Details

sample86.0ms

Algorithm

intervals

Results

31.0ms	89×	body	1280	valid
15.0ms	70×	body	640	valid
13.0ms	264×	body	80	valid
6.0ms	42×	body	320	valid
2.0ms	20×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	7
1	57	6
2	87	6
3	114	6
4	132	6
5	151	6
6	171	6
7	173	6
8	173	6
done	173	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

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))

rewrite24.0ms

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:

9.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series324.0ms

Counts

2 → 6

Calls

2 calls:

109.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
215.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify32.0ms

Counts

57 → 57

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	202	424
1	995	365
2	5001	359
done	5001	359

prune147.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite61.0ms

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:

9.0ms

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

18.0ms

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

29.0ms

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

series968.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms

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

635.0ms

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

220.0ms

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

simplify68.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	488	2207
1	2528	1901
2	5001	1871
done	5001	1871

prune410.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

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))))

rewrite210.0ms

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)))
28.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
135.0ms	(* (/ 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)))))
18.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series1.8s

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
830.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
229.0ms	(* (/ 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)))))
650.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify79.0ms

Counts

317 → 317

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1331	7346
1	5001	6415
done	5001	6415

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize19.0ms

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)))

rewrite223.0ms

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:

25.0ms	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
122.0ms	(* (/ 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)))))
51.0ms	(* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))))
8.0ms	(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))

series2.0s

Counts

4 → 12

Calls

4 calls:

830.0ms	(/ (* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
238.0ms	(* (/ 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)))))
652.0ms	(* (/ (cos th) (cbrt (sqrt 2.0))) (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))))
294.0ms	(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))

simplify60.0ms

Counts

315 → 315

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1239	5826
1	5001	4890
done	5001	4890

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes191.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	23
1	22	23
done	22	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

801.0ms	2521×	body	1280	valid
450.0ms	2120×	body	640	valid
394.0ms	7985×	body	80	valid
156.0ms	1005×	body	320	valid
53.0ms	511×	body	160	valid