Details

sample161.0ms

Algorithm

intervals

Results

48.0ms	81×	body	1280	valid
34.0ms	264×	body	80	valid
30.0ms	65×	body	640	valid
11.0ms	36×	body	320	valid
2.0ms	13×	body	160	valid

simplify291.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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: 0.3b

localize12.0ms

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))

rewrite32.0ms

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:

10.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
21.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series458.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
323.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.2s

Counts

57 → 57

Iterations

Useful iterations: done (1.2s)

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

prune299.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

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)))) (cbrt (sqrt 2.0)))

0.3b

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

rewrite93.0ms

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:

10.0ms

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

55.0ms

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

24.0ms

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

series1.5s

Counts

3 → 9

Calls

3 calls:

129.0ms

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

367.0ms

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

962.0ms

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

simplify1.9s

Counts

136 → 136

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	212	3744
1	499	3409
2	3007	2971
done	5002	2932

prune549.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize37.0ms

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

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
150×	`cbrt-prod`
112×	`add-exp-log`
76×	`add-sqr-sqrt`
74×	`add-cube-cbrt` `*-un-lft-identity`
61×	`add-cbrt-cube`
51×	`cbrt-undiv` `div-exp`
31×	`prod-exp` `cbrt-unprod` `div-inv`
30×	`sqrt-prod`
15×	`associate-/l*`
14×	`associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num`
2×	`fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 253

Calls

4 calls:

10.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
100.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
39.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
44.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series2.9s

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
309.0ms	(/ (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
928.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
1.5s	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify639.0ms

Counts

265 → 265

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	388	11121
1	936	10342
done	5001	9197

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a1 a1) (cos th))
0.2b	(* (pow (/ 1 (pow (sqrt 2.0) 8)) 1/9) (fma (cos th) (* a2 a2) (* (* a1 a1) (cos th))))
0.2b	(/ (* (pow (/ 1 (pow (sqrt 2.0) 8)) 1/9) (fma (cos th) (* a2 a2) (* (* a1 a1) (cos th)))) (cbrt (cbrt (sqrt 2.0))))
1.6b	(pow (sqrt 2.0) 8)

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

71×	`unpow-prod-down`
70×	`add-exp-log`
62×	`add-sqr-sqrt`
50×	`times-frac`
42×	`*-un-lft-identity`
39×	`associate-l`
38×	`add-cube-cbrt`
30×	`cbrt-prod`
27×	`pow-exp` `prod-exp`
25×	`div-exp`
20×	`sqrt-prod`
14×	`add-cbrt-cube`
12×	`associate-/r*` `unswap-sqr`
11×	`pow1`
9×	`pow-to-exp`
8×	`sqr-pow`
6×	`rec-exp` `1-exp` `associate-r`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow` `pow-prod-down`
2×	`cbrt-undiv` `*-commutative` `fma-udef` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `sqrt-pow2` `associate-/l*`

Counts

4 → 175

Calls

4 calls:

22.0ms	(* (* a1 a1) (cos th))
129.0ms	(* (pow (/ 1 (pow (sqrt 2.0) 8)) 1/9) (fma (cos th) (* a2 a2) (* (* a1 a1) (cos th))))
72.0ms	(/ (* (pow (/ 1 (pow (sqrt 2.0) 8)) 1/9) (fma (cos th) (* a2 a2) (* (* a1 a1) (cos th)))) (cbrt (cbrt (sqrt 2.0))))
7.0ms	(pow (sqrt 2.0) 8)

series1.6s

Counts

4 → 10

Calls

4 calls:

63.0ms	(* (* a1 a1) (cos th))
1.2s	(* (pow (/ 1 (pow (sqrt 2.0) 8)) 1/9) (fma (cos th) (* a2 a2) (* (* a1 a1) (cos th))))
353.0ms	(/ (* (pow (/ 1 (pow (sqrt 2.0) 8)) 1/9) (fma (cos th) (* a2 a2) (* (* a1 a1) (cos th)))) (cbrt (cbrt (sqrt 2.0))))
0.0ms	(pow (sqrt 2.0) 8)

simplify2.3s

Counts

185 → 185

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	316	4289
1	710	4088
2	3281	3519
done	5000	3273

prune844.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes401.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	26
1	24	26
done	24	26

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.0s	2046×	body	640	valid
2.0s	2557×	body	1280	valid
983.0ms	8014×	body	80	valid
349.0ms	1016×	body	320	valid
96.0ms	490×	body	160	valid