Details

sample153.0ms

Algorithm

intervals

Results

63.0ms	85×	body	1280	valid
24.0ms	250×	body	80	valid
21.0ms	55×	body	640	valid
11.0ms	35×	body	320	valid
5.0ms	21×	body	160	valid

simplify277.0ms

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `sqrt-prod`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
23.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series542.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma a1 a1 (* a2 a2))
140.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
339.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.3s

Counts

70 → 70

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	103	947
1	201	911
2	750	777
3	3465	759
done	5000	758

prune289.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `fma-udef`

Counts

3 → 95

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
33.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
13.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series522.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma a1 a1 (* a2 a2))
332.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
145.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	131	1616
1	253	1531
2	862	1325
3	2958	1317
done	5000	1313

prune385.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.2b	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-r`
34×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`associate-r/` `pow-prod-down` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 716

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
181.0ms	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
40.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

series799.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma a1 a1 (* a2 a2))
369.0ms	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
148.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
236.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

simplify2.5s

Counts

728 → 728

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	605	18939
1	1429	16385
2	3445	14246
done	5000	14052

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(* (* (cos th) (hypot a2 a1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
4.0b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite419.0ms

Algorithm

rewrite-expression-head

Rules

2688×	`sqrt-prod`
2124×	`times-frac`
1102×	`add-sqr-sqrt`
1101×	`add-cube-cbrt` `*-un-lft-identity`
526×	`associate-r`
64×	`associate-/l*`
32×	`add-exp-log` `add-cbrt-cube`
22×	`div-inv`
18×	`associate-/r*`
10×	`pow1` `cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-undiv` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `-commutative` `fma-udef` `hypot-def` `associate-/l/`

Counts

4 → 1259

Calls

4 calls:

18.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
45.0ms	(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
190.0ms	(* (* (cos th) (hypot a2 a1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
3.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series979.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
179.0ms	(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
478.0ms	(* (* (cos th) (hypot a2 a1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
82.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify2.8s

Counts

1271 → 1271

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	872	37667
1	2520	31404
done	5000	24309

prune2.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes245.0ms

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	10	12
1	11	12
done	11	12

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.8s	2515×	body	1280	valid
1.2s	8074×	body	80	valid
1.0s	2125×	body	640	valid
360.0ms	1041×	body	320	valid
185.0ms	511×	body	160	valid