Details

sample90.0ms

Algorithm

intervals

Results

31.0ms	88×	body	1280	valid
16.0ms	77×	body	640	valid
13.0ms	263×	body	80	valid
6.0ms	39×	body	320	valid
2.0ms	17×	body	160	valid

simplify19.0ms

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: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite23.0ms

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))

series350.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
234.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify33.0ms

Counts

57 → 57

Iterations

Useful iterations: 2 (28.0ms)

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

prune155.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.1b	(* (cos th) (hypot a1 a2))
0.3b	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
7.0b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite62.0ms

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:

25.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
9.0ms	(* (cos th) (hypot a1 a2))
25.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
112.0ms	(* (cos th) (hypot a1 a2))
306.0ms	(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
45.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify48.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	305	785
1	1700	625
2	5001	573
done	5001	573

prune282.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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:

8.0ms	(* (cos th) (hypot a1 a2))
7.0ms	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
17.0ms	(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
63.0ms	(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cos th) (hypot a1 a2))
291.0ms	(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
589.0ms	(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
255.0ms	(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

simplify106.0ms

Counts

182 → 182

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	636	2325
1	3767	1967
2	5001	1857
done	5001	1857

prune514.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (* (cos th) (hypot a1 a2)) 1) (sqrt (fma a1 a1 (* a2 a2))))
0.1b	(* (cos th) (hypot a1 a2))
0.3b	(/ (* (pow (* (cos th) (hypot a1 a2)) 1) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
7.0b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

21.0ms	(* (pow (* (cos th) (hypot a1 a2)) 1) (sqrt (fma a1 a1 (* a2 a2))))
9.0ms	(* (cos th) (hypot a1 a2))
17.0ms	(/ (* (pow (* (cos th) (hypot a1 a2)) 1) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
2.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series651.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (pow (* (cos th) (hypot a1 a2)) 1) (sqrt (fma a1 a1 (* a2 a2))))
110.0ms	(* (cos th) (hypot a1 a2))
300.0ms	(/ (* (pow (* (cos th) (hypot a1 a2)) 1) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
46.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify53.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	310	909
1	1542	735
2	5001	671
done	5001	671

prune313.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes122.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	14
1	15	14
done	15	14

end0.0ms

sample2.6s

Algorithm

intervals

Results

813.0ms	2550×	body	1280	valid
438.0ms	2099×	body	640	valid
408.0ms	8227×	body	80	valid
372.0ms	1059×	body	320	valid
51.0ms	494×	body	160	valid