120×	body	640	valid
576.0ms	7985×	body	80	valid
238.0ms	1005×	body	320	valid
78.0ms	511×	body	160	valid