Details

sample77.0ms

Algorithm

intervals

Results

25.0ms	80×	body	1280	valid
13.0ms	253×	body	80	valid
11.0ms	51×	body	640	valid
7.0ms	30×	body	320	valid
2.0ms	19×	body	160	valid

simplify158.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

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)))
12.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series336.0ms

Counts

2 → 6

Calls

2 calls:

114.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
222.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify2.1s

Counts

57 → 57

Iterations

Useful iterations: done (2.1s)

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

prune153.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 3 expressions with local error:

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)))

0.4b

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

rewrite57.0ms

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:

17.0ms

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

27.0ms

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

9.0ms

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

series999.0ms

Counts

3 → 9

Calls

3 calls:

669.0ms

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

219.0ms

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

110.0ms

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

simplify735.0ms

Counts

136 → 136

Iterations

Useful iterations: done (731.0ms)

Iter	Nodes	Cost
0	212	3744
1	470	3409
2	1757	2941
done	5000	2924

prune355.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

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:

18.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
27.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
124.0ms	(* (/ 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)))))
9.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

683.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
865.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
243.0ms	(* (/ 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)))))
117.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))

simplify2.1s

Counts

317 → 317

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	429	11603
1	1159	10896
2	4604	9019
done	5001	8969

prune872.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

205×	`times-frac`
150×	`cbrt-prod` `sqrt-prod`
94×	`add-sqr-sqrt`
92×	`add-cube-cbrt` `*-un-lft-identity`
57×	`add-exp-log`
31×	`add-cbrt-cube`
29×	`associate-/l*`
25×	`div-exp`
21×	`div-inv`
19×	`pow1`
17×	`cbrt-undiv` `associate-/r*`
13×	`pow-flip`
12×	`prod-exp`
10×	`pow1/3`
8×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `sqrt-pow1` `1-exp` `log1p-expm1-u` `add-log-exp` `pow-div`
3×	`frac-2neg` `associate-r` `associate-l` `pow-prod-down` `clear-num` `pow-sqr` `pow-prod-up`
2×	`pow2` `pow-plus` `associate-/l/`
1×	`*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 275

Calls

4 calls:

29.0ms	(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
8.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
33.0ms	(/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
17.0ms	(/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series780.0ms

Counts

4 → 8

Calls

4 calls:

675.0ms	(/ (/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt (cbrt (cbrt (sqrt 2.0))))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
104.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
0.0ms	(/ (/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (sqrt (cbrt (cbrt (sqrt 2.0)))))
0.0ms	(/ 1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify1.1s

Counts

283 → 283

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	405	6782
1	859	6199
2	2483	5600
done	5000	5424

prune779.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes171.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	41
1	24	41
done	24	41

end0.0ms

sample2.3s

Algorithm

intervals

Results

764.0ms	2438×	body	1280	valid
431.0ms	2009×	body	640	valid
392.0ms	8039×	body	80	valid
170.0ms	1046×	body	320	valid
64.0ms	569×	body	160	valid