Details

sample106.0ms

Algorithm

intervals

Results

32.0ms	79×	body	1280	valid
24.0ms	254×	body	80	valid
18.0ms	63×	body	640	valid
8.0ms	37×	body	320	valid
2.0ms	14×	body	160	valid

simplify261.0ms

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	151	12
7	173	12
8	175	12
done	175	12

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.5b	(/ (* (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:

16.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series460.0ms

Counts

2 → 6

Calls

2 calls:

174.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
286.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.3s

Counts

57 → 57

Iterations

Useful iterations: done (1.3s)

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

prune408.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot a2 a1) (cos th))
0.1b	(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
0.5b	(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
6.9b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `sqrt-prod`
9×	`associate-r`
7×	`prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `fma-udef` `hypot-def` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

9.0ms	(* (hypot a2 a1) (cos th))
34.0ms	(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
35.0ms	(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series824.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (hypot a2 a1) (cos th))
254.0ms	(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
367.0ms	(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
57.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	137	1582
1	316	1450
2	1930	1021
done	5001	965

prune706.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot a2 a1) (cos th))
0.2b	(/ (hypot a2 a1) (cbrt (sqrt 2.0)))
0.2b	(/ (* (hypot a2 a1) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(* (/ (* (hypot a2 a1) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a2 a1) (cbrt (sqrt 2.0))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-sqr-sqrt`
59×	`times-frac`
48×	`add-cube-cbrt` `*-un-lft-identity`
44×	`cbrt-prod`
43×	`add-cbrt-cube`
34×	`associate-r`
23×	`prod-exp` `cbrt-unprod`
22×	`sqrt-prod`
18×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
8×	`pow1` `associate-l`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `associate-l/`

Counts

4 → 170

Calls

4 calls:

18.0ms	(* (hypot a2 a1) (cos th))
15.0ms	(/ (hypot a2 a1) (cbrt (sqrt 2.0)))
40.0ms	(/ (* (hypot a2 a1) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
108.0ms	(* (/ (* (hypot a2 a1) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a2 a1) (cbrt (sqrt 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (hypot a2 a1) (cos th))
431.0ms	(/ (hypot a2 a1) (cbrt (sqrt 2.0)))
677.0ms	(/ (* (hypot a2 a1) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
266.0ms	(* (/ (* (hypot a2 a1) (cos th)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a2 a1) (cbrt (sqrt 2.0))))

simplify508.0ms

Counts

182 → 182

Iterations

Useful iterations: done (497.0ms)

Iter	Nodes	Cost
0	240	3751
1	670	3557
done	5000	2925

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot a2 a1) (cos th))
0.2b	(/ (hypot a2 a1) (cbrt (sqrt 2.0)))
0.2b	(/ (* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (cbrt (sqrt 2.0)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (cbrt (sqrt 2.0))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
55×	`times-frac`
49×	`add-sqr-sqrt`
47×	`add-cube-cbrt` `*-un-lft-identity`
44×	`add-cbrt-cube`
42×	`cbrt-prod`
34×	`associate-r`
24×	`prod-exp` `cbrt-unprod`
21×	`sqrt-prod`
17×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`associate-/l/` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

19.0ms	(* (hypot a2 a1) (cos th))
9.0ms	(/ (hypot a2 a1) (cbrt (sqrt 2.0)))
52.0ms	(/ (* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (cbrt (sqrt 2.0)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
47.0ms	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (cbrt (sqrt 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (hypot a2 a1) (cos th))
404.0ms	(/ (hypot a2 a1) (cbrt (sqrt 2.0)))
260.0ms	(/ (* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (cbrt (sqrt 2.0)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
716.0ms	(* (* (hypot a2 a1) (cos th)) (/ (hypot a2 a1) (cbrt (sqrt 2.0))))

simplify4.4s

Counts

174 → 174

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	233	3273
1	658	3091
2	4967	2439
done	5000	2434

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes385.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	15	22
done	15	22

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.3s	2538×	body	1280	valid
1.3s	7981×	body	80	valid
1.2s	2067×	body	640	valid
352.0ms	1043×	body	320	valid
96.0ms	473×	body	160	valid